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We consider object recognition in the context of lifelong learning, where a robotic agent learns to discriminate between a growing number of object classes as it accumulates experience about the environment. We propose an incremental…
We examine the impact of learning Lipschitz continuous models in the context of model-based reinforcement learning. We provide a novel bound on multi-step prediction error of Lipschitz models where we quantify the error using the…
Uncertainty estimation has been extensively studied in recent literature, which can usually be classified as aleatoric uncertainty and epistemic uncertainty. In current aleatoric uncertainty estimation frameworks, it is often neglected that…
This paper solves a new class of optimization problems under uncertainty, called Probable Event Constrained Optimization (PECO), which optimizes an objective function of decision variables and subjects to a set of Probable Event Constraints…
Recent advancements in machine learning have emphasized the need for transparency in model predictions, particularly as interpretability diminishes when using increasingly complex architectures. In this paper, we propose leveraging…
Statistical equilibrium models of coherent structures in two-dimensional and barotropic quasi-geostrophic turbulence are formulated using canonical and microcanonical ensembles, and the equivalence or nonequivalence of ensembles is…
We study binary classification algorithms for which the prediction on any point is not too sensitive to individual examples in the dataset. Specifically, we consider the notions of uniform stability (Bousquet and Elisseeff, 2001) and…
In this paper, a mathematical theory of learning is proposed that has many parallels with information theory. We consider Vapnik's General Setting of Learning in which the learning process is defined to be the act of selecting a hypothesis…
Fine-tuning LLMs on tabular classification tasks can lead to the phenomenon of fine-tuning multiplicity where equally well-performing models make conflicting predictions on the same input. Fine-tuning multiplicity can arise due to…
This paper deals with the convergence time analysis of a class of fixed-time stable systems with the aim to provide a new non-conservative upper bound for its settling time. Our contribution is fourfold. First, we revisit the well-known…
In the last several years, the intimate connection between convex optimization and learning problems, in both statistical and sequential frameworks, has shifted the focus of algorithmic machine learning to examine this interplay. In…
Assessing uncertainty is an important step towards ensuring the safety and reliability of machine learning systems. Existing uncertainty estimation techniques may fail when their modeling assumptions are not met, e.g. when the data…
Algorithmic stability is a central notion in learning theory that quantifies the sensitivity of an algorithm to small changes in the training data. If a learning algorithm satisfies certain stability properties, this leads to many important…
Latent variable models are a fundamental modeling tool in machine learning applications, but they present significant computational and analytical challenges. The popular EM algorithm and its variants, is a much used algorithmic tool; yet…
Theory and application of stochastic approximation (SA) have become increasingly relevant due in part to applications in optimization and reinforcement learning. This paper takes a new look at SA with constant step-size $\alpha>0$, defined…
Many Bayesian Network structure learning algorithms are unstable, with the learned graph sensitive to arbitrary dataset artifacts, such as the ordering of columns (i.e., variable order). PC-Stable attempts to address this issue for the…
Measuring the stability of conclusions derived from Ordinary Least Squares linear regression is critically important, but most metrics either only measure local stability (i.e. against infinitesimal changes in the data), or are only…
Features in machine learning problems are often time-varying and may be related to outputs in an algebraic or dynamical manner. The dynamic nature of these machine learning problems renders current higher order accelerated gradient descent…
Nearly-elastic model systems with one or two degrees of freedom are considered: the system is undergoing a small loss of energy in each collision with the "wall". We show that instabilities in this purely deterministic system lead to…
In the classical stochastic resetting problem, a particle, moving according to some stochastic dynamics, undergoes random interruptions that bring it to a selected domain, and then, the process recommences. Hitherto, the resetting mechanism…