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On a variety of tasks, the performance of neural networks predictably improves with training time, dataset size and model size across many orders of magnitude. This phenomenon is known as a neural scaling law. Of fundamental importance is…
Cyber-physical systems come with increasingly complex architectures and failure modes, which complicates the task of obtaining accurate system reliability models. At the same time, with the emergence of the (industrial) Internet-of-Things,…
In this work, we provide a sharp theory of scaling laws for two-layer neural networks trained on a class of hierarchical multi-index targets, in a genuinely representation-limited regime. We derive exact information-theoretic scaling laws…
We characterize the effectiveness of a classical algorithm for recovering the Markov graph of a general discrete pairwise graphical model from i.i.d. samples. The algorithm is (appropriately regularized) maximum conditional log-likelihood,…
Effective LLM training depends on predictable scaling of key quantities -- such as final loss and optimal hyperparameters -- with model and dataset size. Qiu et al. (2025) recently showed that this predictability can extend beyond scalars:…
We study the problem of learning Bayesian networks where an $\epsilon$-fraction of the samples are adversarially corrupted. We focus on the fully-observable case where the underlying graph structure is known. In this work, we present the…
We study the structure and learnability of sums of independent integer random variables (SIIRVs). For $k \in \mathbb{Z}_{+}$, a $k$-SIIRV of order $n \in \mathbb{Z}_{+}$ is the probability distribution of the sum of $n$ independent random…
Inference is typically intractable in high-treewidth undirected graphical models, making maximum likelihood learning a challenge. One way to overcome this is to restrict parameters to a tractable set, most typically the set of…
We develop a corrective mechanism for neural network approximation: the total available non-linear units are divided into multiple groups and the first group approximates the function under consideration, the second group approximates the…
This work focuses on the estimation of multiple change-points in a time-varying Ising model that evolves piece-wise constantly. The aim is to identify both the moments at which significant changes occur in the Ising model, as well as the…
The inference performance of the pseudolikelihood method is discussed in the framework of the inverse Ising problem when the $\ell_2$-regularized (ridge) linear regression is adopted. This setup is introduced for theoretically investigating…
Recent years have witnessed significant progress in the development of machine learning models across a wide range of fields, fueled by increased computational resources, large-scale datasets, and the rise of deep learning architectures.…
Longest Increasing Subsequence (LIS) is a fundamental statistic of a sequence, and has been studied for decades. While the LIS of a sequence of length $n$ can be computed exactly in time $O(n\log n)$, the complexity of estimating the…
Social and real-world considerations such as robustness, fairness, social welfare and multi-agent tradeoffs have given rise to multi-distribution learning paradigms, such as collaborative learning, group distributionally robust…
The recent work by Dong & Yang (2023) showed for misspecified sparse linear bandits, one can obtain an $O\left(\epsilon\right)$-optimal policy using a polynomial number of samples when the sparsity is a constant, where $\epsilon$ is the…
We provide a static data structure for distance estimation which supports {\it adaptive} queries. Concretely, given a dataset $X = \{x_i\}_{i = 1}^n$ of $n$ points in $\mathbb{R}^d$ and $0 < p \leq 2$, we construct a randomized data…
We design efficient distance approximation algorithms for several classes of structured high-dimensional distributions. Specifically, we show algorithms for the following problems: - Given sample access to two Bayesian networks $P_1$ and…
In this paper, we investigate adaptive nonlinear regression and introduce tree based piecewise linear regression algorithms that are highly efficient and provide significantly improved performance with guaranteed upper bounds in an…
We consider the problem of change-point detection in multivariate time-series. The multivariate distribution of the observations is supposed to follow a graphical model, whose graph and parameters are affected by abrupt changes throughout…
Bayesian structure learning is the NP-hard problem of discovering a Bayesian network that optimally represents a given set of training data. In this paper we study the computational worst-case complexity of exact Bayesian structure learning…