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Multimodal learning has seen remarkable progress, particularly with the emergence of large-scale pre-training across various modalities. However, most current approaches are built on the assumption of a deterministic, one-to-one alignment…

This paper studies the high-dimensional mixed linear regression (MLR) where the output variable comes from one of the two linear regression models with an unknown mixing proportion and an unknown covariance structure of the random…

Metamodels, or the regression analysis of Monte Carlo simulation results, provide a powerful tool to summarize simulation findings. However, an underutilized approach is the multilevel metamodel (MLMM) that accounts for the dependent data…

Multicollinearity produces an inflation in the variance of the Ordinary Least Squares estimators due to the correlation between two or more independent variables (including the constant term). A widely applied solution is to estimate with…

Linear regression is a fundamental and popular statistical method. There are various kinds of linear regression, such as mean regression and quantile regression. In this paper, we propose a new one called distribution regression, which…

Multimodal Mathematical Reasoning (MMR) has recently attracted increasing attention for its capability to solve mathematical problems involving both textual and visual modalities. However, current models still face significant challenges in…

Multi-target regression is concerned with the prediction of multiple continuous target variables using a shared set of predictors. Two key challenges in multi-target regression are: (a) modelling target dependencies and (b) scalability to…

Statistical machine learning algorithms have achieved state-of-the-art results on benchmark datasets, outperforming humans in many tasks. However, the out-of-distribution data and confounder, which have an unpredictable causal relationship,…

Multivariate linear regression is a fundamental statistical task, but classical estimators such as ordinary least squares are highly sensitive to outliers. These may occur as casewise outliers that affect entire observations, or as outlying…

Algorithmic modeling relies on limited information in data to extrapolate outcomes for unseen scenarios, often embedding an element of arbitrariness in its decisions. A perspective on this arbitrariness that has recently gained interest is…

Despite the success of neural networks (NNs), there is still a concern among many over their "black box" nature. Why do they work? Here we present a simple analytic argument that NNs are in fact essentially polynomial regression models.…

Fr\'echet regression extends linear regression to model complex responses in metric spaces, making it particularly relevant for multi-label regression, where eachinstance can have multiple associated labels. However, addressing noise and…

The multitime multiple recurrences are common in analysis of algorithms, computational biology, information theory, queueing theory, filters theory, statistical physics etc. The theoretical part about them is little or not known. That is…

Multi-target regression is concerned with the simultaneous prediction of multiple continuous target variables based on the same set of input variables. It arises in several interesting industrial and environmental application domains, such…

We consider the problem of variable selection in Bayesian multivariate linear regression models, involving multiple response and predictor variables, under multivariate normal errors. In the absence of a known covariance structure,…

Machine learning can provide deep insights into data, allowing machines to make high-quality predictions and having been widely used in real-world applications, such as text mining, visual classification, and recommender systems. However,…

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…

Multivariate statistical analysis is concerned with observations on several variables which are thought to possess some degree of inter-dependence. Driven by problems in genetics and the social sciences, it first flowered in the earlier…

Modal regression, a widely used regression protocol, has been extensively investigated in statistical and machine learning communities due to its robustness to outliers and heavy-tailed noises. Understanding modal regression's theoretical…

We consider the topic of multivariate regression on manifold-valued output, that is, for a multivariate observation, its output response lies on a manifold. Moreover, we propose a new regression model to deal with the presence of grossly…