Related papers: Minimax Bounds for Distributed Logistic Regression
We consider the problem of predicting as well as the best linear combination of d given functions in least squares regression, and variants of this problem including constraints on the parameters of the linear combination. When the input…
We study the problem of communicating a distributed correlated memoryless source over a memoryless network, from source nodes to destination nodes, under quadratic distortion constraints. We establish the following two complementary…
We investigate the problem of center estimation in the high dimensional binary sub-Gaussian Mixture Model with Hidden Markov structure on the labels. We first study the limitations of existing results in the high dimensional setting and…
Using only retrospective data, we study the problem of predicting treatment effects for the same treatment/policy implemented in a different location or time period. We propose a distributionally robust estimator that minimizes the…
Variational inference methods for latent variable statistical models have gained popularity because they are relatively fast, can handle large data sets, and have deterministic convergence guarantees. However, in practice it is unclear…
Given a prediction task, understanding when one can and cannot design a consistent convex surrogate loss, particularly a low-dimensional one, is an important and active area of machine learning research. The prediction task may be given as…
We consider the problem of distributed mean estimation (DME), in which $n$ machines are each given a local $d$-dimensional vector $x_v \in \mathbb{R}^d$, and must cooperate to estimate the mean of their inputs $\mu = \frac 1n\sum_{v = 1}^n…
We investigate the performance of distributed least-mean square (LMS) algorithms for parameter estimation over sensor networks where the regression data of each node are corrupted by white measurement noise. Under this condition, we show…
We introduce a procedure for conditional density estimation under logarithmic loss, which we call SMP (Sample Minmax Predictor). This estimator minimizes a new general excess risk bound for statistical learning. On standard examples, this…
It is a common phenomenon that for high-dimensional and nonparametric statistical models, rate-optimal estimators balance squared bias and variance. Although this balancing is widely observed, little is known whether methods exist that…
Given a single observation from a Gaussian distribution with unknown mean $\theta$, we design computationally efficient procedures that can approximately generate an observation from a different target distribution $Q_{\theta}$ uniformly…
The Poisson model is frequently employed to describe count data, but in a Bayesian context it leads to an analytically intractable posterior probability distribution. In this work, we analyze a variational Gaussian approximation to the…
We study transfer learning for estimation in latent variable network models. In our setting, the conditional edge probability matrices given the latent variables are represented by $P$ for the source and $Q$ for the target. We wish to…
We consider the problem of predicting as well as the best linear combination of d given functions in least squares regression under L^\infty constraints on the linear combination. When the input distribution is known, there already exists…
It is of fundamental importance to find algorithms obtaining optimal performance for learning of statistical models in distributed and communication limited systems. Aiming at characterizing the optimal strategies, we consider learning of…
Maximum entropy models are increasingly being used to describe the collective activity of neural populations with measured mean neural activities and pairwise correlations, but the full space of probability distributions consistent with…
When multiple users share a common link in direct transmission, packet loss and network collision may occur due to the simultaneous arrival of traffics at the source node. To tackle this problem, users may resort to an indirect path: the…
Many problems of interest for cyber-physical network systems can be formulated as Mixed-Integer Linear Programs in which the constraints are distributed among the agents. In this paper we propose a distributed algorithmic framework to solve…
We consider optimal designs for general multinomial logistic models, which cover baseline-category, cumulative, adjacent-categories, and continuation-ratio logit models, with proportional odds, non-proportional odds, or partial proportional…
Sparse linear regression with ill-conditioned Gaussian random designs is widely believed to exhibit a statistical/computational gap, but there is surprisingly little formal evidence for this belief, even in the form of examples that are…