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Recently, sparsity-based algorithms are proposed for super-resolution spectrum estimation. However, to achieve adequately high resolution in real-world signal analysis, the dictionary atoms have to be close to each other in frequency,…
We consider the problem of estimating the factors of a rank-$1$ matrix with i.i.d. Gaussian, rank-$1$ measurements that are nonlinearly transformed and corrupted by noise. Considering two prototypical choices for the nonlinearity, we study…
Markov random fields area popular model for high-dimensional probability distributions. Over the years, many mathematical, statistical and algorithmic problems on them have been studied. Until recently, the only known algorithms for…
Answering multiple-choice questions in a setting in which no supporting documents are explicitly provided continues to stand as a core problem in natural language processing. The contribution of this article is two-fold. First, it describes…
The master equation and, more generally, Markov processes are routinely used as models for stochastic processes. They are often justified on the basis of randomization and coarse-graining assumptions. Here instead, we derive n-th order…
Ranking populations such as institutions based on certain characteristics is often of interest, and these ranks are typically estimated using samples drawn from the populations. Due to sample randomness, it is important to quantify the…
Markov chains are a natural and well understood tool for describing one-dimensional patterns in time or space. We show how to infer $k$-th order Markov chains, for arbitrary $k$, from finite data by applying Bayesian methods to both…
The aim of the paper is to examine the computational complexity and algorithmics of enumeration, the task to output all solutions of a given problem, from the point of view of parameterized complexity. First we define formally different…
In this work we introduce a new and richer class of finite order Markov chain models and address the following model selection problem: find the Markov model with the minimal set of parameters (minimal Markov model) which is necessary to…
We study the sample complexity of stochastic convex optimization when problem parameters, e.g., the distance to optimality, are unknown. We pursue two strategies. First, we develop a reliable model selection method that avoids overfitting…
Fairness is crucial for neural networks which are used in applications with important societal implication. Recently, there have been multiple attempts on improving fairness of neural networks, with a focus on fairness testing (e.g.,…
Most problems in Machine Learning cater to classification and the objects of universe are classified to a relevant class. Ranking of classified objects of universe per decision class is a challenging problem. We in this paper propose a…
We consider the problem of selecting important nodes in a random network, where the nodes connect to each other randomly with certain transition probabilities. The node importance is characterized by the stationary probabilities of the…
The selection of the best classification algorithm for a given dataset is a very widespread problem. It is also a complex one, in the sense it requires to make several important methodological choices. Among them, in this work we focus on…
A large set of signals can sometimes be described sparsely using a dictionary, that is, every element can be represented as a linear combination of few elements from the dictionary. Algorithms for various signal processing applications,…
Fast distributed algorithms that output a feasible solution for constraint satisfaction problems, such as maximal independent sets, have been heavily studied. There has been much less research on distributed sampling problems, where one…
Developing feature selection algorithms that move beyond a pure correlational to a more causal analysis of observational data is an important problem in the sciences. Several algorithms attempt to do so by discovering the Markov blanket of…
A rank-select index for a sequence $B=(b_1,\ldots,b_n)$ of $n$ bits is a data structure that, if provided with an operation to access $\Theta(\log n)$ arbitrary consecutive bits of $B$ in constant time (thus $B$ is stored outside of the…
Introduced the quantitative measure of the structural complexity of the graph (complex network, etc.) based on a procedure similar to the renormalization process, considering the difference between actual and averaged graph structures on…
Low-rank decomposition plays a central role in accelerating convolutional neural network (CNN), and the rank of decomposed kernel-tensor is a key parameter that determines the complexity and accuracy of a neural network. In this paper, we…