Generalized Additive Models (GAMs) have recently experienced a resurgence in popularity due to their interpretability, which arises from expressing the target value as a sum of non-linear transformations of the features. Despite the current enthusiasm for GAMs, their susceptibility to concurvity - i.e., (possibly non-linear) dependencies between the features - has hitherto been largely overlooked. Here, we demonstrate how concurvity can severly impair the interpretability of GAMs and propose a remedy: a conceptually simple, yet effective regularizer which penalizes pairwise correlations of the non-linearly transformed feature variables. This procedure is applicable to any differentiable additive model, such as Neural Additive Models or NeuralProphet, and enhances interpretability by eliminating ambiguities due to self-canceling feature contributions. We validate the effectiveness of our regularizer in experiments on synthetic as well as real-world datasets for time-series and tabular data. Our experiments show that concurvity in GAMs can be reduced without significantly compromising prediction quality, improving interpretability and reducing variance in the feature importances.

Data valuation is a growing research field that studies the influence of individual data points for machine learning (ML) models. Data Shapley, inspired by cooperative game theory and economics, is an effective method for data valuation. However, it is well-known that the Shapley value (SV) can be computationally expensive. Fortunately, Jia et al. (2019) showed that for K-Nearest Neighbors (KNN) models, the computation of Data Shapley is surprisingly simple and efficient. In this note, we revisit the work of Jia et al. (2019) and propose a more natural and interpretable utility function that better reflects the performance of KNN models. We derive the corresponding calculation procedure for the Data Shapley of KNN classifiers/regressors with the new utility functions. Our new approach, dubbed soft-label KNN-SV, achieves the same time complexity as the original method. We further provide an efficient approximation algorithm for soft-label KNN-SV based on locality sensitive hashing (LSH). Our experimental results demonstrate that Soft-label KNN-SV outperforms the original method on most datasets in the task of mislabeled data detection, making it a better baseline for future work on data valuation.

This paper considers a multi-environment linear regression model in which data from multiple experimental settings are collected. The joint distribution of the response variable and covariates may vary across different environments, yet the conditional expectations of $y$ given the unknown set of important variables are invariant. Such a statistical model is related to the problem of endogeneity, causal inference, and transfer learning. The motivation behind it is illustrated by how the goals of prediction and attribution are inherent in estimating the true parameter and the important variable set. We construct a novel environment invariant linear least squares (EILLS) objective function, a multi-environment version of linear least-squares regression that leverages the above conditional expectation invariance structure and heterogeneity among different environments to determine the true parameter. Our proposed method is applicable without any additional structural knowledge and can identify the true parameter under a near-minimal identification condition. We establish non-asymptotic $\ell_2$ error bounds on the estimation error for the EILLS estimator in the presence of spurious variables. Moreover, we further show that the $\ell_0$ penalized EILLS estimator can achieve variable selection consistency in high-dimensional regimes. These non-asymptotic results demonstrate the sample efficiency of the EILLS estimator and its capability to circumvent the curse of endogeneity in an algorithmic manner without any prior structural knowledge. To the best of our knowledge, this paper is the first to realize statistically efficient invariance learning in the general linear model.

Persistent homology is a methodology central to topological data analysis that extracts and summarizes the topological features within a dataset as a persistence diagram; it has recently gained much popularity from its myriad successful applications to many domains. However, its algebraic construction induces a metric space of persistence diagrams with a highly complex geometry. In this paper, we prove convergence of the $k$-means clustering algorithm on persistence diagram space and establish theoretical properties of the solution to the optimization problem in the Karush--Kuhn--Tucker framework. Additionally, we perform numerical experiments on various representations of persistent homology, including embeddings of persistence diagrams as well as diagrams themselves and their generalizations as persistence measures; we find that $k$-means clustering performance directly on persistence diagrams and measures outperform their vectorized representations.

Odor sensory evaluation has a broad application in food, clothing, cosmetics, and other fields. Traditional artificial sensory evaluation has poor repeatability, and the machine olfaction represented by the electronic nose (E-nose) is difficult to reflect human feelings. Olfactory electroencephalogram (EEG) contains odor and individual features associated with human olfactory preference, which has unique advantages in odor sensory evaluation. However, the difficulty of cross-subject olfactory EEG recognition greatly limits its application. It is worth noting that E-nose and olfactory EEG are more advantageous in representing odor information and individual emotions, respectively. In this paper, an E-nose and olfactory EEG multimodal learning method is proposed for cross-subject olfactory preference recognition. Firstly, the olfactory EEG and E-nose multimodal data acquisition and preprocessing paradigms are established. Secondly, a complementary multimodal data mining strategy is proposed to effectively mine the common features of multimodal data representing odor information and the individual features in olfactory EEG representing individual emotional information. Finally, the cross-subject olfactory preference recognition is achieved in 24 subjects by fusing the extracted common and individual features, and the recognition effect is superior to the state-of-the-art recognition methods. Furthermore, the advantages of the proposed method in cross-subject olfactory preference recognition indicate its potential for practical odor evaluation applications.

