Neural networks (NNs) achieve outstanding performance in many domains; however, their decision processes are often opaque and their inference can be computationally expensive in resource-constrained environments. We recently proposed Differentiable Logic Networks (DLNs) to address these issues for tabular classification based on relaxing discrete logic into a differentiable form, thereby enabling gradient-based learning of networks built from binary logic operations. DLNs offer interpretable reasoning and substantially lower inference cost. We extend the DLN framework to supervised tabular regression. Specifically, we redesign the final output layer to support continuous targets and unify the original two-phase training procedure into a single differentiable stage. We evaluate the resulting model on 15 public regression benchmarks, comparing it with modern neural networks and classical regression baselines. Regression DLNs match or exceed baseline accuracy while preserving interpretability and fast inference. Our results show that DLNs are a viable, cost-effective alternative for regression tasks, especially where model transparency and computational efficiency are important.
Conformal prediction is a framework for predictive inference with a distribution-free, finite-sample guarantee. However, it tends to provide uninformative prediction sets when calibration data are scarce. This paper introduces Synthetic-powered predictive inference (SPPI), a novel framework that incorporates synthetic data -- e.g., from a generative model -- to improve sample efficiency. At the core of our method is a score transporter: an empirical quantile mapping that aligns nonconformity scores from trusted, real data with those from synthetic data. By carefully integrating the score transporter into the calibration process, SPPI provably achieves finite-sample coverage guarantees without making any assumptions about the real and synthetic data distributions. When the score distributions are well aligned, SPPI yields substantially tighter and more informative prediction sets than standard conformal prediction. Experiments on image classification and tabular regression demonstrate notable improvements in predictive efficiency in data-scarce settings.
Language models have recently been shown capable of performing regression tasks wherein numeric predictions are represented as decoded strings. In this work, we provide theoretical grounds for this capability and furthermore investigate the utility of causal auto-regressive sequence models when they are applied to any feature representation. We find that, despite being trained in the usual way - for next-token prediction via cross-entropy loss - decoding-based regression is as performant as traditional approaches for tabular regression tasks, while being flexible enough to capture arbitrary distributions, such as in the task of density estimation.
Tabular data are fundamental in common machine learning applications, ranging from finance to genomics and healthcare. This paper focuses on tabular regression tasks, a field where deep learning (DL) methods are not consistently superior to machine learning (ML) models due to the challenges posed by irregular target functions inherent in tabular data, causing sensitive label changes with minor variations from features. To address these issues, we propose a novel Arithmetic-Aware Pre-training and Adaptive-Regularized Fine-tuning framework (APAR), which enables the model to fit irregular target function in tabular data while reducing the negative impact of overfitting. In the pre-training phase, APAR introduces an arithmetic-aware pretext objective to capture intricate sample-wise relationships from the perspective of continuous labels. In the fine-tuning phase, a consistency-based adaptive regularization technique is proposed to self-learn appropriate data augmentation. Extensive experiments across 10 datasets demonstrated that APAR outperforms existing GBDT-, supervised NN-, and pretrain-finetune NN-based methods in RMSE (+9.43% $\sim$ 20.37%), and empirically validated the effects of pre-training tasks, including the study of arithmetic operations. Our code and data are publicly available at https://github.com/johnnyhwu/APAR.
Feature selection is an essential process in machine learning, especially when dealing with high-dimensional datasets. It helps reduce the complexity of machine learning models, improve performance, mitigate overfitting, and decrease computation time. This paper presents a novel feature selection framework, shap-select. The framework conducts a linear or logistic regression of the target on the Shapley values of the features, on the validation set, and uses the signs and significance levels of the regression coefficients to implement an efficient heuristic for feature selection in tabular regression and classification tasks. We evaluate shap-select on the Kaggle credit card fraud dataset, demonstrating its effectiveness compared to established methods such as Recursive Feature Elimination (RFE), HISEL (a mutual information-based feature selection method), Boruta and a simpler Shapley value-based method. Our findings show that shap-select combines interpretability, computational efficiency, and performance, offering a robust solution for feature selection.
