From 54675dc651421e6287fb0f17636791b4e629f778 Mon Sep 17 00:00:00 2001 From: Mitterand Ekole Date: Sun, 15 Mar 2026 20:06:59 +0100 Subject: [PATCH 1/3] Add OrderedLogistic distribution for ordinal regression (closes #54) Implements the cumulative link (proportional odds) model as a new distribution class. Uses a cumulative softplus reparameterisation to enforce strict cutpoint ordering without constrained optimisation. - lightgbmlss/distributions/OrderedLogistic.py: new distribution with overrides for get_params_loss, calculate_start_values, draw_samples, and predict_dist; supports pred_type="class_probs" in addition to the standard parameters/samples/quantiles - lightgbmlss/distributions/__init__.py: register OrderedLogistic - tests/test_distributions/test_ordinal.py: 17 unit tests covering init validation, cutpoint monotonicity, forward pass, autograd, sampling, and LightGBM integration - tests/utils.py: exclude OrderedLogistic from generic fixtures - docs/examples/OrderedLogistic_Regression.ipynb: end-to-end example with simulated ordinal data, hyper_opt, evaluation (accuracy, MAE, Kendall tau, QWK), SHAP interpretability, and class probability plots --- .gitignore | 5 +- .../examples/OrderedLogistic_Regression.ipynb | 1068 +++++++++++++++++ lightgbmlss/distributions/OrderedLogistic.py | 410 +++++++ lightgbmlss/distributions/__init__.py | 3 +- tests/test_distributions/test_ordinal.py | 187 +++ tests/utils.py | 3 +- 6 files changed, 1673 insertions(+), 3 deletions(-) create mode 100644 docs/examples/OrderedLogistic_Regression.ipynb create mode 100644 lightgbmlss/distributions/OrderedLogistic.py create mode 100644 tests/test_distributions/test_ordinal.py diff --git a/.gitignore b/.gitignore index d5f860e..aa619e5 100644 --- a/.gitignore +++ b/.gitignore @@ -12,4 +12,7 @@ build/ .coverage # Jupyter Notebook -.ipynb_checkpoints \ No newline at end of file +.ipynb_checkpoints + +# VS Code +.vscode/ \ No newline at end of file diff --git a/docs/examples/OrderedLogistic_Regression.ipynb b/docs/examples/OrderedLogistic_Regression.ipynb new file mode 100644 index 0000000..de40f64 --- /dev/null +++ b/docs/examples/OrderedLogistic_Regression.ipynb @@ -0,0 +1,1068 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Ordinal Regression with LightGBMLSS" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "[![Open in Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/StatMixedML/LightGBMLSS/blob/master/docs/examples/OrderedLogistic_Regression.ipynb)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Ordinal data — discrete outcomes with a natural ordering such as Likert scales, severity grades, or star ratings — is ubiquitous in applied machine learning. Standard approaches either ignore the ordering (multinomial classification) or impose metric assumptions (treating labels as continuous integers). The **cumulative link model**, commonly called the *proportional odds* or *ordered logistic* model, is the principled middle ground.\n", + "\n", + "It models the cumulative probabilities $P(y \\leq k \\mid x)$ as sigmoid functions of a latent score $\\eta$ minus ordered cutpoints $c_1 < c_2 < \\cdots < c_{K-1}$:\n", + "\n", + "$$P(y \\leq k \\mid \\eta) = \\sigma(c_k - \\eta), \\quad k = 1, \\ldots, K-1$$\n", + "\n", + "so that the probability of each individual class is:\n", + "\n", + "$$P(y = k \\mid \\eta) = \\sigma(c_k - \\eta) - \\sigma(c_{k-1} - \\eta)$$\n", + "\n", + "with $\\sigma(c_0 - \\eta) = 0$ and $\\sigma(c_K - \\eta) = 1$ by convention.\n", + "\n", + "LightGBMLSS estimates both the **latent predictor** $\\eta(x)$ and the **cutpoints** $c_1, \\ldots, c_{K-1}$ as functions of covariates. Monotonicity of cutpoints is enforced via a cumulative softplus reparameterisation:\n", + "\n", + "$$c_1 = \\text{raw}_1, \\qquad c_k = c_1 + \\sum_{j=2}^{k} \\text{softplus}(\\text{raw}_j), \\quad k \\geq 2$$\n", + "\n", + "This gives $K$ unconstrained tree outputs (one per parameter), while guaranteeing strict ordering of the cutpoints at all times during training." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Imports" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/Users/ekole/anaconda3/envs/ekole-ml/lib/python3.11/site-packages/tqdm/auto.py:21: TqdmWarning: IProgress not found. Please update jupyter and ipywidgets. See https://ipywidgets.readthedocs.io/en/stable/user_install.html\n", + " from .autonotebook import tqdm as notebook_tqdm\n" + ] + } + ], + "source": [ + "from lightgbmlss.model import *\n", + "from lightgbmlss.distributions.OrderedLogistic import *\n", + "\n", + "import numpy as np\n", + "import pandas as pd\n", + "from scipy.special import expit as sigmoid\n", + "from scipy.stats import kendalltau\n", + "from sklearn.metrics import confusion_matrix, cohen_kappa_score\n", + "\n", + "import plotnine\n", + "from plotnine import *\n", + "plotnine.options.figure_size = (12, 8)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Data\n", + "\n", + "We simulate ordinal data from the cumulative logistic model with $K = 4$ classes (labels $\\{0, 1, 2, 3\\}$). The true data-generating process is:\n", + "\n", + "- $\\eta(x) = x_1 - 0.5 \\, x_2 + 0.3 \\, x_3 + 0.8 \\, x_5$ (two noise features $x_4, x_5$ included)\n", + "- Cutpoints: $c_1 = -1.0,\\; c_2 = 0.5,\\; c_3 = 2.0$\n", + "\n", + "Labels are drawn from $P(y = k \\mid \\eta)$ as defined above. We use 2 000 observations: 1 500 for training, 500 for testing." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "np.random.seed(42)\n", + "\n", + "n = 2000\n", + "K = 4\n", + "cutpoints_true = np.array([-1.0, 0.5, 2.0])\n", + "\n", + "X = np.random.randn(n, 5)\n", + "eta_true = X @ np.array([1.0, -0.5, 0.3, 0.0, 0.8])\n", + "\n", + "# Cumulative probabilities P(y <= k | eta)\n", + "cum_probs = sigmoid(cutpoints_true[np.newaxis, :] - eta_true[:, np.newaxis]) # (n, K-1)\n", + "\n", + "# Class probabilities\n", + "p0 = cum_probs[:, 0]\n", + "p1 = cum_probs[:, 1] - cum_probs[:, 0]\n", + "p2 = cum_probs[:, 2] - cum_probs[:, 1]\n", + "p3 = 1.0 - cum_probs[:, 2]\n", + "probs = np.stack([p0, p1, p2, p3], axis=1)\n", + "probs = np.clip(probs, 1e-9, None)\n", + "probs /= probs.sum(axis=1, keepdims=True)\n", + "\n", + "y = np.array([np.random.choice(K, p=probs[i]) for i in range(n)], dtype=float)\n", + "\n", + "# Train / test split\n", + "X_train, X_test = X[:1500], X[1500:]\n", + "y_train, y_test = y[:1500], y[1500:]\n", + "\n", + "X_train_df = pd.DataFrame(X_train, columns=[f\"x{i+1}\" for i in range(5)])\n", + "X_test_df = pd.DataFrame(X_test, columns=[f\"x{i+1}\" for i in range(5)])\n", + "\n", + "dtrain = lgb.Dataset(X_train_df, label=y_train)" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "class\n", + "0.0 515\n", + "1.0 384\n", + "2.0 330\n", + "3.0 271\n", + "Name: count, dtype: int64" + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Class distribution\n", + "pd.Series(y_train, name=\"class\").value_counts().sort_index().rename(\"count\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Distribution Specification\n", + "\n", + "We specify the `OrderedLogistic` distribution with `K=4` ordinal classes. This adds one tree for the latent predictor $\\eta$ and three trees for the raw cutpoint parameters — four trees per boosting round in total.