Related papers: A nested hierarchy of second order upper bounds on…
In this paper we consider the problem of binary hypothesis testing with finite memory systems. Let $X_1,X_2,\ldots$ be a sequence of independent identically distributed Bernoulli random variables, with expectation $p$ under $\mathcal{H}_0$…
Second-order optimality conditions are essential for nonsmooth optimization, where both the objective and constraint functions are Lipschitz continuous and second-order directionally differentiable. This paper provides no-gap second-order…
In using the Bayesian network (BN) to construct the complex multistate system's reliability model as described in Part I, the memory storage requirements of the node probability table (NPT) will exceed the random access memory (RAM) of the…
We characterize the minimax rate of estimating the second-order calibration error for binary classification, which quantifies whether a higher-order predictor's epistemic-uncertainty estimate matches the conditional variance of the label…
Hierarchical clustering of networks consists in finding a tree of communities, such that lower levels of the hierarchy reveal finer-grained community structures. There are two main classes of algorithms tackling this problem. Divisive…
We design new algorithms for the combinatorial pure exploration problem in the multi-arm bandit framework. In this problem, we are given $K$ distributions and a collection of subsets $\mathcal{V} \subset 2^{[K]}$ of these distributions, and…
Bayesian Neural Networks (BNNs) are trained to optimize an entire distribution over their weights instead of a single set, having significant advantages in terms of, e.g., interpretability, multi-task learning, and calibration. Because of…
This paper presents new lower and upper bounds for the compression rate of binary prefix codes optimized over memoryless sources according to various nonlinear codeword length objectives. Like the most well-known redundancy bounds for…
Research in reinforcement learning has produced algorithms for optimal decision making under uncertainty that fall within two main types. The first employs a Bayesian framework, where optimality improves with increased computational time.…
We introduce a novel method for bounding high-order multi-dimensional polynomials in finite element approximations. The method involves precomputing optimal piecewise-linear bounding boxes for polynomial basis functions, which can then be…
The size and complexity of software and hardware systems have significantly increased in the past years. As a result, it is harder to guarantee their correct behavior. One of the most successful methods for automated verification of…
With the advent of high-throughput profiling methods, interest in reverse engineering the structure and dynamics of biochemical networks is high. Recently an algorithm for reverse engineering of biochemical networks was developed by…
Diverse higher-order structures, foundational for supporting a network's "meta-functions", play a vital role in structure, functionality, and the emergence of complex dynamics. Nevertheless, the problem of dismantling them has been…
Lifted inference algorithms exploit symmetries in probabilistic models to speed up inference. They show impressive performance when calculating unconditional probabilities in relational models, but often resort to non-lifted inference when…
In this paper we consider the minimization of a continuous function that is potentially not differentiable or not twice differentiable on the boundary of the feasible region. By exploiting an interior point technique, we present first- and…
Current state-of-the-art solution techniques for solving bilevel optimization problems either assume strong problem regularity criteria or are computationally intractable. In this paper we address power system problems of bilevel structure,…
In random parameter estimation, Bayesian lower bounds (BLBs) for the mean-square error have been noticed to not be tight in a number of cases, even when the sample size, or the signal-to-noise ratio, grow to infinity. In this paper, we…
We consider the problem of discriminating finite-dimensional quantum processes, also called quantum supermaps, that can consist of multiple time steps. Obtaining the ultimate performance for discriminating quantum processes is of…
We establish or refute the optimality of inexact second-order methods for unconstrained nonconvex optimization from the point of view of worst-case evaluation complexity, improving and generalizing the results of Cartis, Gould and Toint…
A restricted Boltzmann machine (RBM) is a two-layer neural network with shared weights and has been extensively studied for dimensionality reduction, data representation and recommendation systems in the literature. The traditional RBM…