Related papers: Phase Transitions in Approximate Ranking
The problem of ranking/ordering instances, instead of simply classifying them, has recently gained much attention in machine learning. In this paper we formulate the ranking problem in a rigorous statistical framework. The goal is to learn…
We establish the convergence rates and asymptotic distributions of the common break change-point estimators, obtained by least squares and maximum likelihood in panel data models and compare their asymptotic variances. Our model assumptions…
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…
Noisy matrix completion has attracted significant attention due to its applications in recommendation systems, signal processing and image restoration. Most existing works rely on (weighted) least squares methods under various low-rank…
The interplay between computational efficiency and statistical accuracy in high-dimensional inference has drawn increasing attention in the literature. In this paper, we study computational and statistical boundaries for submatrix…
This paper studies sequential search models that (1) incorporate unobserved product quality, which can be correlated with endogenous observable characteristics (such as price) and endogenous search cost variables (such as product rankings…
Current deep neural networks are highly overparameterized (up to billions of connection weights) and nonlinear. Yet they can fit data almost perfectly through variants of gradient descent algorithms and achieve unexpected levels of…
Denoising score matching plays a pivotal role in the performance of diffusion-based generative models. However, the empirical optimal score--the exact solution to the denoising score matching--leads to memorization, where generated samples…
We consider the problem of ranking $n$ players from partial pairwise comparison data under the Bradley-Terry-Luce model. For the first time in the literature, the minimax rate of this ranking problem is derived with respect to the Kendall's…
The growing amount of applications that generate vast amount of data in short time scales render the problem of partial monitoring, coupled with prediction, a rather fundamental one. We study the aforementioned canonical problem under the…
We propose and analyze an approximate message passing (AMP) algorithm for the matrix tensor product model, which is a generalization of the standard spiked matrix models that allows for multiple types of pairwise observations over a…
Signal-to-noise ratios (SNR) play a crucial role in various statistical models, with important applications in tasks such as estimating heritability in genomics. The method-of-moments estimator is a widely used approach for estimating SNR,…
In this paper, we study the linear transformation model in the most general setup. This model includes many important and popular models in statistics and econometrics as special cases. Although it has been studied for many years, the…
Learning-to-rank techniques have proven to be extremely useful for prioritization problems, where we rank items in order of their estimated probabilities, and dedicate our limited resources to the top-ranked items. This work exposes a…
We describe several algorithms for matrix completion and matrix approximation when only some of its entries are known. The approximation constraint can be any whose approximated solution is known for the full matrix. For low rank…
Predictive posterior densities (PPDs) are of interest in approximate Bayesian inference. Typically, these are estimated by simple Monte Carlo (MC) averages using samples from the approximate posterior. We observe that the signal-to-noise…
A few iterations of alternating least squares with a random starting point provably suffice to produce nearly optimal spectral- and Frobenius-norm accuracies of low-rank approximations to a matrix; iterating to convergence is unnecessary.…
This paper investigates the performance of the adaptive matched filtering (AMF) in cluttered environments, particularly when operating with superimposed signals. Since the instantaneous signal-to-clutter-plus-noise ratio (SCNR) is a random…
Estimating linear, mean-square continuous functionals is a pivotal challenge in statistics. In high-dimensional contexts, this estimation is often performed under the assumption of exact model sparsity, meaning that only a small number of…
This paper studies systematic exploration for reinforcement learning with rich observations and function approximation. We introduce a new model called contextual decision processes, that unifies and generalizes most prior settings. Our…