When assessing the quality of prediction models in machine learning, confidence intervals (CIs) for the generalization error, which measures predictive performance, are a crucial tool. Luckily, there exist many methods for computing such CIs and new promising approaches are continuously being proposed. Typically, these methods combine various resampling procedures, most popular among them cross-validation and bootstrapping, with different variance estimation techniques. Unfortunately, however, there is currently no consensus on when any of these combinations may be most reliably employed and how they generally compare. In this work, we conduct a large-scale study comparing CIs for the generalization error, the first one of such size, where we empirically evaluate 13 different CI methods on a total of 19 tabular regression and classification problems, using seven different inducers and a total of eight loss functions. We give an overview of the methodological foundations and inherent challenges of constructing CIs for the generalization error and provide a concise review of all 13 methods in a unified framework. Finally, the CI methods are evaluated in terms of their relative coverage frequency, width, and runtime. Based on these findings, we can identify a subset of methods that we would recommend. We also publish the datasets as a benchmarking suite on OpenML and our code on GitHub to serve as a basis for further studies.
Despite the prevalence and significance of tabular data across numerous industries and fields, it has been relatively underexplored in the realm of deep learning. Even today, neural networks are often overshadowed by techniques such as gradient boosted decision trees (GBDT). However, recent models are beginning to close this gap, outperforming GBDT in various setups and garnering increased attention in the field. Inspired by this development, we introduce a novel stochastic deep learning model specifically designed for tabular data. The foundation of this model is a Transformer-based architecture, carefully adapted to cater to the unique properties of tabular data through strategic architectural modifications and leveraging two forms of stochastic competition. First, we employ stochastic "Local Winner Takes All" units to promote generalization capacity through stochasticity and sparsity. Second, we introduce a novel embedding layer that selects among alternative linear embedding layers through a mechanism of stochastic competition. The effectiveness of the model is validated on a variety of widely-used, publicly available datasets. We demonstrate that, through the incorporation of these elements, our model yields high performance and marks a significant advancement in the application of deep learning to tabular data.
Neural Processes (NPs) are deep probabilistic models that represent stochastic processes by conditioning their prior distributions on a set of context points. Despite their obvious advantages in uncertainty estimation for complex distributions, NPs enforce parameterization coupling between the conditional prior model and the posterior model, thereby risking introducing a misspecified prior distribution. We hereby revisit the NP objectives and propose R\'enyi Neural Processes (RNP) to ameliorate the impacts of prior misspecification by optimizing an alternative posterior that achieves better marginal likelihood. More specifically, by replacing the standard KL divergence with the R\'enyi divergence between the model posterior and the true posterior, we scale the density ratio $\frac{p}{q}$ by the power of (1-$\alpha$) in the divergence gradients with respect to the posterior. This hyper parameter $\alpha$ allows us to dampen the effects of the misspecified prior for the posterior update, which has been shown to effectively avoid oversmoothed predictions and improve the expressiveness of the posterior model. Our extensive experiments show consistent log-likelihood improvements over state-of-the-art NP family models which adopt both the variational inference or maximum likelihood estimation objectives. We validate the effectiveness of our approach across multiple benchmarks including regression and image inpainting tasks, and show significant performance improvements of RNPs in real-world regression problems where the underlying prior model is misspecifed.
Generating calibrated and sharp neural network predictive distributions for regression problems is essential for optimal decision-making in many real-world applications. To address the miscalibration issue of neural networks, various methods have been proposed to improve calibration, including post-hoc methods that adjust predictions after training and regularization methods that act during training. While post-hoc methods have shown better improvement in calibration compared to regularization methods, the post-hoc step is completely independent of model training. We introduce a novel end-to-end model training procedure called Quantile Recalibration Training, integrating post-hoc calibration directly into the training process without additional parameters. We also present a unified algorithm that includes our method and other post-hoc and regularization methods, as particular cases. We demonstrate the performance of our method in a large-scale experiment involving 57 tabular regression datasets, showcasing improved predictive accuracy while maintaining calibration. We also conduct an ablation study to evaluate the significance of different components within our proposed method, as well as an in-depth analysis of the impact of the base model and different hyperparameters on predictive accuracy.
