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no code implementations • 2 Oct 2021 • Wasim Huleihel, Arya Mazumdar, Soumyabrata Pal

Specifically, we show that any (possibly randomized) algorithm must make $\mathsf{Q} = \Omega(\frac{n^2}{k^2\chi^4(p||q)}\log^2n)$ adaptive queries (on expectation) to the adjacency matrix of the graph to detect the planted subgraph with probability more than $1/2$, where $\chi^2(p||q)$ is the Chi-Square distance.

no code implementations • 2 Sep 2021 • Sami Davies, Arya Mazumdar, Soumyabrata Pal, Cyrus Rashtchian

Mixtures of high dimensional Gaussian distributions have been studied extensively in statistics and learning theory.

no code implementations • 19 Jul 2021 • Arya Mazumdar, Soumyabrata Pal

With universality, it is known that $\tilde{\Theta}(k^2)$ 1bCS measurements are necessary and sufficient for support recovery (where $k$ denotes the sparsity).

no code implementations • NeurIPS 2021 • Venkata Gandikota, Arya Mazumdar, Soumyabrata Pal

In this work, we study the number of measurements sufficient for recovering the supports of all the component vectors in a mixture in both these models.

1 code implementation • NeurIPS 2021 • Wasim Huleihel, Arya Mazumdar, Soumyabrata Pal

In particular, we provide algorithms for fuzzy clustering in this setting that asks $O(\mathsf{poly}(k)\log n)$ similarity queries and run with polynomial-time-complexity, where $n$ is the number of items.

no code implementations • 17 Mar 2021 • Avishek Ghosh, Raj Kumar Maity, Arya Mazumdar, Kannan Ramchandran

Furthermore, our algorithm resists the presence of Byzantine machines, which may create \emph{fake local minima} near the saddle points of the loss function, also known as saddle-point attack.

1 code implementation • 9 Dec 2020 • Nishant Yadav, Rajat Sen, Daniel N. Hill, Arya Mazumdar, Inderjit S. Dhillon

Previous queries in the user session can provide useful context for the user's intent and can be leveraged to suggest auto-completions that are more relevant while adhering to the user's prefix.

no code implementations • NeurIPS 2020 • Venkata Gandikota, Arya Mazumdar, Soumyabrata Pal

We look at a hitherto unstudied problem of query complexity upper bound of recovering all the hyperplanes, especially for the case when the hyperplanes are sparse.

no code implementations • ICML 2020 • Arya Mazumdar, Soumyabrata Pal

Mixture of linear regressions is a popular learning theoretic model that is used widely to represent heterogeneous data.

1 code implementation • NeurIPS 2020 • Shashanka Ubaru, Sanjeeb Dash, Arya Mazumdar, Oktay Gunluk

We then present a hierarchical partitioning approach that exploits the label hierarchy in large scale problems to divide up the large label space and create smaller sub-problems, which can then be solved independently via the grouping approach.

no code implementations • NeurIPS 2020 • Avishek Ghosh, Raj Kumar Maity, Arya Mazumdar

We develop a distributed second order optimization algorithm that is communication-efficient as well as robust against Byzantine failures of the worker machines.

no code implementations • 20 Feb 2020 • Venkata Gandikota, Arya Mazumdar, Ankit Singh Rawat

In this paper, we present distributed generalized clustering algorithms that can handle large scale data across multiple machines in spite of straggling or unreliable machines.

no code implementations • 19 Jan 2020 • Akshay Krishnamurthy, Arya Mazumdar, Andrew Mcgregor, Soumyabrata Pal

Our second approach uses algebraic and combinatorial tools and applies to binomial mixtures with shared trial parameter $N$ and differing success parameters, as well as to mixtures of geometric distributions.

no code implementations • NeurIPS 2019 • Akshay Krishnamurthy, Arya Mazumdar, Andrew Mcgregor, Soumyabrata Pal

Ourtechniques are quite different from those in the previous work: for the noiselesscase, we rely on a property of sparse polynomials and for the noisy case, we providenew connections to learning Gaussian mixtures and use ideas from the theory of

no code implementations • 21 Nov 2019 • Avishek Ghosh, Raj Kumar Maity, Swanand Kadhe, Arya Mazumdar, Kannan Ramchandran

Moreover, we analyze the compressed gradient descent algorithm with error feedback (proposed in \cite{errorfeed}) in a distributed setting and in the presence of Byzantine worker machines.

no code implementations • 18 Nov 2019 • Venkata Gandikota, Daniel Kane, Raj Kumar Maity, Arya Mazumdar

In this work, we present a family of vector quantization schemes \emph{vqSGD} (Vector-Quantized Stochastic Gradient Descent) that provide an asymptotic reduction in the communication cost with convergence guarantees in first-order distributed optimization.

no code implementations • 30 Oct 2019 • Akshay Krishnamurthy, Arya Mazumdar, Andrew Mcgregor, Soumyabrata Pal

