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An old problem in multivariate statistics is that linear Gaussian models are often unidentifiable, i.e. some parameters cannot be uniquely estimated. In factor (component) analysis, an orthogonal rotation of the factors is unidentifiable,…

This paper proposes a fast and accurate method for sparse regression in the presence of missing data. The underlying statistical model encapsulates the low-dimensional structure of the incomplete data matrix and the sparsity of the…

The standard margin-based structured prediction commonly uses a maximum loss over all possible structured outputs. The large-margin formulation including latent variables not only results in a non-convex formulation but also increases the…

Providing a model that achieves a strong predictive performance and is simultaneously interpretable by humans is one of the most difficult challenges in machine learning research due to the conflicting nature of these two objectives. To…

Blockwise missing data occurs frequently when we integrate multisource or multimodality data where different sources or modalities contain complementary information. In this paper, we consider a high-dimensional linear regression model with…

Linear regression models have been extensively considered in the literature. However, in some practical applications they may not be appropriate all over the range of the covariate. In this paper, a more flexible model is introduced by…

Gaussian process regression is a frequently used statistical method for flexible yet fully probabilistic non-linear regression modeling. A common obstacle is its computational complexity which scales poorly with the number of observations.…

Missing data theory deals with the statistical methods in the occurrence of missing data. Missing data occurs when some values are not stored or observed for variables of interest. However, most of the statistical theory assumes that data…

We explicitly construct zero loss neural network classifiers. We write the weight matrices and bias vectors in terms of cumulative parameters, which determine truncation maps acting recursively on input space. The configurations for the…

The problem of finding a vector $x$ which obeys a set of quadratic equations $|a_k^\top x|^2=y_k$, $k=1,\cdots,m$, plays an important role in many applications. In this paper we consider the case when both $x$ and $a_k$ are real-valued…

In this paper the problem of best linear unbiased estimation is investigated for continuous-time regression models. We prove several general statements concerning the explicit form of the best linear unbiased estimator (BLUE), in particular…

We study prediction in the functional linear model with functional outputs : $Y=SX+\epsilon $ where the covariates $X$ and $Y$ belong to some functional space and $S$ is a linear operator. We provide the asymptotic mean square prediction…

Longitudinal data are important in numerous fields, such as healthcare, sociology and seismology, but real-world datasets present notable challenges for practitioners because they can be high-dimensional, contain structured missingness…

This study deals with the missing link prediction problem: the problem of predicting the existence of missing connections between entities of interest. We address link prediction using coupled analysis of relational datasets represented as…

This paper aims to front with dimensionality reduction in regression setting when the predictors are a mixture of functional variable and high-dimensional vector. A flexible model, combining both sparse linear ideas together with…

Classifiers that are linear in their parameters, and trained by optimizing a convex loss function, have predictable behavior with respect to changes in the training data, initial conditions, and optimization. Such desirable properties are…

In this study, we propose a function-on-function linear quantile regression model that allows for more than one functional predictor to establish a more flexible and robust approach. The proposed model is first transformed into a…

We provide efficient algorithms for the problem of distribution learning from high-dimensional Gaussian data where in each sample, some of the variable values are missing. We suppose that the variables are missing not at random (MNAR). The…

We propose a method to detect model misspecifications in nonlinear causal additive and potentially heteroscedastic noise models. We aim to identify predictor variables for which we can infer the causal effect even in cases of such…

This paper introduces a concept of a derivative of the optimal value function in linear programming (LP). Basically, it is the the worst case optimal value of an interval LP problem when the nominal data the data are inflated to intervals…