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Low-dimensional embeddings for data from disparate sources play critical roles in multi-modal machine learning, multimedia information retrieval, and bioinformatics. In this paper, we propose a supervised dimensionality reduction method…

To find efficient screening methods for high dimensional linear regression models, this paper studies the relationship between model fitting and screening performance. Under a sparsity assumption, we show that a subset that includes the…

In this paper, we study the problem of learning multi-dimensional Gaussian Mixture Models (GMMs), with a specific focus on model order selection and efficient mixing distribution estimation. We first establish an information-theoretic lower…

High-dimensional limit theorems have been shown useful to derive tuning rules for finding the optimal scaling in random-walk Metropolis algorithms. The assumptions under which weak convergence results are proved are however restrictive: the…

Node embedding methods find latent lower-dimensional representations which are used as features in machine learning models. In the last few years, these methods have become extremely popular as a replacement for manual feature engineering.…

Spatial autocorrelation in regression models can lead to downward biased standard errors and thus incorrect inference. The most common correction in applied economics is the spatial heteroskedasticity and autocorrelation consistent (HAC)…

In recent years, data dimensionality has increasingly become a concern, leading to many parameter and dimension reduction techniques being proposed in the literature. A parameter-wise co-clustering model, for data modelled via continuous…

In this paper we consider the problem of segmenting $n$ aligned random sequences of equal length $m$, into a finite number of independent blocks. We propose to use a penalized maximum likelihood criterion to infer simultaneously the number…

The celebrated Takens' embedding theorem provides a theoretical foundation for reconstructing the full state of a dynamical system from partial observations. However, the classical theorem assumes that the underlying system is deterministic…

Tasking machine learning to predict segments of a time series requires estimating the parameters of a ML model with input/output pairs from the time series. Using the equivalence between statistical data assimilation and supervised machine…

Accurate spatiotemporal pattern analysis is critical in fields such as urban traffic, meteorology, and public health monitoring. However, existing methods face performance bottlenecks, typically yielding only incremental gains and often…

High accuracy complex computer models, or simulators, require large resources in time and memory to produce realistic results. Statistical emulators are computationally cheap approximations of such simulators. They can be built to replace…

In this paper, we address the problem of predicting a response variable in the context of both, spatially correlated and high-dimensional data. To reduce the dimensionality of the predictor variables, we apply the sufficient dimension…

This paper develops robust confidence intervals in high-dimensional and left-censored regression. Type-I censored regression models are extremely common in practice, where a competing event makes the variable of interest unobservable.…

Fitting statistical models is computationally challenging when the sample size or the dimension of the dataset is huge. An attractive approach for down-scaling the problem size is to first partition the dataset into subsets and then fit…

We study high-dimensional linear models with error-in-variables. Such models are motivated by various applications in econometrics, finance and genetics. These models are challenging because of the need to account for measurement errors to…

Stochastic gradient methods enable learning probabilistic models from large amounts of data. While large step-sizes (learning rates) have shown to be best for least-squares (e.g., Gaussian noise) once combined with parameter averaging,…

We propose a new metaheuristic training scheme that combines Stochastic Gradient Descent (SGD) and Discrete Optimization in an unconventional way. Our idea is to define a discrete neighborhood of the current SGD point containing a number of…

By using dimensionless conductances as scaling variables, the conventional one-parameter scaling theory of localization fails for non-reciprocal non-Hermitian systems such as the Hanato-Nelson model. Here, we propose a one-parameter scaling…

Estimation of small failure probabilities is one of the most important and challenging computational problems in reliability engineering. The failure probability is usually given by an integral over a high-dimensional uncertain parameter…