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We introduce a framework for performing regression between two Hilbert spaces. This is done based on Kirszbraun's extension theorem, to the best of our knowledge, the first application of this technique to supervised learning. We analyze…
The availability of precise and accurate simulation is a limiting factor for interpreting and forecasting data in many fields of science and engineering. Often, one or more distinct simulation software applications are developed, each with…
The Fr\'echet regression is a useful method for modeling random objects in a general metric space given Euclidean covariates. However, the conventional approach could be sensitive to outlying objects in the sense that the distance from the…
Metric embedding is a powerful tool used extensively in mathematics and computer science. We devise a new method of using metric embeddings recursively, which turns out to be particularly effective in $\ell_p$ spaces, $p>2$, yielding…
This work studies the computational aspects of multivariate convex regression in dimensions $d \ge 5$. Our results include the \emph{first} estimators that are minimax optimal (up to logarithmic factors) with polynomial runtime in the…
First-order optimization methods are crucial for solving large-scale data processing problems, particularly those involving convex non-smooth composite objectives. For such problems with convex non-smooth composite objectives, we introduce…
In this paper we propose a variant of the random coordinate descent method for solving linearly constrained convex optimization problems with composite objective functions. If the smooth part of the objective function has Lipschitz…
We propose an accelerated meta-algorithm, which allows to obtain accelerated methods for convex unconstrained minimization in different settings. As an application of the general scheme we propose nearly optimal methods for minimizing…
This paper presents a new methodology, called AFSSEN, to simultaneously select significant predictors and produce smooth estimates in a high-dimensional function-on-scalar linear model with a sub-Gaussian errors. Outcomes are assumed to lie…
We study a functional linear regression model that deals with functional responses and allows for both functional covariates and high-dimensional vector covariates. The proposed model is flexible and nests several functional regression…
This paper is concerned with inference on the regression function of a high-dimensional linear model when outcomes are missing at random. We propose an estimator which combines a Lasso pilot estimate of the regression function with a bias…
In this paper we present the framework of symmetry in nonparametric regression. This generalises the framework of covariate sparsity, where the regression function depends only on at most $s < d$ of the covariates, which is a special case…
Random projections are able to perform dimension reduction efficiently for datasets with nonlinear low-dimensional structures. One well-known example is that random matrices embed sparse vectors into a low-dimensional subspace nearly…
We propose a general approach to evaluating the performance of robust estimators based on adversarial losses under misspecified models. We first show that adversarial risk is equivalent to the risk induced by a distributional adversarial…
The performance of online convex optimization algorithms in a dynamic environment is often expressed in terms of the dynamic regret, which measures the decision maker's performance against a sequence of time-varying comparators. In the…
The self-concordant-like property of a smooth convex function is a new analytical structure that generalizes the self-concordant notion. While a wide variety of important applications feature the self-concordant-like property, this concept…
Most existing distance metric learning methods assume perfect side information that is usually given in pairwise or triplet constraints. Instead, in many real-world applications, the constraints are derived from side information, such as…
We propose a non-parametric variant of binary regression, where the hypothesis is regularized to be a Lipschitz function taking a metric space to [0,1] and the loss is logarithmic. This setting presents novel computational and statistical…
We propose a theoretical framework for an adaptive learning rate policy for the Mean Absolute Error loss function and Quantile loss function and evaluate its effectiveness for regression tasks. The framework is based on the theory of…
We propose a stochastic optimization method for the minimization of the sum of three convex functions, one of which has Lipschitz continuous gradient as well as restricted strong convexity. Our approach is most suitable in the setting where…