Related papers: Hierarchical learning in polynomial Support Vector…
The learning properties of finite size polynomial Support Vector Machines are analyzed in the case of realizable classification tasks. The normalization of the high order features acts as a squeezing factor, introducing a strong anisotropy…
We study the typical learning properties of the recently proposed Support Vectors Machines. The generalization error on linearly separable tasks, the capacity, the typical number of Support Vectors, the margin, and the robustness or noise…
Using methods of Statistical Physics, we investigate the generalization performance of support vector machines (SVMs), which have been recently introduced as a general alternative to neural networks. For nonlinear classification rules, the…
Well-calibrated probabilistic regression models are a crucial learning component in robotics applications as datasets grow rapidly and tasks become more complex. Unfortunately, classical regression models are usually either probabilistic…
Machine learning is the dominant approach to artificial intelligence, through which computers learn from data and experience. In the framework of supervised learning, a necessity for a computer to learn from data accurately and efficiently…
We propose an algorithm for exploring the entire regularization path of asymmetric-cost linear support vector machines. Empirical evidence suggests the predictive power of support vector machines depends on the regularization parameters of…
In most papers establishing consistency for learning algorithms it is assumed that the observations used for training are realizations of an i.i.d. process. In this paper we go far beyond this classical framework by showing that support…
The neural network-based approach to solving partial differential equations has attracted considerable attention due to its simplicity and flexibility in representing the solution of the partial differential equation. In training a neural…
In deep learning theory, a critical question is to understand how neural networks learn hierarchical features. In this work, we study the learning of hierarchical polynomials of \textit{multiple nonlinear features} using three-layer neural…
We consider the problem of learning a classifier from observed functional data. Here, each data-point takes the form of a single time-series and contains numerous features. Assuming that each such series comes with a binary label, the…
The purpose of this report is in examining the generalization performance of Support Vector Machines (SVM) as a tool for pattern recognition and object classification. The work is motivated by the growing popularity of the method that is…
In this paper we borrow concepts from Information Theory and Statistical Mechanics to perform a pattern recognition procedure on a set of x-ray hazelnut images. We identify two relevant statistical scales, whose ratio affects the…
The amount of information in the form of features and variables avail- able to machine learning algorithms is ever increasing. This can lead to classifiers that are prone to overfitting in high dimensions, high di- mensional models do not…
The proposed feature selection method builds a histogram of the most stable features from random subsets of a training set and ranks the features based on a classifier based cross-validation. This approach reduces the instability of…
This paper analyzes a new regularized learning scheme for high dimensional partially linear support vector machine. The proposed approach consists of an empirical risk and the Lasso-type penalty for linear part, as well as the standard…
The support vector machine (SVM) is a widely used machine learning tool for classification based on statistical learning theory. Given a set of training data, the SVM finds a hyperplane that separates two different classes of data points by…
We propose a randomized algorithm for training Support vector machines(SVMs) on large datasets. By using ideas from Random projections we show that the combinatorial dimension of SVMs is $O({log} n)$ with high probability. This estimate of…
Support Vector Machines (SVMs) with various kernels have played dominant role in machine learning for many years, finding numerous applications. Although they have many attractive features interpretation of their solutions is quite…
Much as replacing hand-designed features with learned functions has revolutionized how we solve perceptual tasks, we believe learned algorithms will transform how we train models. In this work we focus on general-purpose learned optimizers…
Polynomial networks and factorization machines are two recently-proposed models that can efficiently use feature interactions in classification and regression tasks. In this paper, we revisit both models from a unified perspective. Based on…