Related papers: Convex-area-wise Linear Regression and Algorithms …
We consider the problem of predicting a response variable from a set of covariates on a data set that differs in distribution from the training data. Causal parameters are optimal in terms of predictive accuracy if in the new distribution…
Many real-world large-scale regression problems can be formulated as Multi-task Learning (MTL) problems with a massive number of tasks, as in retail and transportation domains. However, existing MTL methods still fail to offer both the…
Linear Discriminant Analysis (LDA) is a fundamental method for classification. Its simple linear structure facilitates interpretation, and it is naturally suited to multi-class settings. LDA is also closely connected to several classical…
Multi-view data have been routinely collected in various fields of science and engineering. A general problem is to study the predictive association between multivariate responses and multi-view predictor sets, all of which can be of high…
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…
Linear regression without correspondences concerns the recovery of a signal in the linear regression setting, where the correspondences between the observations and the linear functionals are unknown. The associated maximum likelihood…
Sparse covariance matrices play crucial roles by encoding the interdependencies between variables in numerous fields such as genetics and neuroscience. Despite substantial studies on sparse covariance matrices, existing methods face several…
Causal representation learning (CRL) has garnered increasing interest from the causal inference and artificial intelligence communities due to its potential to disentangle complex data-generating mechanism into causally interpretable latent…
We develop an algorithmic theory of convex optimization over discrete sets. Using a combination of algebraic and geometric tools we are able to provide polynomial time algorithms for solving broad classes of convex combinatorial…
The reduced-rank vector autoregressive (VAR) model can be interpreted as a supervised factor model, where two factor modelings are simultaneously applied to response and predictor spaces. This article introduces a new model, called vector…
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,…
Data assimilation is a method that combines observations (that is, real world data) of a state of a system with model output for that system in order to improve the estimate of the state of the system and thereby the model output. The model…
This paper proposes and analyzes a communication-efficient distributed optimization framework for general nonconvex nonsmooth signal processing and machine learning problems under an asynchronous protocol. At each iteration, worker machines…
For high dimensional sparse linear regression problems, we propose a sequential convex relaxation algorithm (iSCRA-TL1) by solving inexactly a sequence of truncated $\ell_1$-norm regularized minimization problems, in which the working index…
A computationally efficient method to solve non-convex programming problems with linear equality constraints is presented. The proposed method is based on a recursively feasible and descending sequential convex programming procedure proven…
In recent years, the modeling and analysis of interval-valued time series have garnered significant attention in the fields of econometrics and statistics. However, the existing literature primarily focuses on regression tasks while…
Analysis of high-dimensional data is currently a popular field of research, thanks to many applications e.g. in genetics (DNA data in genomewide association studies), spectrometry or web analysis. At the same time, the type of problems that…
We propose a novel nonparametric regression method that models complex input-output relationships as the sum of convex and concave components. The method-Identifiable Convex-Concave Nonparametric Least Squares (ICCNLS)-decomposes the target…
Machine Learning requires a large amount of training data in order to build accurate models. Sometimes the data arrives over time, requiring significant storage space and recalculating the model to account for the new data. On-line learning…
Accurate uncertainty quantification is critical for reliable predictive modeling. Existing methods typically address either aleatoric uncertainty due to measurement noise or epistemic uncertainty resulting from limited data, but not both in…