Rule set learning has recently been frequently revisited because of its interpretability. Existing methods have several shortcomings though. First, most existing methods impose orders among rules, either explicitly or implicitly, which makes the models less comprehensible. Second, due to the difficulty of handling conflicts caused by overlaps (i.e., instances covered by multiple rules), existing methods often do not consider probabilistic rules. Third, learning classification rules for multi-class target is understudied, as most existing methods focus on binary classification or multi-class classification via the ``one-versus-rest" approach. To address these shortcomings, we propose TURS, for Truly Unordered Rule Sets. To resolve conflicts caused by overlapping rules, we propose a novel model that exploits the probabilistic properties of our rule sets, with the intuition of only allowing rules to overlap if they have similar probabilistic outputs. We next formalize the problem of learning a TURS model based on the MDL principle and develop a carefully designed heuristic algorithm. We benchmark against a wide range of rule-based methods and demonstrate that our method learns rule sets that have lower model complexity and highly competitive predictive performance. In addition, we empirically show that rules in our model are empirically ``independent" and hence truly unordered.

Learning from Label Proportions (LLP) is a learning problem where only aggregate level labels are available for groups of instances, called bags, during training, and the aim is to get the best performance at the instance-level on the test data. This setting arises in domains like advertising and medicine due to privacy considerations. We propose a novel algorithmic framework for this problem that iteratively performs two main steps. For the first step (Pseudo Labeling) in every iteration, we define a Gibbs distribution over binary instance labels that incorporates a) covariate information through the constraint that instances with similar covariates should have similar labels and b) the bag level aggregated label. We then use Belief Propagation (BP) to marginalize the Gibbs distribution to obtain pseudo labels. In the second step (Embedding Refinement), we use the pseudo labels to provide supervision for a learner that yields a better embedding. In the final iteration, a classifier is trained using the pseudo labels. Our algorithm displays strong gains against several SOTA baselines (up to 15%) for the LLP Binary Classification problem on various dataset types - tabular and Image. We achieve these improvements with minimal computational overhead above standard supervised learning due to Belief Propagation, for large bag sizes, even for a million samples. Learning from Label Proportions (henceforth LLP) has seen renewed interest in recent times due to the rising concerns of privacy and leakage of sensitive information (Ardehaly & Culotta, 2017; Busa-Fekete et al., 2023; Zhang et al., 2022; Kobayashi et al., 2022; Yu et al., 2014). In the LLP binary classification setting, all the training instances are aggregated into bags and only the aggregated label count for a bag is available, i.e. proportion of 1's in a bag. Features of all instances are available. This can be seen as a form of weak supervision compared to providing instance-level labels.

This paper considers the sequential design of remedial control actions in response to system anomalies for the ultimate objective of preventing blackouts. A physics-guided reinforcement learning (RL) framework is designed to identify effective sequences of real-time remedial look-ahead decisions accounting for the long-term impact on the system's stability. The paper considers a space of control actions that involve both discrete-valued transmission line-switching decisions (line reconnections and removals) and continuous-valued generator adjustments. To identify an effective blackout mitigation policy, a physics-guided approach is designed that uses power-flow sensitivity factors associated with the power transmission network to guide the RL exploration during agent training. Comprehensive empirical evaluations using the open-source Grid2Op platform demonstrate the notable advantages of incorporating physical signals into RL decisions, establishing the gains of the proposed physics-guided approach compared to its black box counterparts. One important observation is that strategically~\emph{removing} transmission lines, in conjunction with multiple real-time generator adjustments, often renders effective long-term decisions that are likely to prevent or delay blackouts.

Neuronal morphology is essential for studying brain functioning and understanding neurodegenerative disorders. As the acquiring of real-world morphology data is expensive, computational approaches especially learning-based ones e.g. MorphVAE for morphology generation were recently studied, which are often conducted in a way of randomly augmenting a given authentic morphology to achieve plausibility. Under such a setting, this paper proposes \textbf{MorphGrower} which aims to generate more plausible morphology samples by mimicking the natural growth mechanism instead of a one-shot treatment as done in MorphVAE. Specifically, MorphGrower generates morphologies layer by layer synchronously and chooses a pair of sibling branches as the basic generation block, and the generation of each layer is conditioned on the morphological structure of previous layers and then generate morphologies via a conditional variational autoencoder with spherical latent space. Extensive experimental results on four real-world datasets demonstrate that MorphGrower outperforms MorphVAE by a notable margin. Our code will be publicly available to facilitate future research.

Empirical process theory for i.i.d. observations has emerged as a ubiquitous tool for understanding the generalization properties of various statistical problems. However, in many applications where the data exhibit temporal dependencies (e.g., in finance, medical imaging, weather forecasting etc.), the corresponding empirical processes are much less understood. Motivated by this observation, we present a general bound on the expected supremum of empirical processes under standard $\beta/\rho$-mixing assumptions. Unlike most prior work, our results cover both the long and the short-range regimes of dependence. Our main result shows that a non-trivial trade-off between the complexity of the underlying function class and the dependence among the observations characterizes the learning rate in a large class of nonparametric problems. This trade-off reveals a new phenomenon, namely that even under long-range dependence, it is possible to attain the same rates as in the i.i.d. setting, provided the underlying function class is complex enough. We demonstrate the practical implications of our findings by analyzing various statistical estimators in both fixed and growing dimensions. Our main examples include a comprehensive case study of generalization error bounds in nonparametric regression over smoothness classes in fixed as well as growing dimension using neural nets, shape-restricted multivariate convex regression, estimating the optimal transport (Wasserstein) distance between two probability distributions, and classification under the Mammen-Tsybakov margin condition -- all under appropriate mixing assumptions. In the process, we also develop bounds on $L_r$ ($1\le r\le 2$)-localized empirical processes with dependent observations, which we then leverage to get faster rates for (a) tuning-free adaptation, and (b) set-structured learning problems.