Used car pricing is a critical aspect of the automotive industry, influenced by many economic factors and market dynamics. With the recent surge in online marketplaces and increased demand for used cars, accurate pricing would benefit both buyers and sellers by ensuring fair transactions. However, the transition towards automated pricing algorithms using machine learning necessitates the comprehension of model uncertainties, specifically the ability to flag predictions that the model is unsure about. Although recent literature proposes the use of boosting algorithms or nearest neighbor-based approaches for swift and precise price predictions, encapsulating model uncertainties with such algorithms presents a complex challenge. We introduce ProbSAINT, a model that offers a principled approach for uncertainty quantification of its price predictions, along with accurate point predictions that are comparable to state-of-the-art boosting techniques. Furthermore, acknowledging that the business prefers pricing used cars based on the number of days the vehicle was listed for sale, we show how ProbSAINT can be used as a dynamic forecasting model for predicting price probabilities for different expected offer duration. Our experiments further indicate that ProbSAINT is especially accurate on instances where it is highly certain. This proves the applicability of its probabilistic predictions in real-world scenarios where trustworthiness is crucial.
Out-of-Distribution (OOD) generalization, a cornerstone for building robust machine learning models capable of handling data diverging from the training set's distribution, is an ongoing challenge in deep learning. While significant progress has been observed in computer vision and natural language processing, its exploration in tabular data, ubiquitous in many industrial applications, remains nascent. To bridge this gap, we present Wild-Tab, a large-scale benchmark tailored for OOD generalization in tabular regression tasks. The benchmark incorporates 3 industrial datasets sourced from fields like weather prediction and power consumption estimation, providing a challenging testbed for evaluating OOD performance under real-world conditions. Our extensive experiments, evaluating 10 distinct OOD generalization methods on Wild-Tab, reveal nuanced insights. We observe that many of these methods often struggle to maintain high-performance levels on unseen data, with OOD performance showing a marked drop compared to in-distribution performance. At the same time, Empirical Risk Minimization (ERM), despite its simplicity, delivers robust performance across all evaluations, rivaling the results of state-of-the-art methods. Looking forward, we hope that the release of Wild-Tab will facilitate further research on OOD generalization and aid in the deployment of machine learning models in various real-world contexts where handling distribution shifts is a crucial requirement.
Neural additive models (NAMs) enhance the transparency of deep neural networks by handling input features in separate additive sub-networks. However, they lack inherent mechanisms that provide calibrated uncertainties and enable selection of relevant features and interactions. Approaching NAMs from a Bayesian perspective, we augment them in three primary ways, namely by a) providing credible intervals for the individual additive sub-networks; b) estimating the marginal likelihood to perform an implicit selection of features via an empirical Bayes procedure; and c) facilitating the ranking of feature pairs as candidates for second-order interaction in fine-tuned models. In particular, we develop Laplace-approximated NAMs (LA-NAMs), which show improved empirical performance on tabular datasets and challenging real-world medical tasks.
Gradient boosting machines (GBMs) based on decision trees consistently demonstrate state-of-the-art results on regression and classification tasks with tabular data, often outperforming deep neural networks. However, these models do not provide well-calibrated predictive uncertainties, which prevents their use for decision making in high-risk applications. The Bayesian treatment is known to improve predictive uncertainty calibration, but previously proposed Bayesian GBM methods are either computationally expensive, or resort to crude approximations. Variational inference is often used to implement Bayesian neural networks, but is difficult to apply to GBMs, because the decision trees used as weak learners are non-differentiable. In this paper, we propose to implement Bayesian GBMs using variational inference with soft decision trees, a fully differentiable alternative to standard decision trees introduced by Irsoy et al. Our experiments demonstrate that variational soft trees and variational soft GBMs provide useful uncertainty estimates, while retaining good predictive performance. The proposed models show higher test likelihoods when compared to the state-of-the-art Bayesian GBMs in 7/10 tabular regression datasets and improved out-of-distribution detection in 5/10 datasets.