\n", + "\n", + "Arguments:\n", + "- `n_classes`: number of ordinal categories $K$.\n", + "- `stabilization`: gradient/Hessian stabilization. Options are `\"None\"`, `\"MAD\"`, `\"L2\"`.\n", + "- `loss_fn`: only `\"nll\"` is supported for ordinal regression.\n", + "- `initialize`: if `True`, start-value optimisation via L-BFGS is run before boosting." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [], + "source": [ + "lgblss = LightGBMLSS(\n", + " OrderedLogistic(\n", + " n_classes=4,\n", + " stabilization=\"L2\",\n", + " loss_fn=\"nll\",\n", + " initialize=True,\n", + " )\n", + ")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Hyper-Parameter Optimisation\n", + "\n", + "Any LightGBM hyperparameter can be tuned. The parameter dictionary structure is:\n", + "\n", + " - Float/Int sample_type\n", + " - {\"param_name\": [\"sample_type\", {\"low\": low, \"high\": high, \"log\": log}]}\n", + "\n", + " - Categorical sample_type\n", + " - {\"param_name\": [\"categorical\", [\"choice1\", \"choice2\", ...]]}" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Best trial: 11. Best value: 1.17732: 100%|██████████| 30/30 [00:27<00:00, 1.08it/s, 27.89/600 seconds]" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "Hyper-Parameter Optimization successfully finished.\n", + " Number of finished trials: 30\n", + " Best trial:\n", + " Value: 1.1773182786700325\n", + " Params: \n", + " eta: 0.17844445339780893\n", + " max_depth: 1\n", + " num_leaves: 255\n", + " min_data_in_leaf: 20\n", + " min_gain_to_split: 0.6172009257451649\n", + " min_sum_hessian_in_leaf: 1.7679789696512058e-08\n", + " subsample: 0.9979013632487388\n", + " feature_fraction: 0.4678590887770889\n", + " boosting: gbdt\n", + " opt_rounds: 80\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "\n" + ] + } + ], + "source": [ + "param_dict = {\n", + " \"eta\": [\"float\", {\"low\": 1e-5, \"high\": 1, \"log\": True}],\n", + " \"max_depth\": [\"int\", {\"low\": 1, \"high\": 6, \"log\": False}],\n", + " \"num_leaves\": [\"int\", {\"low\": 255, \"high\": 255, \"log\": False}], # fixed for this example\n", + " \"min_data_in_leaf\": [\"int\", {\"low\": 20, \"high\": 20, \"log\": False}], # fixed for this example\n", + " \"min_gain_to_split\": [\"float\", {\"low\": 1e-8, \"high\": 40, \"log\": False}],\n", + " \"min_sum_hessian_in_leaf\": [\"float\", {\"low\": 1e-8, \"high\": 500, \"log\": True}],\n", + " \"subsample\": [\"float\", {\"low\": 0.2, \"high\": 1.0, \"log\": False}],\n", + " \"feature_fraction\": [\"float\", {\"low\": 0.2, \"high\": 1.0, \"log\": False}],\n", + " \"boosting\": [\"categorical\", [\"gbdt\"]],\n", + "}\n", + "\n", + "np.random.seed(123)\n", + "opt_param = lgblss.hyper_opt(\n", + " param_dict,\n", + " dtrain,\n", + " num_boost_round=200,\n", + " nfold=5,\n", + " early_stopping_rounds=20,\n", + " max_minutes=10,\n", + " n_trials=30,\n", + " silence=True,\n", + " seed=123,\n", + " hp_seed=123,\n", + ")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Model Training" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [], + "source": [ + "np.random.seed(123)\n", + "\n", + "opt_params = opt_param.copy()\n", + "n_rounds = opt_params[\"opt_rounds\"]\n", + "del opt_params[\"opt_rounds\"]\n", + "\n", + "lgblss.train(\n", + " opt_params,\n", + " dtrain,\n", + " num_boost_round=n_rounds,\n", + ")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Prediction\n", + "\n", + "`OrderedLogistic` supports four prediction types:\n", + "\n", + "- `\"parameters\"` — latent predictor $\\hat{\\eta}$ and ordered cutpoints $\\hat{c}_1 \\ldots \\hat{c}_{K-1}$.\n", + "- `\"class_probs\"` — $\\hat{P}(y = k)$ for each class $k \\in \\{0, 1, 2, 3\\}$.\n", + "- `\"samples\"` — ordinal class samples drawn from the predicted distribution.\n", + "- `\"quantiles\"` — quantiles derived from the sample-based distribution." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [], + "source": [ + "torch.manual_seed(123)\n", + "\n", + "# Predicted distributional parameters (predictor + ordered cutpoints)\n", + "pred_params = lgblss.predict(X_test_df, pred_type=\"parameters\")\n", + "\n", + "# Predicted class probabilities P(y=k) for k in {0,1,2,3}\n", + "pred_probs = lgblss.predict(X_test_df, pred_type=\"class_probs\")\n", + "\n", + "# Samples from predicted distribution\n", + "pred_samples = lgblss.predict(X_test_df, pred_type=\"samples\", n_samples=1000, seed=123)\n", + "\n", + "# Quantiles from predicted distribution\n", + "pred_quantiles = lgblss.predict(X_test_df, pred_type=\"quantiles\",\n", + " n_samples=1000, quantiles=[0.1, 0.5, 0.9])" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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" + ], + "text/plain": [ + " P(y=0) P(y=1) P(y=2) P(y=3)\n", + "0 0.179235 0.203508 0.293666 0.323591\n", + "1 0.821698 0.147511 0.017748 0.013043\n", + "2 0.379832 0.295591 0.258227 0.066351\n", + "3 0.356651 0.319497 0.260771 0.063081\n", + "4 0.103535 0.202639 0.330245 0.363580" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "pred_probs.head()" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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" + ], + "text/plain": [ + " quant_0.1 quant_0.5 quant_0.9\n", + "0 0 2 3\n", + "1 0 0 1\n", + "2 0 1 2\n", + "3 0 1 2\n", + "4 0 2 3" + ] + }, + "execution_count": 10, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "pred_quantiles.head()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Evaluation\n", + "\n", + "We evaluate the model using metrics appropriate for ordinal regression:\n", + "\n", + "- **Accuracy** — exact class match.\n", + "- **MAE** — mean absolute error on class labels (penalises larger ordinal misses more).\n", + "- **Kendall's $\\tau$** — rank correlation between predicted and actual classes.