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The effectiveness of non-parametric, kernel-based methods for function estimation comes at the price of high computational complexity, which hinders their applicability in adaptive, model-based control. Motivated by approximation techniques…

Various iterative reconstruction algorithms for inverse problems can be unfolded as neural networks. Empirically, this approach has often led to improved results, but theoretical guarantees are still scarce. While some progress on…

We study the generalization performance of unregularized gradient methods for separable linear classification. While previous work mostly deal with the binary case, we focus on the multiclass setting with $k$ classes and establish novel…

We study the design and analysis of switchback experiments conducted on a single aggregate unit. The design problem is to partition the continuous time space into intervals and switch treatments between intervals, in order to minimize the…

The fundamental task of general density estimation $p(x)$ has been of keen interest to machine learning. In this work, we attempt to systematically characterize methods for density estimation. Broadly speaking, most of the existing methods…

Segmented regression models offer model flexibility and interpretability as compared to the global parametric and the nonparametric models, and yet are challenging in both estimation and inference. We consider a four-regime segmented model…

Neural scaling laws establish a predictable relationship between model performance and data or compute, offering crucial guidance for resource allocation in new domains and tasks. Yet such laws are most needed precisely where they are…

Stochastic Gradient Descent (SGD) based methods have been widely used for training large-scale machine learning models that also generalize well in practice. Several explanations have been offered for this generalization performance, a…

Modeling the temporal behavior of data is of primordial importance in many scientific and engineering fields. Baseline methods assume that both the dynamic and observation equations follow linear-Gaussian models. However, there are many…

Transfer learning seeks to accelerate sequential decision-making by leveraging offline data from related agents. However, data from heterogeneous sources that differ in observed features, distributions, or unobserved confounders often…

Residual-based adaptive strategies are widely used in scientific machine learning but remain largely heuristic. We introduce a unifying variational framework that formalizes these methods by integrating convex transformations of the…

Several learning applications require solving high-dimensional regression problems where the relevant features belong to a small number of (overlapping) groups. For very large datasets and under standard sparsity constraints, hard…

Due to the drastic gap in complexity between sequential and batch statistical learning, recent work has studied a smoothed sequential learning setting, where Nature is constrained to select contexts with density bounded by 1/{\sigma} with…

In this paper, we consider the problem of reconstructing piecewise smooth functions to high accuracy from nonuniform samples of their Fourier transform. We use the framework of nonuniform generalized sampling (NUGS) to do this, and to…

Semiparametric regression offers a flexible framework for modeling non-linear relationships between a response and covariates. A prime example are generalized additive models where splines (say) are used to approximate non-linear functional…

With the wide adoption of machine learning techniques, requirements have evolved beyond sheer high performance, often requiring models to be trustworthy. A common approach to increase the trustworthiness of such systems is to allow them to…

Stochastic computational models in the form of pure jump processes occur frequently in the description of chemical reactive processes, of ion channel dynamics, and of the spread of infections in populations. For spatially extended models,…

We present a novel method to compute componentwise transient bounds, ultimate bounds, and invariant regions for a class of switching continuous-time linear systems with perturbation bounds that may depend nonlinearly on a delayed state. The…

We propose a data segmentation methodology for the high-dimensional linear regression problem where regression parameters are allowed to undergo multiple changes. The proposed methodology, MOSEG, proceeds in two stages: first, the data are…

While standard statistical inference techniques and machine learning generalization bounds assume that tests are run on data selected independently of the hypotheses, practical data analysis and machine learning are usually iterative and…