Related papers: Random Projections for Linear Support Vector Machi…
Commonly used classification algorithms in machine learning, such as support vector machines, minimize a convex surrogate loss on training examples. In practice, these algorithms are surprisingly robust to errors in the training data. In…
This article deals with random projections applied as a data reduction technique for Bayesian regression analysis. We show sufficient conditions under which the entire $d$-dimensional distribution is approximately preserved under random…
The Support Vector Machine (SVM) is one of the most widely used classification methods. In this paper, we consider the soft-margin SVM used on data points with independent features, where the sample size $n$ and the feature dimension $p$…
We show how, using linear-algebraic tools developed to prove Tverberg's theorem in combinatorial geometry, we can design new models of multi-class support vector machines (SVMs). These supervised learning protocols require fewer conditions…
Supervised manifold learning methods learn data representations by preserving the geometric structure of data while enhancing the separation between data samples from different classes. In this work, we propose a theoretical study of…
Support vector machine (SVM) has been one of the most popular learning algorithms, with the central idea of maximizing the minimum margin, i.e., the smallest distance from the instances to the classification boundary. Recent theoretical…
Support Vector Machine (SVM) is a powerful tool in binary classification, known to attain excellent misclassification rates. On the other hand, many realworld classification problems, such as those found in medical diagnosis, churn or fraud…
In this paper, we propose a probabilistic reduced-dimensional vector autoregressive (PredVAR) model to extract low-dimensional dynamics from high-dimensional noisy data. The model utilizes an oblique projection to partition the measurement…
Given a training set with binary classification, the Support Vector Machine identifies the hyperplane maximizing the margin between the two classes of training data. This general formulation is useful in that it can be applied without…
Random projections (RP) are a popular tool for reducing dimensionality while preserving local geometry. In many applications the data set to be projected is given to us in advance, yet the current RP techniques do not make use of…
We study the following basic machine learning task: Given a fixed set of $d$-dimensional input points for a linear regression problem, we wish to predict a hidden response value for each of the points. We can only afford to attain the…
In this paper, we propose a probabilistic reduced-dimensional vector autoregressive (PredVAR) model with oblique projections. This model partitions the measurement space into a dynamic subspace and a static subspace that do not need to be…
When performing classification tasks, raw high dimensional features often contain redundant information, and lead to increased computational complexity and overfitting. In this paper, we assume the data samples lie on a single underlying…
Solving large-scale optimization on-the-fly is often a difficult task for real-time computer graphics applications. To tackle this challenge, model reduction is a well-adopted technique. Despite its usefulness, model reduction often…
Support Vector Machine (SVM) is an efficient classification approach, which finds a hyperplane to separate data from different classes. This hyperplane is determined by support vectors. In existing SVM formulations, the objective function…
The support vector machine (SVM) is an important class of learning machines for function approach, pattern recognition, and time-serious prediction, etc. It maps samples into the feature space by so-called support vectors of selected…
Because of the advance in technologies, modern statistical studies often encounter linear models with the number of explanatory variables much larger than the sample size. Estimation and variable selection in these high-dimensional problems…
We consider the problem of estimating the number of distinct elements in a large data set (or, equivalently, the support size of the distribution induced by the data set) from a random sample of its elements. The problem occurs in many…
Fitting linear regression models can be computationally very expensive in large-scale data analysis tasks if the sample size and the number of variables are very large. Random projections are extensively used as a dimension reduction tool…
We study a general smallest intersecting ball problem and its soft-margin variant in high-dimensional Euclidean spaces for input objects that are compact and convex. These two problems link and unify a series of fundamental problems in…