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no code implementations • 12 Mar 2023 • Andrea Agazzi, Jianfeng Lu, Sayan Mukherjee

We analyze Elman-type Recurrent Reural Networks (RNNs) and their training in the mean-field regime.

no code implementations • 22 Jun 2022 • Michele Caprio, Sayan Mukherjee

We state concentration inequalities for the output of the hidden layers of a stochastic deep neural network (SDNN), as well as for the output of the whole SDNN.

no code implementations • 15 Dec 2021 • Xizhi Liu, Sayan Mukherjee

Given a partition of a graph into connected components, the membership oracle asserts whether any two vertices of the graph lie in the same component or not.

no code implementations • 2 Aug 2021 • Ramin Bashizade, Xiangyu Zhang, Sayan Mukherjee, Alvin R. Lebeck

In this paper, we propose a high-throughput accelerator for Markov Random Field (MRF) inference, a powerful model for representing a wide range of applications, using MCMC with Gibbs sampling.

1 code implementation • 31 May 2021 • Anna K. Yanchenko, Mohammadreza Soltani, Robert J. Ravier, Sayan Mukherjee, Vahid Tarokh

In this work, we instead take the perspective of relating deep features to well-studied, hand-crafted features that are meaningful for the application of interest.

no code implementations • 14 Dec 2020 • Ziyang Ding, Sayan Mukherjee

Reservoir computing and deep sequential models, on the one hand, have demonstrated efficient, robust, and superior performance in modeling simple and chaotic dynamical systems.

no code implementations • NeurIPS Workshop TDA_and_Beyond 2020 • Mikael Vejdemo-Johansson, Sayan Mukherjee

Multiple hypothesis testing requires a control procedure.

no code implementations • 11 Jun 2020 • Anna K. Yanchenko, Sayan Mukherjee

Stanza strikes a balance between competitive forecasting accuracy and probabilistic, interpretable inference for highly structured time series.

no code implementations • 5 Mar 2020 • Xiangyu Zhang, Ramin Bashizade, Yicheng Wang, Cheng Lyu, Sayan Mukherjee, Alvin R. Lebeck

Applying the framework to guide design space exploration shows that statistical robustness comparable to floating-point software can be achieved by slightly increasing the bit representation, without floating-point hardware requirements.

no code implementations • 27 Oct 2019 • Xiangyu Zhang, Sayan Mukherjee, Alvin R. Lebeck

Although a common approach is to compare the end-point result quality using community-standard benchmarks and metrics, we claim a probabilistic architecture should provide some measure (or guarantee) of statistical robustness.

1 code implementation • 24 Aug 2019 • Samuel I. Berchuck, Felipe A. Medeiros, Sayan Mukherjee

As big spatial data becomes increasingly prevalent, classical spatiotemporal (ST) methods often do not scale well.

no code implementations • 2 Jul 2019 • Zilong Zou, Sayan Mukherjee, Harbir Antil, Wilkins Aquino

To manage the computational cost of propagating increasing numbers of particles through the loss function, we employ a recently developed local reduced basis method to build an efficient surrogate loss function that is used in the Gibbs update formula in place of the true loss.

1 code implementation • 15 Nov 2018 • Weiwei Li, Jan Hannig, Sayan Mukherjee

The problem of dimension reduction is of increasing importance in modern data analysis.

1 code implementation • 12 Mar 2018 • Zilong Tan, Kimberly Roche, Xiang Zhou, Sayan Mukherjee

We provide theoretical guarantees for our learning algorithms, demonstrating the robustness of parameter estimation.

1 code implementation • 21 Feb 2018 • Zilong Tan, Sayan Mukherjee

We propose a representation of Gaussian processes (GPs) based on powers of the integral operator defined by a kernel function, we call these stochastic processes integral Gaussian processes (IGPs).

no code implementations • ICML 2017 • Zilong Tan, Sayan Mukherjee

We present an efficient algorithm for learning mixed membership models when the number of variables p is much larger than the number of hidden components k. This algorithm reduces the computational complexity of state-of-the-art tensor methods, which require decomposing an $O(p^3)$ tensor, to factorizing $O(p/k)$ sub-tensors each of size $O(k^3)$.

1 code implementation • 25 Feb 2017 • Zilong Tan, Sayan Mukherjee

We present an efficient algorithm for learning mixed membership models when the number of variables $p$ is much larger than the number of hidden components $k$.

2 code implementations • 21 Nov 2016 • Lorin Crawford, Anthea Monod, Andrew X. Chen, Sayan Mukherjee, Raúl Rabadán

We introduce a novel statistic, the smooth Euler characteristic transform (SECT), which is designed to integrate shape information into regression models by representing shapes and surfaces as a collection of curves.

Applications

no code implementations • 17 Mar 2016 • Shiwen Zhao, Barbara E. Engelhardt, Sayan Mukherjee, David B. Dunson

We illustrate the utility of our approach on simulated data, comparing results from MELD to alternative methods, and we show the promise of our approach through the application of MELD to several data sets.

1 code implementation • 5 Aug 2015 • Lorin Crawford, Kris C. Wood, Xiang Zhou, Sayan Mukherjee

State-of-the-art methods for genomic selection and association mapping are based on kernel regression and linear models, respectively.

no code implementations • 13 Apr 2015 • Gregory Darnell, Stoyan Georgiev, Sayan Mukherjee, Barbara E. Engelhardt

In this paper we develop an approach for dimension reduction that exploits the assumption of low rank structure in high dimensional data to gain both computational and statistical advantages.

1 code implementation • 11 Nov 2014 • Shiwen Zhao, Chuan Gao, Sayan Mukherjee, Barbara E. Engelhardt

Latent factor models are the canonical statistical tool for exploratory analyses of low-dimensional linear structure for an observation matrix with p features across n samples.

no code implementations • 29 Oct 2013 • Garvesh Raskutti, Sayan Mukherjee

Using this equivalence, it follows that (1) mirror descent is the steepest descent direction along the Riemannian manifold of the exponential family; (2) mirror descent with log-likelihood loss applied to parameter estimation in exponential families asymptotically achieves the classical Cram\'er-Rao lower bound and (3) natural gradient descent for manifolds corresponding to exponential families can be implemented as a first-order method through mirror descent.

no code implementations • 7 Nov 2012 • Stoyan Georgiev, Sayan Mukherjee

Scalability of statistical estimators is of increasing importance in modern applications and dimension reduction is often used to extract relevant information from data.

no code implementations • 18 Dec 2009 • Simón Lunagómez, Sayan Mukherjee, Robert L. Wolpert, Edoardo M. Airoldi

A parametrization of hypergraphs based on the geometry of points in $\mathbf{R}^d$ is developed.

no code implementations • NeurIPS 2008 • Qiang Wu, Sayan Mukherjee, Feng Liang

We developed localized sliced inverse regression for supervised dimension reduction.

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