Related papers: A Selection Premium Decomposition for the Expected…
We study the problem of distributed multi-view representation learning. In this problem, $K$ agents observe each one distinct, possibly statistically correlated, view and independently extracts from it a suitable representation in a manner…
We are interested in recovering information on a stochastic block model from the subgraph discovered by an exploring random walk. Stochastic block models correspond to populations structured into a finite number of types, where two…
We analyze the Brownian Motion limit of a prototypical unit step reinforced random-walk on the half line. A reinforced random walk is one which changes the weight of any edge (or vertex) visited to increase the frequency of return visits.…
We study a model of market economics wherein the $(n+1)$-st customer, for each $n\geqslant N$, with $N$ being a prespecified positive integer, draws a sample of (random) size $K_{n}$, either with replacement or without, from the customers…
Brownian motion is a Gaussian process described by the central limit theorem. However, exponential decays of the positional probability density function $P(X,t)$ of packets of spreading random walkers, were observed in numerous situations…
We provide a novel characterization of semiparametric efficiency in a generic supervised learning setting where the outcome mean function -- defined as the conditional expectation of the outcome of interest given the other observed…
We consider the maximum process of a random walk with additive independent noise in form of $\max_{i=1,\dots,n}(S_i+Y_i)$. The random walk may have dependent increments, but its sample path is assumed to converge weakly to a fractional…
Across science and policy, decision-makers often need to draw conclusions about the best candidate among competing alternatives. For instance, researchers may seek to infer the effectiveness of the most successful treatment or determine…
We define the reflection of a random walk at a general barrier and derive, in case the increments are light tailed and have negative mean, a necessary and sufficient criterion for the global maximum of the reflected process to be finite…
We propose information-directed sampling -- a new approach to online optimization problems in which a decision-maker must balance between exploration and exploitation while learning from partial feedback. Each action is sampled in a manner…
We consider a model for a queue in which only a fixed number $N$ of customers can join. Each customer joins the queue independently at an exponentially distributed time. Assuming further that the service times are independent and follow an…
Motivated by the psychological literature on the "peak-end rule" for remembered experience, we perform an analysis within a random walk framework of a discrete choice model where agents' future choices depend on the peak memory of their…
Randomized rankings have been of recent interest to achieve ex-ante fairer exposure and better robustness than deterministic rankings. We propose a set of natural axioms for randomized group-fair rankings and prove that there exists a…
A new method is proposed for variable screening, variable selection and prediction in linear regression problems where the number of predictors can be much larger than the number of observations. The method involves minimizing a penalized…
A family of models of individual discrete choice are constructed by means of statistical averaging of choices made by a subject in a reinforcement learning process, where the subject has short, k-term memory span. The choice probabilities…
In this paper we study sums of powers of affine functions in (mostly) one variable. Although quite simple, this model is a generalization of two well-studied models: Waring decomposition and sparsest shift. For these three models there are…
Challenging research in various fields has driven a wide range of methodological advances in variable selection for regression models with high-dimensional predictors. In comparison, selection of nonlinear functions in models with additive…
It is well known that if a submartingale $X$ is bounded then the increasing predictable process $Y$ and the martingale $M$ from the Doob decomposition $% X=Y+M$ can be unbounded. In this paper for some classes of increasing convex functions…
In [1], the authors consider a random walk $(Z_{n,1},\ldots,Z_{n,K+1})\in \mathbb{Z}^{K+1}$ with the constraint that each coordinate of the walk is at distance one from the following one. A functional central limit theorem for the first…
The bias-variance decomposition is a central result in statistics and machine learning, but is typically presented only for the squared error. We present a generalization of the bias-variance decomposition where the prediction error is a…