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Let $C$ be a nonempty closed and convex subset of a uniformly smooth and uniformly convex real Banach space $E$ with dual space $E^*$. We present a novel hybrid method for finding a common solution of a family of equilibrium problems, a…
Randomized trials are considered the gold standard for estimating causal effects. Trial findings are often used to inform policy and programming efforts, yet their results may not generalize well to a relevant target population due to…
The empirical loss, commonly referred to as the average loss, is extensively utilized for training machine learning models. However, in order to address the diverse performance requirements of machine learning models, the use of the…
This paper introduces a new version of the smoothly trimmed mean with a more general version of weights, which can be used as an alternative to the classical trimmed mean. We derive its asymptotic variance and to further investigate its…
We use a discrete-time formulation to study the asymmetric avalanche process [Phys. Rev. Lett. vol. 87, 084301 (2001)] on a finite ring and obtain an exact expression for the average avalanche size of particles as a function of toppling…
In this paper we propose a procedure for robust estimation in the context of generalized linear models based on the maximum Lq-likelihood method. Alongside this, an estimation algorithm that represents a natural extension of the usual…
We develop sampling algorithms to fit Bayesian hierarchical models, the computational complexity of which scales linearly with the number of observations and the number of parameters in the model. We focus on crossed random effect and…
Accurate computation of robust estimates for extremal quantiles of empirical distributions is an essential task for a wide range of applicative fields, including economic policymaking and the financial industry. Such estimates are…
We compute the distribution of triplets of stationary points in the energy landscape of the spherical p-spin model, by evaluating the quenched three-point complexity by means of the Kac-Rice formalism. We show the occurrence of transitions…
This paper considers an empirical risk minimization problem under heavy-tailed settings, where data does not have finite variance, but only has $p$-th moment with $p \in (1,2)$. Instead of using estimation procedure based on truncated…
We analyze statistical features of the ``optimization landscape'' in a random version of one of the simplest constrained optimization problems of the least-square type: finding the best approximation for the solution of an overcomplete…
A general framework for dealing with both linear regression and clustering problems is described. It includes Gaussian clusterwise linear regression analysis with random covariates and cluster analysis via Gaussian mixture models with…
We consider the "all-for-one" decentralized learning problem for generalized linear models. The features of each sample are partitioned among several collaborating agents in a connected network, but only one agent observes the response…
Conventional simulations of complex systems in the canonical ensemble suffer from the quasi-ergodicity problem. A simulation in generalized ensemble overcomes this difficulty by performing a random walk in potential energy space and other…
We provide a unified analysis of the predictive risk of ridge regression and regularized discriminant analysis in a dense random effects model. We work in a high-dimensional asymptotic regime where $p, n \to \infty$ and $p/n \to \gamma \in…
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…
Trajectory optimization under uncertainty underpins a wide range of applications in robotics. However, existing methods are limited in terms of reasoning about sources of epistemic and aleatoric uncertainty, space and time correlations,…
The present paper gives a statistical adventure towards exploring the average case complexity behavior of computer algorithms. Rather than following the traditional count based analytical (pen and paper) approach, we instead talk in terms…
Regression analysis is commonly conducted in survey sampling. However, existing methods fail when the relationships vary across different areas or domains. In this paper, we propose a unified framework to study the group-wise covariate…
Data clustering is a fundamental problem with a wide range of applications. Standard methods, eg the $k$-means method, usually require solving a non-convex optimization problem. Recently, total variation based convex relaxation to the…