This paper revisits datasets and evaluation criteria for Symbolic Regression (SR), specifically focused on its potential for scientific discovery. Focused on a set of formulas used in the existing datasets based on Feynman Lectures on Physics, we recreate 120 datasets to discuss the performance of symbolic regression for scientific discovery (SRSD). For each of the 120 SRSD datasets, we carefully review the properties of the formula and its variables to design reasonably realistic sampling ranges of values so that our new SRSD datasets can be used for evaluating the potential of SRSD such as whether or not an SR method can (re)discover physical laws from such datasets. We also create another 120 datasets that contain dummy variables to examine whether SR methods can choose necessary variables only. Besides, we propose to use normalized edit distances (NED) between a predicted equation and the true equation trees for addressing a critical issue that existing SR metrics are either binary or errors between the target values and an SR model's predicted values for a given input. We conduct benchmark experiments on our new SRSD datasets using various representative SR methods. The experimental results show that we provide a more realistic performance evaluation, and our user study shows that the NED correlates with human judges significantly more than an existing SR metric. We publish repositories of our code and 240 SRSD datasets.
Gradient-boosted regression trees (GBRTs) are hugely popular for solving tabular regression problems, but provide no estimate of uncertainty. We propose Instance-Based Uncertainty estimation for Gradient-boosted regression trees (IBUG), a simple method for extending any GBRT point predictor to produce probabilistic predictions. IBUG computes a non-parametric distribution around a prediction using the $k$-nearest training instances, where distance is measured with a tree-ensemble kernel. The runtime of IBUG depends on the number of training examples at each leaf in the ensemble, and can be improved by sampling trees or training instances. Empirically, we find that IBUG achieves similar or better performance than the previous state-of-the-art across 22 benchmark regression datasets. We also find that IBUG can achieve improved probabilistic performance by using different base GBRT models, and can more flexibly model the posterior distribution of a prediction than competing methods. We also find that previous methods suffer from poor probabilistic calibration on some datasets, which can be mitigated using a scalar factor tuned on the validation data. Source code is available at https://www.github.com/jjbrophy47/ibug.
The acquisition of labels for supervised learning can be expensive. To improve the sample efficiency of neural network regression, we study active learning methods that adaptively select batches of unlabeled data for labeling. We present a framework for constructing such methods out of (network-dependent) base kernels, kernel transformations, and selection methods. Our framework encompasses many existing Bayesian methods based on Gaussian process approximations of neural networks as well as non-Bayesian methods. Additionally, we propose to replace the commonly used last-layer features with sketched finite-width neural tangent kernels and to combine them with a novel clustering method. To evaluate different methods, we introduce an open-source benchmark consisting of 15 large tabular regression data sets. Our proposed method outperforms the state-of-the-art on our benchmark, scales to large data sets, and works out-of-the-box without adjusting the network architecture or training code. We provide open-source code that includes efficient implementations of all kernels, kernel transformations, and selection methods, and can be used for reproducing our results.
The existing literature on deep learning for tabular data proposes a wide range of novel architectures and reports competitive results on various datasets. However, the proposed models are usually not properly compared to each other and existing works often use different benchmarks and experiment protocols. As a result, it is unclear for both researchers and practitioners what models perform best. Additionally, the field still lacks effective baselines, that is, the easy-to-use models that provide competitive performance across different problems. In this work, we perform an overview of the main families of DL architectures for tabular data and raise the bar of baselines in tabular DL by identifying two simple and powerful deep architectures. The first one is a ResNet-like architecture which turns out to be a strong baseline that is often missing in prior works. The second model is our simple adaptation of the Transformer architecture for tabular data, which outperforms other solutions on most tasks. Both models are compared to many existing architectures on a diverse set of tasks under the same training and tuning protocols. We also compare the best DL models with Gradient Boosted Decision Trees and conclude that there is still no universally superior solution.