In the era of information proliferation, discerning the credibility of news content poses an ever-growing challenge. This paper introduces RELIANCE, a pioneering ensemble learning system designed for robust information and fake news credibility evaluation. Comprising five diverse base models, including Support Vector Machine (SVM), naive Bayes, logistic regression, random forest, and Bidirectional Long Short Term Memory Networks (BiLSTMs), RELIANCE employs an innovative approach to integrate their strengths, harnessing the collective intelligence of the ensemble for enhanced accuracy. Experiments demonstrate the superiority of RELIANCE over individual models, indicating its efficacy in distinguishing between credible and non-credible information sources. RELIANCE, also surpasses baseline models in information and news credibility assessment, establishing itself as an effective solution for evaluating the reliability of information sources.

Categorical variables often appear in datasets for classification and regression tasks, and they need to be encoded into numerical values before training. Since many encoders have been developed and can significantly impact performance, choosing the appropriate encoder for a task becomes a time-consuming yet important practical issue. This study broadly classifies machine learning models into three categories: 1) ATI models that implicitly perform affine transformations on inputs, such as multi-layer perceptron neural network; 2) Tree-based models that are based on decision trees, such as random forest; and 3) the rest, such as kNN. Theoretically, we prove that the one-hot encoder is the best choice for ATI models in the sense that it can mimic any other encoders by learning suitable weights from the data. We also explain why the target encoder and its variants are the most suitable encoders for tree-based models. This study conducted comprehensive computational experiments to evaluate 14 encoders, including one-hot and target encoders, along with eight common machine-learning models on 28 datasets. The computational results agree with our theoretical analysis. The findings in this study shed light on how to select the suitable encoder for data scientists in fields such as fraud detection, disease diagnosis, etc.

We study a family of distributed stochastic optimization algorithms where gradients are sampled by a token traversing a network of agents in random-walk fashion. Typically, these random-walks are chosen to be Markov chains that asymptotically sample from a desired target distribution, and play a critical role in the convergence of the optimization iterates. In this paper, we take a novel approach by replacing the standard linear Markovian token by one which follows a nonlinear Markov chain - namely the Self-Repellent Radom Walk (SRRW). Defined for any given 'base' Markov chain, the SRRW, parameterized by a positive scalar {\alpha}, is less likely to transition to states that were highly visited in the past, thus the name. In the context of MCMC sampling on a graph, a recent breakthrough in Doshi et al. (2023) shows that the SRRW achieves O(1/{\alpha}) decrease in the asymptotic variance for sampling. We propose the use of a 'generalized' version of the SRRW to drive token algorithms for distributed stochastic optimization in the form of stochastic approximation, termed SA-SRRW. We prove that the optimization iterate errors of the resulting SA-SRRW converge to zero almost surely and prove a central limit theorem, deriving the explicit form of the resulting asymptotic covariance matrix corresponding to iterate errors. This asymptotic covariance is always smaller than that of an algorithm driven by the base Markov chain and decreases at rate O(1/{\alpha}^2) - the performance benefit of using SRRW thereby amplified in the stochastic optimization context. Empirical results support our theoretical findings.

Further, we propose a novel inference algorithm and establish theoretical properties for a state-of-the-art NeSy system that are crucial for learning. Our proposed learning framework builds upon NeSy energy-based models (NeSy-EBMs) (Pryor et al., 2023), a general class of NeSy systems that encompasses a variety of existing NeSy methods, including DeepProblog (Manhaeve et al., 2018; 2021), SATNet (Wang et al., 2019), logic tensor networks (Badreddine et al., 2022), and NeuPSL (Pryor et al., 2023). NeSy-EBMs use neural network outputs to parameterize an energy function and formulate an inference problem that may be non-smooth and constrained. Thus, predictions are not guaranteed to be a function of the inputs and parameters with an explicit form or to be differentiable, and traditional deep learning techniques are not directly applicable. We therefore equivalently formulate NeSy-EBM learning as a bilevel problem and, to support smooth first-order gradient-based optimization, propose a smoothing strategy that is novel to NeSy learning. Specifically, we replace the constrained NeSy energy function with its Moreau envelope. The augmented Lagrangian method for equality-constrained minimization is then applied with the new formulation.

In causal discovery, non-Gaussianity has been used to characterize the complete configuration of a Linear Non-Gaussian Acyclic Model (LiNGAM), encompassing both the causal ordering of variables and their respective connection strengths. However, LiNGAM can only deal with the finite-dimensional case. To expand this concept, we extend the notion of variables to encompass vectors and even functions, leading to the Functional Linear Non-Gaussian Acyclic Model (Func-LiNGAM). Our motivation stems from the desire to identify causal relationships in brain-effective connectivity tasks involving, for example, fMRI and EEG datasets. We demonstrate why the original LiNGAM fails to handle these inherently infinite-dimensional datasets and explain the availability of functional data analysis from both empirical and theoretical perspectives. We establish theoretical guarantees of the identifiability of the causal relationship among non-Gaussian random vectors and even random functions in infinite-dimensional Hilbert spaces. To address the issue of sparsity in discrete time points within intrinsic infinite-dimensional functional data, we propose optimizing the coordinates of the vectors using functional principal component analysis. Experimental results on synthetic data verify the ability of the proposed framework to identify causal relationships among multivariate functions using the observed samples. For real data, we focus on analyzing the brain connectivity patterns derived from fMRI data.