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Human intuition allows to detect abnormal driving scenarios in situations they never experienced before. Like humans detect those abnormal situations and take countermeasures to prevent collisions, self-driving cars need anomaly detection…

We study the infinite-horizon restless bandit problem with the average reward criterion, in both discrete-time and continuous-time settings. A fundamental goal is to efficiently compute policies that achieve a diminishing optimality gap as…

Necessary and sufficient conditions are presented for the (first-order) theory of a universal class of algebraic structures (algebras) to admit a model completion, extending a characterization provided by Wheeler. For varieties of algebras…

Detecting out-of-distribution (OOD) instances is crucial for the reliable deployment of machine learning models in real-world scenarios. OOD inputs are commonly expected to cause a more uncertain prediction in the primary task; however,…

We introduce Bifurcation Logic, BL, which combines a basic classical modality with separating conjunction * together with its naturally associated multiplicative implication, that is defined using the modal ordering. Specifically, a formula…

We consider the problem of binary classification with abstention in the relatively less studied \emph{bounded-rate} setting. We begin by obtaining a characterization of the Bayes optimal classifier for an arbitrary input-label distribution…

Motivated by Arveson's conjecture, we introduce a notion of hyperrigidity for a partial order on the state space of a $C^*$-algebra $B$. We show how this property is equivalent to the existence of a boundary: a subset of the pure states…

A general, variational approach to derive low-order reduced systems is presented. The approach is based on the concept of optimal parameterizing manifold (OPM) that substitutes the more classical notions of invariant or slow manifold when…

This paper makes 3 contributions. First, it generalizes the Lindeberg\textendash Feller and Lyapunov Central Limit Theorems to Hilbert Spaces by way of $L^2$. Second, it generalizes these results to spaces in which sample failure and…

Anomaly detection (AD) is a crucial machine learning task that aims to learn patterns from a set of normal training samples to identify abnormal samples in test data. Most existing AD studies assume that the training and test data are drawn…

This paper investigates the challenges of optimal online policy learning under missing data. State-of-the-art algorithms implicitly assume that rewards are always observable. I show that when rewards are missing at random, the Upper…

In this work, we propose learnable Bernoulli dropout (LBD), a new model-agnostic dropout scheme that considers the dropout rates as parameters jointly optimized with other model parameters. By probabilistic modeling of Bernoulli dropout,…

A one dimensional disordered particle hopping rate asymmetric exclusion process (ASEP) with open boundaries and a random sequential dynamics is studied analytically. Combining the exact results of the steady states in the pure case with a…

This paper provides a baseline system for First-shot-compliant unsupervised anomaly detection (ASD) for machine condition monitoring. First-shot ASD does not allow systems to do machine-type dependent hyperparameter tuning or tool…

Out-of-distribution (OOD) detection is essential to prevent anomalous inputs from causing a model to fail during deployment. While improved OOD detection methods have emerged, they often rely on the final layer outputs and require a full…

We analyse the convergence of an approximate, fully inexact, ADMM algorithm under additive, deterministic and probabilistic error models. We consider the generalized ADMM scheme that is derived from generalized Lagrangian penalty with…

The framework of Integral Quadratic Constraints of Lessard et al. (2014) reduces the computation of upper bounds on the convergence rate of several optimization algorithms to semi-definite programming (SDP). Followup work by Nishihara et…

We show that H\"older continuity of the gradient is not only a sufficient condition, but also a necessary condition for the existence of a global upper bound on the error of the first-order Taylor approximation. We also relate this global…

We study the problem of linear contextual bandits with paid observations, where at each round the learner selects an action in order to minimize its loss in a given context, and can then decide to pay a fixed cost to observe the loss of any…

Approximate Bayesian computation (ABC) or likelihood-free inference algorithms are used to find approximations to posterior distributions without making explicit use of the likelihood function, depending instead on simulation of sample data…