Related papers: Covariance Prediction via Convex Optimization
Covariance regression analysis is an approach to linking the covariance of responses to a set of explanatory variables $X$, where $X$ can be a vector, matrix, or tensor. Most of the literature on this topic focuses on the "Fixed-$X$"…
Incomplete covariate vectors are known to be problematic for estimation and inferences on model parameters, but their impact on prediction performance is less understood. We develop an imputation-free method that builds on a random…
Predict a new response from a covariate is a challenging task in regression, which raises new question since the era of high-dimensional data. In this paper, we are interested in the inverse regression method from a theoretical viewpoint.…
Predicting the value of a function $f$ at a new point given its values at old points is an ubiquitous scientific endeavor, somewhat less developed when $f$ produces multiple values that depend on one another, e.g. when it outputs…
Most inverse optimization models impute unspecified parameters of an objective function to make an observed solution optimal for a given optimization problem with a fixed feasible set. We propose two approaches to impute unspecified…
In this paper, we propose a predictor-corrector type Consensus Based Optimization (CBO) algorithm on a convex feasible set. Our proposed algorithm generalizes the CBO algorithm in [11] to tackle a constrained optimization problem for the…
Measuring the accuracy of cross-sectional predictions is a subjective problem. Generally, this problem is avoided. In contrast, this paper confronts subjectivity up front by eliciting an impartial decision-maker's preferences. These…
Invariance (defined in a general sense) has been one of the most effective priors for representation learning. Direct factorization of parametric models is feasible only for a small range of invariances, while regularization approaches,…
Functional linear regression analysis aims to model regression relations which include a functional predictor. The analog of the regression parameter vector or matrix in conventional multivariate or multiple-response linear regression…
For linear models that may have asymmetric errors, we study variable selection by cross-validation. The data are split into training and validation sets, with the number of observations in the validation set much larger than in the training…
The majority of machine learning methods can be regarded as the minimization of an unavailable risk function. To optimize the latter, given samples provided in a streaming fashion, we define a general stochastic Newton algorithm and its…
We derive approximation algorithms for the nonnegative matrix factorization problem, i.e. the problem of factorizing a matrix as the product of two matrices with nonnegative coefficients. We form convex approximations of this problem which…
Equivariant models leverage prior knowledge on symmetries to improve predictive performance, but misspecified architectural constraints can harm it instead. While work has explored learning or relaxing constraints, selecting among…
Consider a random vector with finite second moments. If its precision matrix is an M-matrix, then all partial correlations are non-negative. If that random vector is additionally Gaussian, the corresponding Markov random field (GMRF) is…
In classical inverse linear optimization, one assumes a given solution is a candidate to be optimal. Real data is imperfect and noisy, so there is no guarantee this assumption is satisfied. Inspired by regression, this paper presents a…
Approximations of functions with finite data often do not respect certain "structural" properties of the functions. For example, if a given function is non-negative, a polynomial approximation of the function is not necessarily also…
AIMS. The maximum-likelihood method is the standard approach to obtain model fits to observational data and the corresponding confidence regions. We investigate possible sources of bias in the log-likelihood function and its subsequent…
We consider estimation of a sparse parameter vector that determines the covariance matrix of a Gaussian random vector via a sparse expansion into known "basis matrices". Using the theory of reproducing kernel Hilbert spaces, we derive lower…
Consider a polyhedral convex cone which is given by a finite number of linear inequalities. We investigate the problem to project this cone into a subspace and show that this problem is closely related to linear vector optimization: We…
This article describes a multivariate polynomial regression method where the uncertainty of the input parameters are approximated with Gaussian distributions, derived from the central limit theorem for large weighted sums, directly from the…