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We present a new and general method of weighted least square univariate regression where the dependent variable is expanded as a series of suitably chosen functions of the independent variables. Each term of the series is obtained by an…
Neural networks achieve outstanding accuracy in classification and regression tasks. However, understanding their behavior still remains an open challenge that requires questions to be addressed on the robustness, explainability and…
We explore algorithms and limitations for sparse optimization problems such as sparse linear regression and robust linear regression. The goal of the sparse linear regression problem is to identify a small number of key features, while the…
The presence of data corruption in user-generated streaming data, such as social media, motivates a new fundamental problem that learns reliable regression coefficient when features are not accessible entirely at one time. Until now,…
This paper is concerned with optimizing the global minimum-variance portfolio's (GMVP) weights in high-dimensional settings where both observation and population dimensions grow at a bounded ratio. Optimizing the GMVP weights is highly…
We present a detailed analysis of the class of regression decision tree algorithms which employ a regulized piecewise-linear node-splitting criterion and have regularized linear models at the leaves. From a theoretic standpoint, based on…
Recent work introduced a robust computational framework combining embedded mathematical structures, advanced optimization, and neural network architecture, leading to the discovery of multiple unstable self-similar solutions for key fluid…
In today's era of big data, robust least-squares regression becomes a more challenging problem when considering the adversarial corruption along with explosive growth of datasets. Traditional robust methods can handle the noise but suffer…
In this paper, we propose an easy-to-implement residual-based specification testing procedure for detecting structural changes in factor models, which is powerful against both smooth and abrupt structural changes with unknown break dates.…
Concerning bivariate least squares linear regression, the classical results obtained for extreme structural models in earlier attempts are reviewed using a new formalism in terms of deviation (matrix) traces which, for homoscedastic data,…
High-dimensional time series data appear in many scientific areas in the current data-rich environment. Analysis of such data poses new challenges to data analysts because of not only the complicated dynamic dependence between the series,…
The iterations of many sparse estimation algorithms are comprised of a fixed linear filter cascaded with a thresholding nonlinearity, which collectively resemble a typical neural network layer. Consequently, a lengthy sequence of algorithm…
Hierarchical optimization refers to problems with interdependent decision variables and objectives, such as minimax and bilevel formulations. While various algorithms have been proposed, existing methods and analyses lack adaptivity in…
In this paper, new results in random matrix theory are derived which allow us to construct a shrinkage estimator of the global minimum variance (GMV) portfolio when the shrinkage target is a random object. More specifically, the shrinkage…
This paper solves the dynamic portfolio choice problem. Using an explicit solution with a power utility, we construct a bridge between a continuous and discrete VAR model to assess portfolio sensitivities. We find, from a well analyzed…
In many prediction problems, it is not uncommon that the number of variables used to construct a forecast is of the same order of magnitude as the sample size, if not larger. We then face the problem of constructing a prediction in the…
In many real-world applications, optimization problems evolve continuously over time and are often subject to stochastic noise. We consider a stochastic time-varying optimization problem in which the objective function $f(x;t)$ changes…
The paper deals with regression problems, in which the nonsmooth target is assumed to switch between different operating modes. Specifically, piecewise smooth (PWS) regression considers target functions switching deterministically via a…
Motivated by applications in neuroimaging analysis, we propose a new regression model, Sparse TensOr REsponse regression (STORE), with a tensor response and a vector predictor. STORE embeds two key sparse structures: element-wise sparsity…
We propose a novel sparse sliced inverse regression method based on random projections in a large $p$ small $n$ setting. Embedded in a generalized eigenvalue framework, the proposed approach finally reduces to parallel execution of…