Search Results for author: Hrushikesh Mhaskar

Found 13 papers, 0 papers with code

Tractability of approximation by general shallow networks

no code implementations7 Aug 2023 Hrushikesh Mhaskar, Tong Mao

In this paper, we present a sharper version of the results in the paper Dimension independent bounds for general shallow networks; Neural Networks, \textbf{123} (2020), 142-152.

Approximation by non-symmetric networks for cross-domain learning

no code implementations6 May 2023 Hrushikesh Mhaskar

Motivated by applications such as invariant learning, transfer learning, and synthetic aperture radar imaging, we initiate in this paper a general approach to study the approximation capabilities of kernel based networks using non-symmetric kernels.

Transfer Learning Translation

Encoding of data sets and algorithms

no code implementations2 Mar 2023 Katarina Doctor, Tong Mao, Hrushikesh Mhaskar

This involves creating a grid on the hypothetical spaces of data sets and algorithms so as to identify a finite set of probability distributions from which the data sets are sampled and a finite set of algorithms.

Local approximation of operators

no code implementations13 Feb 2022 Hrushikesh Mhaskar

We study different smoothness classes for the operators, and also propose a method for approximation of $\mathcal{F}(F)$ using only information in a small neighborhood of $F$, resulting in an effective reduction in the number of parameters involved.

Time Series Analysis Uncertainty Quantification

A manifold learning approach for gesture recognition from micro-Doppler radar measurements

no code implementations4 Oct 2021 Eric Mason, Hrushikesh Mhaskar, Adam Guo

To demonstrate the fact that our methods are agnostic to the domain knowledge, we examine the classification problem in a simple video data set.

Gesture Recognition

Kernel distance measures for time series, random fields and other structured data

no code implementations29 Sep 2021 Srinjoy Das, Hrushikesh Mhaskar, Alexander Cloninger

Applications are demonstrated for clustering of synthetic and real-life time series and image data, and the performance of kdiff is compared to competing distance measures for clustering.

Clustering Time Series +1

Cautious Active Clustering

no code implementations3 Aug 2020 Alexander Cloninger, Hrushikesh Mhaskar

Our approach is to consider the unknown probability measure as a convex combination of the conditional probabilities for each class.

Classification Clustering +1

A direct approach for function approximation on data defined manifolds

no code implementations1 Aug 2019 Hrushikesh Mhaskar

Function approximation on this unknown manifold is then a two stage procedure: first, one approximates the Laplace-Beltrami operator (and its eigen-decomposition) on this manifold using a graph Laplacian, and next, approximates the target function using the eigen-functions.

An analysis of training and generalization errors in shallow and deep networks

no code implementations17 Feb 2018 Hrushikesh Mhaskar, Tomaso Poggio

We argue that the minimal expected value of the square loss is inappropriate to measure the generalization error in approximation of compositional functions in order to take full advantage of the compositional structure.

Theory of Deep Learning III: explaining the non-overfitting puzzle

no code implementations30 Dec 2017 Tomaso Poggio, Kenji Kawaguchi, Qianli Liao, Brando Miranda, Lorenzo Rosasco, Xavier Boix, Jack Hidary, Hrushikesh Mhaskar

In this note, we show that the dynamics associated to gradient descent minimization of nonlinear networks is topologically equivalent, near the asymptotically stable minima of the empirical error, to linear gradient system in a quadratic potential with a degenerate (for square loss) or almost degenerate (for logistic or crossentropy loss) Hessian.

General Classification

Why and When Can Deep -- but Not Shallow -- Networks Avoid the Curse of Dimensionality: a Review

no code implementations2 Nov 2016 Tomaso Poggio, Hrushikesh Mhaskar, Lorenzo Rosasco, Brando Miranda, Qianli Liao

The paper characterizes classes of functions for which deep learning can be exponentially better than shallow learning.

Deep vs. shallow networks : An approximation theory perspective

no code implementations10 Aug 2016 Hrushikesh Mhaskar, Tomaso Poggio

The paper announces new results for a non-smooth activation function - the ReLU function - used in present-day neural networks, as well as for the Gaussian networks.

Learning Functions: When Is Deep Better Than Shallow

no code implementations3 Mar 2016 Hrushikesh Mhaskar, Qianli Liao, Tomaso Poggio

While the universal approximation property holds both for hierarchical and shallow networks, we prove that deep (hierarchical) networks can approximate the class of compositional functions with the same accuracy as shallow networks but with exponentially lower number of training parameters as well as VC-dimension.

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