Related papers: Piecewise linear regression and classification
The sparse factorization of a large matrix is fundamental in modern statistical learning. In particular, the sparse singular value decomposition and its variants have been utilized in multivariate regression, factor analysis, biclustering,…
The sparse linear regression problem is difficult to handle with usual sparse optimization models when both predictors and measurements are either quantized or represented in low-precision, due to non-convexity. In this paper, we provide a…
We propose a penalized likelihood framework for estimating multiple precision matrices from different classes. Most existing methods either incorporate no information on relationships between the precision matrices, or require this…
With the development of machine learning and Big Data, the concepts of linear and non-linear optimization techniques are becoming increasingly valuable for many quantitative disciplines. Problems of that nature are typically solved using…
Sparse Bayesian learning is a state-of-the-art supervised learning algorithm that can choose a subset of relevant samples from the input data and make reliable probabilistic predictions. However, in the presence of high-dimensional data…
Machine learning is increasingly used to guide branch-and-cut (B&C) for mixed-integer linear programming by learning score-based policies for selecting branching variables and cutting planes. Many approaches train on local signals from…
We consider the problem of learning a mixture of Random Utility Models (RUMs). Despite the success of RUMs in various domains and the versatility of mixture RUMs to capture the heterogeneity in preferences, there has been only limited…
Principal component analysis (PCA) has been widely applied to dimensionality reduction and data pre-processing for different applications in engineering, biology and social science. Classical PCA and its variants seek for linear projections…
This study introduces a general semiparametric clusterwise index distribution model to analyze how latent clusters affect the covariate-response relationships. By employing sufficient dimension reduction to account for the effects of…
We propose a new approach for 3D instance segmentation based on sparse convolution and point affinity prediction, which indicates the likelihood of two points belonging to the same instance. The proposed network, built upon submanifold…
Multinomial Logistic Regression is a well-studied tool for classification and has been widely used in fields like image processing, computer vision and, bioinformatics, to name a few. Under a supervised classification scenario, a…
Sparse Principal Component Analysis (sPCA) is a cardinal technique for obtaining combinations of features, or principal components (PCs), that explain the variance of high-dimensional datasets in an interpretable manner. This involves…
The objective of clustering is to discover natural groups in datasets and to identify geometrical structures which might reside there, without assuming any prior knowledge on the characteristics of the data. The problem can be seen as…
Cutting planes are a crucial component of state-of-the-art mixed-integer programming solvers, with the choice of which subset of cuts to add being vital for solver performance. We propose new distance-based measures to qualify the value of…
Model order reduction has been extensively studied over the last two decades. Projection-based methods such as the Proper Orthogonal Decomposition and the Reduced Basis Method enjoy the important advantages of Galerkin methods in the…
In many situations, the choice of an adequate similarity measure or metric on the feature space dramatically determines the performance of machine learning methods. Building automatically such measures is the specific purpose of…
Autonomous mobile robots must maintain safety, but should not sacrifice performance, leading to the classical reach-avoid problem: find a trajectory that is guaranteed to reach a goal and avoid obstacles. This paper addresses the near…
This paper revisits cluster-based retrieval that partitions the inverted index into multiple groups and skips the index partially at cluster and document levels during online inference using a learned sparse representation. It proposes an…
Conformal prediction (CP) for regression can be challenging, especially when the output distribution is heteroscedastic, multimodal, or skewed. Some of the issues can be addressed by estimating a distribution over the output, but in…
Algorithms for binary classification based on adaptive tree partitioning are formulated and analyzed for both their risk performance and their friendliness to numerical implementation. The algorithms can be viewed as generating a set…