Variational autoencoders (VAEs) are popular models for representation learning but their encoders are susceptible to overfitting (Cremer et al., 2018) because they are trained on a finite training set instead of the true (continuous) data distribution $p_{\mathrm{data}}(\mathbf{x})$. Diffusion models, on the other hand, avoid this issue by keeping the encoder fixed. This makes their representations less interpretable, but it simplifies training, enabling accurate and continuous approximations of $p_{\mathrm{data}}(\mathbf{x})$. In this paper, we show that overfitting encoders in VAEs can be effectively mitigated by training on samples from a pre-trained diffusion model. These results are somewhat unexpected as recent findings (Alemohammad et al., 2023; Shumailov et al., 2023) observe a decay in generative performance when models are trained on data generated by another generative model. We analyze generalization performance, amortization gap, and robustness of VAEs trained with our proposed method on three different data sets. We find improvements in all metrics compared to both normal training and conventional data augmentation methods, and we show that a modest amount of samples from the diffusion model suffices to obtain these gains.

We propose an approach to do learning in Gaussian factor graphs. We treat all relevant quantities (inputs, outputs, parameters, latents) as random variables in a graphical model, and view both training and prediction as inference problems with different observed nodes. Our experiments show that these problems can be efficiently solved with belief propagation (BP), whose updates are inherently local, presenting exciting opportunities for distributed and asynchronous training. Our approach can be scaled to deep networks and provides a natural means to do continual learning: use the BP-estimated parameter marginals of the current task as parameter priors for the next. On a video denoising task we demonstrate the benefit of learnable parameters over a classical factor graph approach and we show encouraging performance of deep factor graphs for continual image classification on MNIST.

Counterfactual Explanations are becoming a de-facto standard in post-hoc interpretable machine learning. For a given classifier and an instance classified in an undesired class, its counterfactual explanation corresponds to small perturbations of that instance that allows changing the classification outcome. This work aims to leverage Counterfactual Explanations to detect the important decision boundaries of a pre-trained black-box model. This information is used to build a supervised discretization of the features in the dataset with a tunable granularity. Using the discretized dataset, an optimal Decision Tree can be trained that resembles the black-box model, but that is interpretable and compact. Numerical results on real-world datasets show the effectiveness of the approach in terms of accuracy and sparsity.

In the setting of conference peer review, the conference aims to accept high-quality papers and reject low-quality papers based on noisy review scores. A recent work proposes the isotonic mechanism, which can elicit the ranking of paper qualities from an author with multiple submissions to help improve the conference's decisions. However, the isotonic mechanism relies on the assumption that the author's utility is both an increasing and a convex function with respect to the review score, which is often violated in peer review settings (e.g.~when authors aim to maximize the number of accepted papers). In this paper, we propose a sequential review mechanism that can truthfully elicit the ranking information from authors while only assuming the agent's utility is increasing with respect to the true quality of her accepted papers. The key idea is to review the papers of an author in a sequence based on the provided ranking and conditioning the review of the next paper on the review scores of the previous papers. Advantages of the sequential review mechanism include 1) eliciting truthful ranking information in a more realistic setting than prior work; 2) improving the quality of accepted papers, reducing the reviewing workload and increasing the average quality of papers being reviewed; 3) incentivizing authors to write fewer papers of higher quality.

Neural operators have been explored as surrogate models for simulating physical systems to overcome the limitations of traditional partial differential equation (PDE) solvers. However, most existing operator learning methods assume that the data originate from a single physical mechanism, limiting their applicability and performance in more realistic scenarios. To this end, we propose Physical Invariant Attention Neural Operator (PIANO) to decipher and integrate the physical invariants (PI) for operator learning from the PDE series with various physical mechanisms. PIANO employs self-supervised learning to extract physical knowledge and attention mechanisms to integrate them into dynamic convolutional layers. Compared to existing techniques, PIANO can reduce the relative error by 13.6\%-82.2\% on PDE forecasting tasks across varying coefficients, forces, or boundary conditions. Additionally, varied downstream tasks reveal that the PI embeddings deciphered by PIANO align well with the underlying invariants in the PDE systems, verifying the physical significance of PIANO. The source code will be publicly available at: https://github.com/optray/PIANO.