相关论文: Topological trivialization in non-convex empirical…

We address the practical construction of asymptotic confidence intervals for smooth (i.e., path-wise differentiable), real-valued statistical parameters by targeted learning from independent and identically distributed data in contexts…

The effectiveness of non-parametric, kernel-based methods for function estimation comes at the price of high computational complexity, which hinders their applicability in adaptive, model-based control. Motivated by approximation techniques…

There has been a recent surge of interest in the study of asymptotic reconstruction performance in various cases of generalized linear estimation problems in the teacher-student setting, especially for the case of i.i.d standard normal…

In analyses with severe data-limitations, augmenting the target dataset with information from ancillary datasets in the application domain, called source datasets, can lead to significantly improved statistical procedures. However, existing…

We study the asymmetric matrix factorization problem under a natural nonconvex formulation with arbitrary overparametrization. The model-free setting is considered, with minimal assumption on the rank or singular values of the observed…

Optimization of conditional convex risk measure is a central theme in dynamic portfolio selection theory, which has not yet systematically studied in the previous literature perhaps since conditional convex risk measures are neither random…

Let $(Y_i,\theta_i)$, $i=1,...,n$, be independent random vectors distributed like $(Y,\theta) \sim G^*$, where the marginal distribution of $\theta$ is completely unknown, and the conditional distribution of $Y$ conditional on $\theta$ is…

Decentralized optimization is a promising parallel computation paradigm for large-scale data analytics and machine learning problems defined over a network of nodes. This paper is concerned with decentralized non-convex composite problems…

We derive a new asymptotic expansion for the global excess risk of a local-$k$-nearest neighbour classifier, where the choice of $k$ may depend upon the test point. This expansion elucidates conditions under which the dominant contribution…

Fitting a function by using linear combinations of a large number $N$ of `simple' components is one of the most fruitful ideas in statistical learning. This idea lies at the core of a variety of methods, from two-layer neural networks to…

In this paper we introduce a generalization of classical risk measures in which the risk is represented by a step function taking two values, corresponding to two endogenously determined market regimes. This extends the traditional…

Let y=A\beta+\epsilon, where y is an N\times1 vector of observations, \beta is a p\times1 vector of unknown regression coefficients, A is an N\times p design matrix and \epsilon is a spherically symmetric error term with unknown scale…

Convergence properties of empirical risk minimizers can be conveniently expressed in terms of the associated population risk. To derive bounds for the performance of the estimator under covariate shift, however, pointwise convergence rates…

The celebrated Bernstein von-Mises theorem ensures that credible regions from Bayesian posterior are well-calibrated when the model is correctly-specified, in the frequentist sense that their coverage probabilities tend to the nominal…

The notion of generalization in classical Statistical Learning is often attached to the postulate that data points are independent and identically distributed (IID) random variables. While relevant in many applications, this postulate may…

We consider the question of estimating a solution to a system of equations that involve convex nonlinearities, a problem that is common in machine learning and signal processing. Because of these nonlinearities, conventional estimators…

Transfer learning for nonparametric regression is considered. We first study the non-asymptotic minimax risk for this problem and develop a novel estimator called the confidence thresholding estimator, which is shown to achieve the minimax…

How to obtain a graph from data samples is an important problem in graph signal processing. One way to formulate this graph learning problem is based on Gaussian maximum likelihood estimation, possibly under particular topology constraints.…

This paper studies few-shot learning via representation learning, where one uses $T$ source tasks with $n_1$ data per task to learn a representation in order to reduce the sample complexity of a target task for which there is only $n_2 (\ll…

Selecting the best regularization parameter in inverse problems is a classical and yet challenging problem. Recently, data-driven approaches have become popular to tackle this challenge. These approaches are appealing since they do require…