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Modeling of high-dimensional data is very important to categorize different classes. We develop a new mixture model called Multinomial cluster-weighted model (MCWM). We derive the identifiability of a general class of MCWM. We estimate the…

This paper investigates the problem of robust model predictive control (RMPC) of linear-time-invariant (LTI) discrete-time systems subject to structured uncertainty and bounded disturbances. Typically, the constrained RMPC problem with…

The best subset selection (or "best subsets") estimator is a classic tool for sparse regression, and developments in mathematical optimization over the past decade have made it more computationally tractable than ever. Notwithstanding its…

The key innovation of our analytical method, CaRT, lies in establishing a new hierarchical, distributed architecture to guarantee the safety and robustness of a given learning-based motion planning policy. First, in a nominal setting, the…

The Container Relocation Problem (CRP) is concerned with finding a sequence of moves of containers that minimizes the number of relocations needed to retrieve all containers, while respecting a given order of retrieval. However, the…

A class of recovering algorithms for 1-bit compressive sensing (CS) named Soft Consistency Reconstructions (SCRs) are proposed. Recognizing that CS recovery is essentially an optimization problem, we endeavor to improve the characteristics…

The Classical Tukey-Huber Contamination Model (CCM) is a usual framework to describe the mechanism of outliers generation in robust statistics. In a data set with $n$ observations and $p$ variables, under the CCM, an outlier is a unit, even…

In this paper we propose a robust Model Predictive Control where a Gated Recurrent Unit network model is used to learn the input-output dynamic of the system under control. Robust satisfaction of input and output constraints and recursive…

Notwithstanding the popularity of conventional clustering algorithms such as K-means and probabilistic clustering, their clustering results are sensitive to the presence of outliers in the data. Even a few outliers can compromise the…

Model-based clustering approaches concern the paradigm of exploratory data analysis relying on the finite mixture model to automatically find a latent structure governing observed data. They are one of the most popular and successful…

Shanghai Composite Index prediction has become a hot issue for many investors and academic researchers. Deep learning models are widely applied in multivariate time series forecasting, including recurrent neural networks (RNN),…

Designing learning algorithms that are resistant to perturbations of the underlying data distribution is a problem of wide practical and theoretical importance. We present a general approach to this problem focusing on unsupervised…

Cluster-weighted modeling (CWM) is a mixture approach for modeling the joint probability of a response variable and a set of explanatory variables. The parameters are estimated by means of the expectation-maximization algorithm according to…

This paper studies the problem of distributionally robust model predictive control (MPC) using total variation distance ambiguity sets. For a discrete-time linear system with additive disturbances, we provide a conditional value-at-risk…

Conformal prediction (CP) converts any model's output to prediction sets with a guarantee to cover the true label with (adjustable) high probability. Robust CP extends this guarantee to worst-case (adversarial) inputs. Existing baselines…

Convolutional Neural Networks (CNNs) have recently emerged as the dominant model in computer vision. If provided with enough training data, they predict almost any visual quantity. In a discrete setting, such as classification, CNNs are not…

The patterns of particulate matter with diameters that are generally 2.5 micrometers and smaller (PM2.5) are heterogeneous in China nationwide but can be homogeneous region-wide. To reduce the adverse effects from PM2.5, policymakers need…

Constructing uncertainty sets as unions of multiple subsets has emerged as an effective approach for creating compact and flexible uncertainty representations in data-driven robust optimization (RO). This paper focuses on two separate…

Recurrent Neural Network (RNN) and its variations such as Long Short-Term Memory (LSTM) and Gated Recurrent Unit (GRU), have become standard building blocks for learning online data of sequential nature in many research areas, including…

Relative error estimation has been recently used in regression analysis. A crucial issue of the existing relative error estimation procedures is that they are sensitive to outliers. To address this issue, we employ the $\gamma$-likelihood…