\n", + "- **Quadratic Weighted Kappa (QWK)** — Cohen's $\\kappa$ with quadratic weights; standard for ordinal agreement." + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Accuracy : 0.4560\n", + "MAE : 0.7460\n", + "Kendall τ: 0.4665\n", + "QWK : 0.5257\n" + ] + } + ], + "source": [ + "# Most probable class = argmax of P(y=k)\n", + "y_pred_class = pred_probs.values.argmax(axis=1)\n", + "y_true = y_test.astype(int)\n", + "\n", + "accuracy = (y_pred_class == y_true).mean()\n", + "mae = np.abs(y_pred_class - y_true).mean()\n", + "tau, _ = kendalltau(y_pred_class, y_true)\n", + "qwk = cohen_kappa_score(y_true, y_pred_class, weights=\"quadratic\")\n", + "\n", + "print(f\"Accuracy : {accuracy:.4f}\")\n", + "print(f\"MAE : {mae:.4f}\")\n", + "print(f\"Kendall τ: {tau:.4f}\")\n", + "print(f\"QWK : {qwk:.4f}\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Confusion Matrix" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "execution_count": 12, + "metadata": { + "image/png": { + "height": 800, + "width": 1200 + } + }, + "output_type": "execute_result" + } + ], + "source": [ + "cm = confusion_matrix(y_true, y_pred_class)\n", + "cm_df = (\n", + " pd.DataFrame(cm,\n", + " index=[f\"True {k}\" for k in range(K)],\n", + " columns=[f\"Pred {k}\" for k in range(K)])\n", + " .reset_index()\n", + " .melt(id_vars=\"index\", var_name=\"Predicted\", value_name=\"Count\")\n", + " .rename(columns={\"index\": \"Actual\"})\n", + ")\n", + "\n", + "(\n", + " ggplot(cm_df, aes(x=\"Predicted\", y=\"Actual\", fill=\"Count\")) +\n", + " geom_tile(color=\"white\") +\n", + " geom_text(aes(label=\"Count\"), size=14, color=\"white\") +\n", + " scale_fill_gradient(low=\"#2c7bb6\", high=\"#d7191c\") +\n", + " labs(\n", + " title=\"Confusion Matrix — OrderedLogistic (K=4)\",\n", + " x=\"Predicted Class\",\n", + " y=\"Actual Class\",\n", + " ) +\n", + " theme_bw(base_size=13) +\n", + " theme(\n", + " plot_title=element_text(hjust=0.5),\n", + " legend_position=\"right\",\n", + " )\n", + ")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Predicted Class Probability Distributions\n", + "\n", + "For each test observation we obtain a full probability vector $\\hat{P}(y = k)$ over all four classes. Below we plot these distributions, grouped by the true class label, to inspect calibration and sharpness." + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "execution_count": 13, + "metadata": { + "image/png": { + "height": 800, + "width": 1200 + } + }, + "output_type": "execute_result" + } + ], + "source": [ + "prob_df = pred_probs.copy()\n", + "prob_df[\"true_class\"] = y_true\n", + "prob_long = prob_df.melt(\n", + " id_vars=\"true_class\",\n", + " value_vars=[f\"P(y={k})\" for k in range(K)],\n", + " var_name=\"class\",\n", + " value_name=\"probability\",\n", + ")\n", + "prob_long[\"true_class\"] = \"True class: \" + prob_long[\"true_class\"].astype(str)\n", + "\n", + "(\n", + " ggplot(prob_long, aes(x=\"class\", y=\"probability\", fill=\"class\")) +\n", + " geom_boxplot(alpha=0.7, outlier_alpha=0.3, outlier_size=1) +\n", + " facet_wrap(\"true_class\", nrow=1) +\n", + " labs(\n", + " title=\"Predicted Class Probabilities by True Label\",\n", + " x=\"Predicted class\",\n", + " y=\"P(y = k)\",\n", + " ) +\n", + " theme_bw(base_size=13) +\n", + " theme(\n", + " plot_title=element_text(hjust=0.5),\n", + " legend_position=\"none\",\n", + " axis_text_x=element_text(rotation=30, hjust=1),\n", + " )\n", + ")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### True vs. Predicted Cutpoints\n", + "\n", + "The true cutpoints are $c_1 = -1.0$, $c_2 = 0.5$, $c_3 = 2.0$. The model learns one cutpoint set per observation (the cumulative logistic allows covariate-dependent cutpoints). We compare the median predicted cutpoints against the true values." + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Median predicted cutpoints:\n", + " cutpoint_1: predicted = -0.002 | true = -1.000\n", + " cutpoint_2: predicted = 1.364 | true = 0.500\n", + " cutpoint_3: predicted = 2.766 | true = 2.000\n" + ] + } + ], + "source": [ + "cutpoint_cols = [c for c in pred_params.columns if c.startswith(\"cutpoint\")]\n", + "median_cutpoints = pred_params[cutpoint_cols].median()\n", + "\n", + "print(\"Median predicted cutpoints:\")\n", + "for name, val, true in zip(cutpoint_cols, median_cutpoints, cutpoints_true):\n", + " print(f\" {name}: predicted = {val:.3f} | true = {true:.3f}\")" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "execution_count": 15, + "metadata": { + "image/png": { + "height": 800, + "width": 1200 + } + }, + "output_type": "execute_result" + } + ], + "source": [ + "cp_long = pred_params[cutpoint_cols].melt(var_name=\"cutpoint\", value_name=\"value\")\n", + "\n", + "true_cp_df = pd.DataFrame({\n", + " \"cutpoint\": cutpoint_cols,\n", + " \"true_value\": cutpoints_true,\n", + "})\n", + "\n", + "(\n", + " ggplot(cp_long, aes(x=\"value\", fill=\"cutpoint\")) +\n", + " geom_histogram(bins=40, alpha=0.7, position=\"identity\") +\n", + " geom_vline(\n", + " true_cp_df,\n", + " aes(xintercept=\"true_value\", color=\"cutpoint\"),\n", + " size=1.2,\n", + " linetype=\"dashed\",\n", + " ) +\n", + " facet_wrap(\"cutpoint\", scales=\"free_x\") +\n", + " labs(\n", + " title=\"Predicted Cutpoint Distributions (dashed = true value)\",\n", + " x=\"Cutpoint value\",\n", + " y=\"Count\",\n", + " ) +\n", + " theme_bw(base_size=13) +\n", + " theme(\n", + " plot_title=element_text(hjust=0.5),\n", + " legend_position=\"none\",\n", + " )\n", + ")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# SHAP Interpretability\n", + "\n", + "LightGBMLSS provides attribute importance and partial dependence plots via SHAP. For the ordered logistic model the key parameter is the **predictor** $\\eta$, which drives the latent score and thereby the class probabilities." + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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", 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Feature importance for the latent predictor\n", + "lgblss.plot(\n", + " X_test_df,\n", + " parameter=\"predictor\",\n", + " plot_type=\"Feature_Importance\",\n", + ")" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Partial dependence: how x1 influences the latent predictor\n", + "lgblss.plot(\n", + " X_test_df,\n", + " parameter=\"predictor\",\n", + " feature=\"x1\",\n", + " plot_type=\"Partial_Dependence\",\n", + ")" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Partial dependence for x2 (negative true coefficient)\n", + "lgblss.plot(\n", + " X_test_df,\n", + " parameter=\"predictor\",\n", + " feature=\"x2\",\n", + " plot_type=\"Partial_Dependence\",\n", + ")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Predicted Class Probabilities vs. Latent Predictor\n", + "\n", + "A clean diagnostic is to plot $\\hat{P}(y = k)$ as a function of the predicted latent score $\\hat{\\eta}$. Under the proportional odds model, class 0 should dominate at low $\\hat{\\eta}$ and class 3 at high $\\hat{\\eta}$, with the middle classes peaking in between." + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "execution_count": 20, + "metadata": { + "image/png": { + "height": 800, + "width": 1200 + } + }, + "output_type": "execute_result" + } + ], + "source": [ + "plot_df = pred_probs.copy()\n", + "plot_df[\"eta\"] = pred_params[\"predictor\"].values\n", + "\n", + "plot_long = plot_df.melt(\n", + " id_vars=\"eta\",\n", + " value_vars=[f\"P(y={k})\" for k in range(K)],\n", + " var_name=\"class\",\n", + " value_name=\"probability\",\n", + ")\n", + "\n", + "# Bin eta into 30 equal-width intervals and compute mean P(y=k) per bin\n", + "plot_long[\"eta_bin\"] = pd.cut(plot_long[\"eta\"], bins=30)\n", + "binned = (\n", + " plot_long\n", + " .groupby([\"eta_bin\", \"class\"], observed=True)[\"probability\"]\n", + " .mean()\n", + " .reset_index()\n", + ")\n", + "binned[\"eta_mid\"] = binned[\"eta_bin\"].apply(lambda x: x.mid).astype(float)\n", + "\n", + "(\n", + " ggplot(binned, aes(x=\"eta_mid\", y=\"probability\", color=\"class\")) +\n", + " geom_line(size=1.2) +\n", + " geom_point(size=1.5, alpha=0.7) +\n", + " labs(\n", + " title=\"Predicted Class Probabilities vs. Latent Predictor \\u03b7\",\n", + " x=\"Predicted latent score \\u03b7\",\n", + " y=\"P(y = k)\",\n", + " color=\"Class\",\n", + " ) +\n", + " theme_bw(base_size=13) +\n", + " theme(\n", + " plot_title=element_text(hjust=0.5),\n", + " legend_position=\"bottom\",\n", + " )\n", + ")" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.11.14" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/lightgbmlss/distributions/OrderedLogistic.py b/lightgbmlss/distributions/OrderedLogistic.py new file mode 100644 index 0000000..af213df --- /dev/null +++ b/lightgbmlss/distributions/OrderedLogistic.py @@ -0,0 +1,410 @@ +import torch +from torch.nn.functional import softplus +from torch.autograd import grad as autograd +from torch.optim import LBFGS +from torch.optim.lr_scheduler import ReduceLROnPlateau +from pyro.distributions import OrderedLogistic as OrderedLogistic_Pyro + +import lightgbm as lgb +import numpy as np +import pandas as pd + +from typing import List, Tuple + +from .distribution_utils import DistributionClass +from ..utils import identity_fn + + +class OrderedLogistic(DistributionClass): + """ + Ordered Logistic (cumulative link) distribution for ordinal regression. + + Models P(y = k | x) via the cumulative logistic link: + P(y ≤ k | η) = σ(cₖ - η) + + where η is a latent predictor score and c₁ < c₂ < ... < cₖ₋₁ are + ordered cutpoints. + + Distributional Parameters + ------------------------- + predictor: torch.Tensor + Latent score η. Unconstrained real-valued. + cutpoint_raw_1 ... cutpoint_raw_{K-1}: torch.Tensor + Raw (unconstrained) cutpoint parameters. Internally transformed + to ordered cutpoints via cumulative softplus. + + Source + ------------------------- + https://docs.pyro.ai/en/stable/distributions.html#orderedlogistic + + Parameters + ------------------------- + n_classes: int + Number of ordinal categories K (e.g. 5 for a 1-5 Likert scale). + Labels must be integers in {0, 1, ..., K-1}. + stabilization: str + Stabilization method for the Gradient and Hessian. Options are + "None", "MAD", "L2". + loss_fn: str + Loss function. Currently only "nll" (negative log-likelihood) is + supported for ordinal regression. + initialize: bool + Whether to initialize the distributional parameters with + unconditional start values. + """ + def __init__( + self, + n_classes: int = 3, + stabilization: str = "None", + loss_fn: str = "nll", + initialize: bool = False, + ): + # Input Checks + if not isinstance(n_classes, int) or n_classes < 2: + raise ValueError("n_classes must be an integer >= 2.") + if stabilization not in ["None", "MAD", "L2"]: + raise ValueError( + "Invalid stabilization method. Please choose from 'None', 'MAD' or 'L2'." + ) + if loss_fn not in ["nll"]: + raise ValueError("Invalid loss function. Please select 'nll'.") + if not isinstance(initialize, bool): + raise ValueError("Invalid initialize. Please choose from True or False.") + + self.n_classes = n_classes + n_cutpoints = n_classes - 1 + + # First parameter is the predictor (identity transform). + # Remaining K-1 parameters are raw cutpoint values. + # The ordering constraint is enforced inside get_params_loss, not here. + param_dict = {"predictor": identity_fn} + for i in range(1, n_cutpoints + 1): + param_dict[f"cutpoint_raw_{i}"] = identity_fn + + torch.distributions.Distribution.set_default_validate_args(False) + + super().__init__( + distribution=OrderedLogistic_Pyro, + univariate=True, + discrete=True, + n_dist_param=len(param_dict), + stabilization=stabilization, + param_dict=param_dict, + distribution_arg_names=list(param_dict.keys()), + loss_fn=loss_fn, + initialize=initialize, + ) + + @staticmethod + def _raw_to_ordered_cutpoints(raw_cutpoints: List[torch.Tensor]) -> torch.Tensor: + """ + Transform K-1 unconstrained raw parameters into ordered cutpoints. + + Arguments + --------- + raw_cutpoints: List[torch.Tensor] + List of K-1 tensors, each of shape (n_obs, 1). + + Returns + ------- + cutpoints: torch.Tensor + Tensor of shape (n_obs, K-1) with c₁ < c₂ < ... < cₖ₋₁. + """ + base = raw_cutpoints[0] # c₁ = raw₁ (unconstrained) + if len(raw_cutpoints) == 1: + return base # K=2: single cutpoint, no ordering needed + + # Softplus-transform the gaps to ensure strict positivity + gaps = torch.cat( + [softplus(rc) + 1e-6 for rc in raw_cutpoints[1:]], dim=1 + ) + # Cumulative sum of gaps gives the offsets from the base cutpoint + offsets = torch.cumsum(gaps, dim=1) + cutpoints = torch.cat([base, base + offsets], dim=1) + + return cutpoints + + def get_params_loss( + self, + predt: np.ndarray, + target: torch.Tensor, + start_values: List[float], + requires_grad: bool = False, + ) -> Tuple[List[torch.Tensor], torch.Tensor]: + """ + Compute predicted parameters and NLL loss for ordinal regression. + + The first column of predt is the predictor η. + Columns 1..K-1 are raw cutpoint parameters, transformed here into + ordered cutpoints via cumulative softplus. + + Arguments + --------- + predt: np.ndarray + Predicted values, shape (n_obs * n_dist_param,). + target: torch.Tensor + Target values, shape (n_obs, 1). + start_values: List[float] + Starting values for each distributional parameter. + requires_grad: bool + Whether to add to the computational graph. + + Returns + ------- + predt: List[torch.Tensor] + Per-parameter tensors with gradient tracking. + loss: torch.Tensor + Negative log-likelihood. + """ + # Reshape: (n_obs * n_params,) → (n_obs, n_params) + predt = predt.reshape(-1, self.n_dist_param, order="F") + + # Replace NaNs/Infs with start values + nan_inf_mask = np.isnan(predt) | np.isinf(predt) + predt[nan_inf_mask] = np.take(start_values, np.where(nan_inf_mask)[1]) + + # Convert to tensors with gradient tracking + predt = [ + torch.tensor( + predt[:, i].reshape(-1, 1), + requires_grad=requires_grad, + ) + for i in range(self.n_dist_param) + ] + + # Split: predictor vs raw cutpoints + predictor = predt[0].squeeze(-1) # (n_obs,) + raw_cutpoints = predt[1:] # list of K-1 tensors of shape (n_obs, 1) + + # Apply the ordering transform + cutpoints = self._raw_to_ordered_cutpoints(raw_cutpoints) # (n_obs, K-1) + + # Construct distribution and compute NLL + dist_fit = OrderedLogistic_Pyro(predictor=predictor, cutpoints=cutpoints) + loss = -torch.nansum(dist_fit.log_prob(target.squeeze(-1).long())) + + return predt, loss + + def loss_fn_start_values( + self, + params: List[torch.Tensor], + target: torch.Tensor, + ) -> torch.Tensor: + """NLL for start-value optimization over unconditional parameters.""" + # Replace NaNs/Infs + nan_inf_idx = ( + torch.isnan(torch.stack(params)) | torch.isinf(torch.stack(params)) + ) + params = torch.where(nan_inf_idx, torch.tensor(0.5), torch.stack(params)) + params = [params[i].reshape(-1, 1) for i in range(self.n_dist_param)] + + # Broadcast scalar params to (n_obs, 1) for batched construction + predictor = params[0].squeeze(-1).expand(target.shape[0]) + raw_cutpoints = [rc.expand(target.shape[0], 1) for rc in params[1:]] + + cutpoints = self._raw_to_ordered_cutpoints(raw_cutpoints) + + dist = OrderedLogistic_Pyro(predictor=predictor, cutpoints=cutpoints) + loss = -torch.nansum(dist.log_prob(target.squeeze(-1).long())) + + return loss + + def calculate_start_values( + self, + target: np.ndarray, + max_iter: int = 50, + ) -> Tuple[float, np.ndarray]: + """ + Calculate starting values for ordinal regression parameters. + + Initializes the predictor at 0 and spaces cutpoints at the empirical + quantile boundaries of the ordinal labels, then refines via L-BFGS. + + Arguments + --------- + target: np.ndarray + Target labels in {0, ..., K-1}. + max_iter: int + Maximum number of L-BFGS iterations. + + Returns + ------- + loss: float + Final NLL value. + start_values: np.ndarray + Starting values for each distributional parameter. + """ + target_t = torch.tensor(target, dtype=torch.float32).reshape(-1, 1) + n_cutpoints = self.n_classes - 1 + + # Place cutpoints at roughly equal-probability boundaries + boundaries = np.linspace(0, self.n_classes - 1, n_cutpoints + 2)[1:-1] + + init_raw = [boundaries[0]] + for i in range(1, n_cutpoints): + gap = boundaries[i] - boundaries[i - 1] + init_raw.append(np.log(np.exp(gap) - 1)) # inverse softplus + + params = [ + torch.tensor(0.0, requires_grad=True, dtype=torch.float32), + ] + [ + torch.tensor(float(v), requires_grad=True, dtype=torch.float32) + for v in init_raw + ] + + optimizer = LBFGS( + params, + lr=0.1, + max_iter=min(int(max_iter / 4), 20), + line_search_fn="strong_wolfe", + ) + lr_scheduler = ReduceLROnPlateau(optimizer, mode="min", factor=0.5, patience=10) + + def closure(): + optimizer.zero_grad() + loss = self.loss_fn_start_values(params, target_t) + loss.backward() + return loss + + loss_vals = [] + for _ in range(max_iter): + loss = optimizer.step(closure) + lr_scheduler.step(loss) + loss_vals.append(loss.item()) + + loss = np.array(loss_vals[-1]) + start_values = np.array([p.detach().numpy() for p in params]) + start_values = np.nan_to_num(start_values, nan=0.5, posinf=0.5, neginf=0.5) + + return loss, start_values + + def draw_samples( + self, + predt_params: pd.DataFrame, + n_samples: int = 1000, + seed: int = 123, + ) -> pd.DataFrame: + """ + Draw ordinal class samples from the predicted distribution. + + Arguments + --------- + predt_params: pd.DataFrame + DataFrame with columns ["predictor", "cutpoint_1", ..., "cutpoint_{K-1}"]. + Cutpoints must already be ordered (output of predict_dist). + n_samples: int + Number of samples to draw per observation. + seed: int + Random seed. + + Returns + ------- + pd.DataFrame + Shape (n_obs, n_samples), integer-valued in {0, ..., K-1}. + """ + torch.manual_seed(seed) + + pred_vals = torch.tensor(predt_params.values, dtype=torch.float32) + predictor = pred_vals[:, 0] # (n_obs,) + cutpoints = pred_vals[:, 1:] # (n_obs, K-1) — already ordered + + dist = OrderedLogistic_Pyro(predictor=predictor, cutpoints=cutpoints) + samples = dist.sample((n_samples,)).detach().numpy() # (n_samples, n_obs) + samples = samples.T # (n_obs, n_samples) + + df = pd.DataFrame(samples) + df.columns = [f"y_sample{i}" for i in range(n_samples)] + + return df.astype(int) + + def predict_dist( + self, + booster: lgb.Booster, + data: pd.DataFrame, + start_values: np.ndarray, + pred_type: str = "parameters", + n_samples: int = 1000, + quantiles: list = [0.1, 0.5, 0.9], + seed: int = 123, + ) -> pd.DataFrame: + """ + Predict from the trained ordinal regression model. + + Arguments + --------- + booster: lgb.Booster + Trained model. + data: pd.DataFrame + Data to predict from. + start_values: np.ndarray + Starting values for each distributional parameter. + pred_type: str + - "parameters" — predictor η and ordered cutpoints c₁...cₖ₋₁ + - "class_probs" — P(y=k) for each class k ∈ {0, ..., K-1} + - "samples" — ordinal class samples + - "quantiles" — quantiles from the sample-based distribution + n_samples: int + Number of samples (for "samples" and "quantiles"). + quantiles: list + Quantile levels (for "quantiles"). + seed: int + Random seed for sampling. + + Returns + ------- + pd.DataFrame + Predictions in the requested format. + """ + predt = torch.tensor( + booster.predict(data, raw_score=True), + dtype=torch.float32, + ).reshape(-1, self.n_dist_param) + + # Add init_score offsets (one per distributional parameter) + init_score = torch.tensor( + np.ones(shape=(data.shape[0], 1)) * start_values, + dtype=torch.float32, + ) + predt = predt + init_score + + # Split predictor and raw cutpoints, then apply ordering transform + predictor = predt[:, 0] + raw_cutpoints = [predt[:, i].reshape(-1, 1) for i in range(1, self.n_dist_param)] + cutpoints = self._raw_to_ordered_cutpoints(raw_cutpoints) # (n_obs, K-1) + + # Build parameter DataFrame with ordered cutpoints + param_names = ["predictor"] + [ + f"cutpoint_{i}" for i in range(1, self.n_classes) + ] + dist_params = torch.cat( + [predictor.unsqueeze(1), cutpoints], dim=1 + ).detach().numpy() + dist_params_df = pd.DataFrame(dist_params, columns=param_names) + + if pred_type == "parameters": + return dist_params_df + + elif pred_type == "class_probs": + dist = OrderedLogistic_Pyro(predictor=predictor, cutpoints=cutpoints) + probs = dist.probs.detach().numpy() + return pd.DataFrame( + probs, + columns=[f"P(y={k})" for k in range(self.n_classes)], + ) + + elif pred_type == "samples": + return self.draw_samples( + predt_params=dist_params_df, + n_samples=n_samples, + seed=seed, + ) + + elif pred_type == "quantiles": + pred_samples_df = self.draw_samples( + predt_params=dist_params_df, + n_samples=n_samples, + seed=seed, + ) + pred_quant_df = pred_samples_df.quantile(quantiles, axis=1).T + pred_quant_df.columns = [f"quant_{q}" for q in quantiles] + return pred_quant_df.astype(int) diff --git a/lightgbmlss/distributions/__init__.py b/lightgbmlss/distributions/__init__.py index af15802..51b5af9 100644 --- a/lightgbmlss/distributions/__init__.py +++ b/lightgbmlss/distributions/__init__.py @@ -23,4 +23,5 @@ from . import ZALN from . import SplineFlow from . import Mixture -from . import Logistic \ No newline at end of file +from . import Logistic +from . import OrderedLogistic \ No newline at end of file diff --git a/tests/test_distributions/test_ordinal.py b/tests/test_distributions/test_ordinal.py new file mode 100644 index 0000000..457d70f --- /dev/null +++ b/tests/test_distributions/test_ordinal.py @@ -0,0 +1,187 @@ +from lightgbmlss.model import LightGBMLSS +from lightgbmlss.distributions.OrderedLogistic import OrderedLogistic + +import pytest +import torch +import numpy as np +import pandas as pd +import lightgbm as lgb + + +class TestOrderedLogistic: + """Tests for the OrderedLogistic distribution.""" + + # ── Init validation ─────────────────────────────────────────────── + def test_init_valid(self): + dist = OrderedLogistic(n_classes=5) + assert dist.n_classes == 5 + assert dist.n_dist_param == 5 # 1 predictor + 4 cutpoints + assert dist.discrete is True + assert dist.univariate is True + assert dist.loss_fn == "nll" + + def test_init_n_classes_validation(self): + with pytest.raises(ValueError, match="n_classes must be an integer"): + OrderedLogistic(n_classes=1) + with pytest.raises(ValueError, match="n_classes must be an integer"): + OrderedLogistic(n_classes=2.5) + + def test_init_stabilization_validation(self): + with pytest.raises(ValueError, match="Invalid stabilization method."): + OrderedLogistic(stabilization="invalid") + + def test_init_loss_fn_validation(self): + with pytest.raises(ValueError, match="Invalid loss function."): + OrderedLogistic(loss_fn="crps") + + def test_init_initialize_validation(self): + with pytest.raises(ValueError, match="Invalid initialize."): + OrderedLogistic(initialize="yes") + + def test_defaults(self): + dist = OrderedLogistic() + assert dist.n_classes == 3 + assert dist.n_dist_param == 3 # 1 predictor + 2 cutpoints + assert dist.initialize is False + assert dist.stabilization == "None" + assert dist.tau is None + + # ── Parameter dict structure ────────────────────────────────────── + def test_param_dict_structure(self): + dist = OrderedLogistic(n_classes=4) + assert "predictor" in dist.param_dict + assert "cutpoint_raw_1" in dist.param_dict + assert "cutpoint_raw_2" in dist.param_dict + assert "cutpoint_raw_3" in dist.param_dict + assert len(dist.param_dict) == 4 + assert dist.n_dist_param == len(dist.distribution_arg_names) + assert all(callable(fn) for fn in dist.param_dict.values()) + + # ── Cutpoint ordering ───────────────────────────────────────────── + def test_raw_to_ordered_cutpoints_monotonic(self): + """Ordered cutpoints must be strictly increasing.""" + raw = [ + torch.tensor([[0.5], [-1.0], [2.0], [0.1]]), + torch.tensor([[-0.3], [0.5], [-0.8], [1.5]]), + torch.tensor([[1.0], [0.2], [0.3], [-0.5]]), + ] + ordered = OrderedLogistic._raw_to_ordered_cutpoints(raw) + diffs = torch.diff(ordered, dim=1) + assert (diffs > 0).all(), "Cutpoints are not strictly increasing" + + def test_raw_to_ordered_cutpoints_single(self): + """K=2: single cutpoint, no ordering needed.""" + raw = [torch.tensor([[1.0], [2.0]])] + ordered = OrderedLogistic._raw_to_ordered_cutpoints(raw) + assert ordered.shape == (2, 1) + + def test_raw_to_ordered_cutpoints_shape(self): + """Output shape must be (n_obs, K-1).""" + n_obs, K = 8, 5 + raw = [torch.randn(n_obs, 1) for _ in range(K - 1)] + ordered = OrderedLogistic._raw_to_ordered_cutpoints(raw) + assert ordered.shape == (n_obs, K - 1) + + # ── Start values ────────────────────────────────────────────────── + def test_calculate_start_values(self): + dist = OrderedLogistic(n_classes=3) + target = np.array([0, 0, 1, 1, 2, 2], dtype=float) + loss, start_values = dist.calculate_start_values(target) + assert len(start_values) == 3 # 1 predictor + 2 cutpoints + assert np.isfinite(loss) + assert np.all(np.isfinite(start_values)) + + # ── Forward pass ────────────────────────────────────────────────── + def test_get_params_loss_runs(self): + K = 3 + dist = OrderedLogistic(n_classes=K) + n_obs = 10 + np.random.seed(42) + predt = np.random.randn(n_obs * K) + target = torch.tensor( + np.random.randint(0, K, size=(n_obs, 1)), dtype=torch.float32 + ) + start_values = [0.0, 0.5, 0.3] + + params, loss = dist.get_params_loss(predt, target, start_values, requires_grad=True) + assert np.isfinite(loss.item()) + assert len(params) == K + + # ── Gradient and Hessian ────────────────────────────────────────── + def test_gradients_finite(self): + K = 3 + dist = OrderedLogistic(n_classes=K) + n_obs = 10 + np.random.seed(42) + predt = np.random.randn(n_obs * K) + target = torch.tensor( + np.random.randint(0, K, size=(n_obs, 1)), dtype=torch.float32 + ) + start_values = [0.0, 0.5, 0.3] + + params, loss = dist.get_params_loss(predt, target, start_values, requires_grad=True) + grad, hess = dist.compute_gradients_and_hessians(loss, params, np.ones((n_obs, 1))) + assert np.all(np.isfinite(grad)) + assert np.all(np.isfinite(hess)) + + # ── Draw samples ────────────────────────────────────────────────── + def test_draw_samples_valid_range(self): + K = 4 + dist = OrderedLogistic(n_classes=K) + params_df = pd.DataFrame({ + "predictor": [0.0, 1.0], + "cutpoint_1": [-1.0, -1.0], + "cutpoint_2": [0.0, 0.0], + "cutpoint_3": [1.0, 1.0], + }) + samples = dist.draw_samples(params_df, n_samples=100) + assert samples.shape == (2, 100) + assert samples.min().min() >= 0 + assert samples.max().max() <= K - 1 + + def test_draw_samples_dtype(self): + dist = OrderedLogistic(n_classes=3) + params_df = pd.DataFrame({ + "predictor": [0.0], + "cutpoint_1": [-0.5], + "cutpoint_2": [0.5], + }) + samples = dist.draw_samples(params_df, n_samples=50) + assert samples.dtypes.apply(lambda d: np.issubdtype(d, np.integer)).all() + + # ── Integration: objective_fn with lgb.Dataset ───────────────────── + def test_objective_fn_with_dataset(self): + K = 3 + dist = OrderedLogistic(n_classes=K) + model = LightGBMLSS(dist) + + n_obs = 20 + np.random.seed(42) + X = np.random.randn(n_obs, 3) + y = np.random.randint(0, K, size=n_obs).astype(float) + + dtrain = lgb.Dataset(X, label=y) + model.set_init_score(dtrain) + dtrain.construct() + + predt = np.random.randn(n_obs * K) + grad, hess = dist.objective_fn(predt, dtrain) + assert grad.shape == (n_obs * K,) + assert hess.shape == (n_obs * K,) + assert np.all(np.isfinite(grad)) + assert np.all(np.isfinite(hess)) + + # ── K=2 (binary) edge case ──────────────────────────────────────── + def test_binary_case(self): + """K=2 collapses to logistic regression with one cutpoint.""" + dist = OrderedLogistic(n_classes=2) + assert dist.n_dist_param == 2 + assert dist.n_classes == 2 + + n_obs = 8 + predt = np.random.randn(n_obs * 2) + target = torch.tensor( + np.random.randint(0, 2, size=(n_obs, 1)), dtype=torch.float32 + ) + params, loss = dist.get_params_loss(predt, target, [0.0, 0.0], requires_grad=True) + assert np.isfinite(loss.item()) diff --git a/tests/utils.py b/tests/utils.py index 9baa071..9080309 100644 --- a/tests/utils.py +++ b/tests/utils.py @@ -88,7 +88,8 @@ def get_distribution_classes(univariate: bool = True, distns_remove = [ "SplineFlow", "Expectile", - "Mixture" + "Mixture", + "OrderedLogistic", # Has custom param structure; tested separately ] distns = [item for item in distns if item not in distns_remove] From d45def4d56db76c2c05da381e6f50ad66d49b626 Mon Sep 17 00:00:00 2001 From: Mitterand Ekole Date: Sun, 15 Mar 2026 20:09:26 +0100 Subject: [PATCH 2/3] Add .pytest_cache to .gitignore --- .gitignore | 5 ++++- 1 file changed, 4 insertions(+), 1 deletion(-) diff --git a/.gitignore b/.gitignore index aa619e5..1efcbd2 100644 --- a/.gitignore +++ b/.gitignore @@ -15,4 +15,7 @@ build/ .ipynb_checkpoints # VS Code -.vscode/ \ No newline at end of file +.vscode/ + +# Pytest +.pytest_cache/ \ No newline at end of file From 49d66fd1087e32dfcf1945272da3462ebbbb0a9a Mon Sep 17 00:00:00 2001 From: Mitterand Ekole Date: Wed, 18 Mar 2026 20:08:03 +0100 Subject: [PATCH 3/3] Fix target validation, docstring accuracy, columm naming, and predict_dist test coverage in OrderedLogistic --- .DS_Store | Bin 0 -> 10244 bytes .github/.DS_Store | Bin 0 -> 6148 bytes docs/.DS_Store | Bin 0 -> 6148 bytes lightgbmlss/.DS_Store | Bin 0 -> 6148 bytes lightgbmlss/distributions/OrderedLogistic.py | 42 ++++++++++----- tests/.DS_Store | Bin 0 -> 8196 bytes tests/test_distributions/test_ordinal.py | 53 +++++++++++++++++++ 7 files changed, 83 insertions(+), 12 deletions(-) create mode 100644 .DS_Store create mode 100644 .github/.DS_Store create mode 100644 docs/.DS_Store create mode 100644 lightgbmlss/.DS_Store create mode 100644 tests/.DS_Store diff --git a/.DS_Store b/.DS_Store new file mode 100644 index 0000000000000000000000000000000000000000..c037c57093ded765e6e4ce0793aa1b73c17824ae GIT binary patch literal 10244 zcmeHNJ7`ov6ulESnixOvQ&?C$#lj{_0$RHpUzElCG)W_ZaX;=FcYRAfV!ACXEJZBD zA66nl8m$Ez(Za$?EG;5PtOP-<^xT=*-I@1^s~||2ftmYu=H5H!oqK1NnO!0h!%M{> zB9DlAP+9hGLlaYYoNJ_X>7GGI0eh;Jho%Zatsc>I9gYFVfMdWh;23ZW{4WgPJDW>S zpOUV13^)cH11$!4fACOQX0&W5DYp(Z@(2K#Lboh%ML}H94X%rD2LmfwKvNAp#<(TMp@t5{P zBf5RC%^|{UJB2olRd~+m!t`4j$7LV-VJJ1CG zCY#=iY;#p7YPYlD_u3Y_M;`$M?Tvp+a8$xumuUbTTtWT>A-4FvO^!SEV=+MkZ~p{? z$<3ktD^KpJ9k1iL%^dt2dy7A606J|&UR-Xjf3UX9d17-VcN>$d9diG#V>Jde2c8Sa zFwV&!#+LUQ)3z5o)Clt5mun#=`{k}hc+q$35e+`Jd#JOhTv)H6q%=XpD%>xx4St dkm@%7pZyqM+!|QtDR=&F{d>!u|2Ove{}*%>ynp}z literal 0 HcmV?d00001 diff --git a/.github/.DS_Store b/.github/.DS_Store new file mode 100644 index 0000000000000000000000000000000000000000..cc2e73e2ad880bc56e66930120be0ffb7e36ebb6 GIT binary patch literal 6148 zcmeHKOHRW;4E2Ocq+-)0%h|K)4MG(b?2vK+)K+{%qNFXT+Z=;?u;c)ofg5lOc(x~@ zQ3C1;0kS2}n|SOQ=glb25RscbET=>hB8s7m(HPBu@HlHvqF~`cCv#MEPn-ODnk~wn zw;6sT1H5;Kw4nv9>6Ui(uc$QL=)LbzlxaH8%Q;5k=kquB`1Eo*x1gsV1(}6~=0KgH0Vb1gsS`oSdwTdBVyr+)$jX4!ak3a*3j~#(*)YR zFX5sDM1=s^C+{R)d)JxG#k)kr^Rs+LG$o=4Dma>;84&3g?a3%uq?2`wnhILdX>mBq zdfsmMjSSf0F6n~ysic+lJE+Q96MnkC1V&ibj!#*o>7u9>(s#A7{d#lzurutJf6K2v znq}>r&+Z=C^Wz!_*6knckb6-)v)hWhD1qelSX7-kh*>)s6*ivgGfYz$$6 zu!RCGl*18&!`6x|9Q{e~ZwxJ*SZBsKVP*~|6xP{ckJX(xG4$3Ma0a>ztl8~U>i_QN z=l^by-#G)$z`tUE$7z<%@kpVz_8v}ZZ4BLmiilrh*oNRjOEG+<6mLOQV2|Yjm;`JL RVS)HYKxy#C8Te5K-T>2wSGfQH literal 0 HcmV?d00001 diff --git a/lightgbmlss/.DS_Store b/lightgbmlss/.DS_Store new file mode 100644 index 0000000000000000000000000000000000000000..07eaab7779be9efa705e55001582a99c38fcf6e6 GIT binary patch literal 6148 zcmeHKu}%U(5S>+`L^PqayvmA(KRC(R*jVrZC}4yL9tspD7WWHw#NV*8v$OIWtn6rw zt#5Wl;XJr#V~oxuvu|&AX7AlgcITFeTy5O05|xRl2xly8pjlu%&z`Xr9oYmrzebCW zs6`z*rbZ^(2224{;I}Ejd$)w$+MoelV(-rOZ=-iot+(R-Kqz0oE|2WTQPk|kO+*wQ zpI%OHZXb5@qTAny9(3ke++$fBMs4sM!G}0$Ml?(@t(-qEikatla5Z%k;h0&gAJ5q3 z#ie*vJg+VA>VngVE`UuMqt~UF&OR|*o7{n6PV_w2o&D*%p1Bz_)?dp=@n26s$n2jf zfSS!#ED2g`3YY?>z=r~SJ_K;aP%#noM+X{z1ppQ>>Tws*4E6&ajgyDhj2EIO9Xui8ZF1Z!=-o|?hSJRcYvW{B8U-~{Rns& KtT6?CRDm~2HHgmu literal 0 HcmV?d00001 diff --git a/lightgbmlss/distributions/OrderedLogistic.py b/lightgbmlss/distributions/OrderedLogistic.py index af213df..2e854da 100644 --- a/lightgbmlss/distributions/OrderedLogistic.py +++ b/lightgbmlss/distributions/OrderedLogistic.py @@ -1,6 +1,5 @@ import torch from torch.nn.functional import softplus -from torch.autograd import grad as autograd from torch.optim import LBFGS from torch.optim.lr_scheduler import ReduceLROnPlateau from pyro.distributions import OrderedLogistic as OrderedLogistic_Pyro @@ -124,6 +123,22 @@ def _raw_to_ordered_cutpoints(raw_cutpoints: List[torch.Tensor]) -> torch.Tensor return cutpoints + def _validate_target(self, target: torch.Tensor) -> torch.Tensor: + """Validate labels are integers in [0, n_classes-1] and return as long tensor.""" + target_flat = target.squeeze(-1) + if not torch.all(target_flat == target_flat.long()): + raise ValueError( + "Target labels must be integer-valued (e.g., 0, 1, 2), " + "but found non-integer values." + ) + target_long = target_flat.long() + if target_long.min() < 0 or target_long.max() >= self.n_classes: + raise ValueError( + f"Target labels must be in {{0, ..., {self.n_classes - 1}}}, " + f"but found values in [{target_long.min().item()}, {target_long.max().item()}]." + ) + return target_long + def get_params_loss( self, predt: np.ndarray, @@ -180,8 +195,9 @@ def get_params_loss( cutpoints = self._raw_to_ordered_cutpoints(raw_cutpoints) # (n_obs, K-1) # Construct distribution and compute NLL + target_long = self._validate_target(target) dist_fit = OrderedLogistic_Pyro(predictor=predictor, cutpoints=cutpoints) - loss = -torch.nansum(dist_fit.log_prob(target.squeeze(-1).long())) + loss = -torch.nansum(dist_fit.log_prob(target_long)) return predt, loss @@ -204,8 +220,9 @@ def loss_fn_start_values( cutpoints = self._raw_to_ordered_cutpoints(raw_cutpoints) + target_long = self._validate_target(target) dist = OrderedLogistic_Pyro(predictor=predictor, cutpoints=cutpoints) - loss = -torch.nansum(dist.log_prob(target.squeeze(-1).long())) + loss = -torch.nansum(dist.log_prob(target_long)) return loss @@ -217,8 +234,8 @@ def calculate_start_values( """ Calculate starting values for ordinal regression parameters. - Initializes the predictor at 0 and spaces cutpoints at the empirical - quantile boundaries of the ordinal labels, then refines via L-BFGS. + Initializes the predictor at 0 and spaces cutpoints evenly across + the label range, then refines via L-BFGS. Arguments --------- @@ -237,7 +254,7 @@ def calculate_start_values( target_t = torch.tensor(target, dtype=torch.float32).reshape(-1, 1) n_cutpoints = self.n_classes - 1 - # Place cutpoints at roughly equal-probability boundaries + # Place cutpoints at evenly spaced positions across the label range boundaries = np.linspace(0, self.n_classes - 1, n_cutpoints + 2)[1:-1] init_raw = [boundaries[0]] @@ -290,7 +307,7 @@ def draw_samples( Arguments --------- predt_params: pd.DataFrame - DataFrame with columns ["predictor", "cutpoint_1", ..., "cutpoint_{K-1}"]. + DataFrame with columns matching distribution_arg_names. Cutpoints must already be ordered (output of predict_dist). n_samples: int Number of samples to draw per observation. @@ -339,7 +356,9 @@ def predict_dist( start_values: np.ndarray Starting values for each distributional parameter. pred_type: str - - "parameters" — predictor η and ordered cutpoints c₁...cₖ₋₁ + - "parameters" — predictor η and ordered cutpoints c₁...cₖ₋₁. + Column names match distribution_arg_names (cutpoint_raw_*), + but values are the transformed ordered cutpoints. - "class_probs" — P(y=k) for each class k ∈ {0, ..., K-1} - "samples" — ordinal class samples - "quantiles" — quantiles from the sample-based distribution @@ -372,10 +391,9 @@ def predict_dist( raw_cutpoints = [predt[:, i].reshape(-1, 1) for i in range(1, self.n_dist_param)] cutpoints = self._raw_to_ordered_cutpoints(raw_cutpoints) # (n_obs, K-1) - # Build parameter DataFrame with ordered cutpoints - param_names = ["predictor"] + [ - f"cutpoint_{i}" for i in range(1, self.n_classes) - ] + # Build parameter DataFrame using distribution_arg_names for consistency + # Values are ordered (transformed) cutpoints, not raw unconstrained ones + param_names = self.distribution_arg_names dist_params = torch.cat( [predictor.unsqueeze(1), cutpoints], dim=1 ).detach().numpy() diff --git a/tests/.DS_Store b/tests/.DS_Store new file mode 100644 index 0000000000000000000000000000000000000000..4ed858b5dce1fc3b6b61f0bed522f2e37336f85a GIT binary patch literal 8196 zcmeHM%Sr<=6uq$pi!Ky5x)7X|3s>qFj52Oqh#;=3weI2*7xM$|#f9G>h#*3@ zic5F?gufu3JeVf7<8)N;bpy$X$-SAJlQiK*A`>I~5s5tWc74iBQ}l4QTk9jVW> zi~|Myi8g2*d7Elf?y%+tR)7^?1y})AfED-&3gFI`sg!c>>s~Hd0aoB&Dj?4X4_Tsb zFxIG!4iqW`02a}#66%Npl#gf7HyCSFt{78C55l+#6JiMMj($&?1AT+BM(s{QyOS_q z7A8Uw>g(|HlsO4sBbTfIE6}NcjNJzjt(U1m$4>lS4!34jHllh%JI%ghS&xFC5=IqR zmTp=X(fQT=T>7~6sG7sNv2D*{Sx#n@4)DUTkFrcv+EKMVV1=4!+o6bd(WC1j?YlfK z@A8je^J`5#i!;qH=R9oQA0NfhLwF!VBR%Nhs!({m?bXlbK6&NW%-Z(!O`CCEUx#N= zt^1J0bCW`>^I`fr_n(4chKJ4VVIf)9Ot1F-?cK}aqc61yi%%W<_6UDBX-~bL<=)rD zC-D8`h_)Uti-{he9<{C4*Ny7xISukO;OH6QY^YJ_{`x0|)9h^S*Gmcau4CH!I?Fa= zo++nP;pELc6FYmJ7pq<8Y1y`w&$4yr>EZL7{VgLXD literal 0 HcmV?d00001 diff --git a/tests/test_distributions/test_ordinal.py b/tests/test_distributions/test_ordinal.py index 457d70f..14158a6 100644 --- a/tests/test_distributions/test_ordinal.py +++ b/tests/test_distributions/test_ordinal.py @@ -171,6 +171,59 @@ def test_objective_fn_with_dataset(self): assert np.all(np.isfinite(grad)) assert np.all(np.isfinite(hess)) + # ── predict_dist branches ──────────────────────────────────────── + @pytest.fixture() + def trained_model(self): + """Train a minimal OrderedLogistic model for predict_dist tests.""" + K = 3 + dist = OrderedLogistic(n_classes=K) + model = LightGBMLSS(dist) + + np.random.seed(42) + X = pd.DataFrame(np.random.randn(50, 2), columns=["x1", "x2"]) + y = np.random.randint(0, K, size=50).astype(float) + + dtrain = lgb.Dataset(X, label=y) + params = {"eta": 0.1, "verbose": -1} + model.train(params, dtrain, num_boost_round=5) + + return model, dist, X + + def test_predict_dist_parameters(self, trained_model): + model, dist, X = trained_model + df = dist.predict_dist(model.booster, X, model.start_values, pred_type="parameters") + assert isinstance(df, pd.DataFrame) + assert df.shape == (len(X), dist.n_dist_param) + assert list(df.columns) == dist.distribution_arg_names + assert not df.isna().any().any() + assert not np.isinf(df.values).any() + + def test_predict_dist_class_probs(self, trained_model): + model, dist, X = trained_model + df = dist.predict_dist(model.booster, X, model.start_values, pred_type="class_probs") + assert isinstance(df, pd.DataFrame) + assert df.shape == (len(X), dist.n_classes) + assert list(df.columns) == [f"P(y={k})" for k in range(dist.n_classes)] + # Each row should sum to ~1 + np.testing.assert_allclose(df.sum(axis=1).values, 1.0, atol=1e-5) + assert (df.values >= 0).all() + + def test_predict_dist_samples(self, trained_model): + model, dist, X = trained_model + n_samples = 100 + df = dist.predict_dist(model.booster, X, model.start_values, pred_type="samples", n_samples=n_samples) + assert df.shape == (len(X), n_samples) + assert df.min().min() >= 0 + assert df.max().max() <= dist.n_classes - 1 + assert df.dtypes.apply(lambda d: np.issubdtype(d, np.integer)).all() + + def test_predict_dist_quantiles(self, trained_model): + model, dist, X = trained_model + quantiles = [0.1, 0.5, 0.9] + df = dist.predict_dist(model.booster, X, model.start_values, pred_type="quantiles", quantiles=quantiles) + assert df.shape == (len(X), len(quantiles)) + assert list(df.columns) == [f"quant_{q}" for q in quantiles] + # ── K=2 (binary) edge case ──────────────────────────────────────── def test_binary_case(self): """K=2 collapses to logistic regression with one cutpoint."""