In the problem of learning mixtures of linear regressions, the goal is to learn a collection of signal vectors from a sequence of (possibly noisy) linear measurements, where each measurement is evaluated on an unknown signal drawn uniformly from this collection.

no code implementations • NeurIPS 2019 • Wasim Huleihel, Arya Mazumdar, Muriel Médard, Soumyabrata Pal

In this paper, we look at the more practical scenario of overlapping clusters, and provide upper bounds (with algorithms) on the sufficient number of queries.

no code implementations • NeurIPS Workshop Deep_Invers 2019 • Arya Mazumdar, Ankit Singh Rawat

Rectified linear units, or ReLUs, have become a preferred activation function for artificial neural networks.

no code implementations • 31 Mar 2019 • Arya Mazumdar, Soumyabrata Pal

In this paper, we show that a recently popular model of semi-supervised clustering is equivalent to locally encodable source coding.

no code implementations • 29 Jun 2018 • Raj Kumar Maity, Arya Mazumdar, Soumyabrata Pal

Recently Ermon et al. (2013) pioneered a way to practically compute approximations to large scale counting or discrete integration problems by using random hashes.

no code implementations • 22 May 2018 • Raj Kumar Maity, Ankit Singh Rawat, Arya Mazumdar

We, instead, propose to encode the second-moment of the data with a low density parity-check (LDPC) code.

no code implementations • 12 Apr 2018 • Sainyam Galhotra, Arya Mazumdar, Soumyabrata Pal, Barna Saha

Our next contribution is in using the connectivity of random annulus graphs to provide necessary and sufficient conditions for efficient recovery of communities for {\em the geometric block model} (GBM).

no code implementations • 12 Mar 2018 • Arya Mazumdar, Ankit Singh Rawat

Given a set of observation vectors $\mathbf{y}^i \in \mathbb{R}^d, i =1, 2, \dots , n$, we aim to recover $d\times k$ matrix $A$ and the latent vectors $\{\mathbf{c}^i\} \subset \mathbb{R}^k$ under the model $\mathbf{y}^i = \mathrm{ReLU}(A\mathbf{c}^i +\mathbf{b})$, where $\mathbf{b}\in \mathbb{R}^d$ is a random bias.

no code implementations • NeurIPS 2017 • Arya Mazumdar, Soumyabrata Pal

In this paper, we show that a recently popular model of semisupervised clustering is equivalent to locally encodable source coding.

no code implementations • 16 Sep 2017 • Sainyam Galhotra, Arya Mazumdar, Soumyabrata Pal, Barna Saha

To capture the inherent geometric features of many community detection problems, we propose to use a new random graph model of communities that we call a Geometric Block Model.

no code implementations • ICML 2017 • Shashanka Ubaru, Arya Mazumdar

In this work, we propose a novel approach based on group testing to solve such large multilabel classification problems with sparse label vectors.

no code implementations • NeurIPS 2017 • Arya Mazumdar, Barna Saha

A natural noisy model is where similarity values are drawn independently from some arbitrary probability distribution $f_+$ when the underlying pair of elements belong to the same cluster, and from some $f_-$ otherwise.

no code implementations • NeurIPS 2017 • Arya Mazumdar, Barna Saha

In this paper, we provide the first information theoretic lower bound on the number of queries for clustering with noisy oracle in both situations.

no code implementations • 3 Feb 2017 • Arya Mazumdar, Barna Saha

Entity resolution (ER) is the task of identifying all records in a database that refer to the same underlying entity, and are therefore duplicates of each other.

no code implementations • 28 Jan 2017 • Pan Li, Arya Mazumdar, Olgica Milenkovic

We propose a novel rank aggregation method based on converting permutations into their corresponding Lehmer codes or other subdiagonal images.

no code implementations • 29 Nov 2016 • Arya Mazumdar, Ankit Singh Rawat

Designing an associative memory requires addressing two main tasks: 1) learning phase: given a dataset, learn a concise representation of the dataset in the form of a graphical model (or a neural network), 2) recall phase: given a noisy version of a message vector from the dataset, output the correct message vector via a neurally feasible algorithm over the network learnt during the learning phase.

no code implementations • 7 Apr 2016 • Arya Mazumdar, Barna Saha

A major contribution of this paper is to reduce the query complexity to linear or even sublinear in $n$ when mild side information is provided by a machine, and even in presence of crowd errors which are not correctable via resampling.

no code implementations • 30 Dec 2015 • Shashanka Ubaru, Arya Mazumdar, Yousef Saad

In this paper, we show how matrices from error correcting codes can be used to find such low rank approximations and matrix decompositions, and extend the framework to linear least squares regression problems.

no code implementations • NeurIPS 2015 • Arya Mazumdar, Ankit Singh Rawat

An associative memory is a structure learned from a dataset $\mathcal{M}$ of vectors (signals) in a way such that, given a noisy version of one of the vectors as input, the nearest valid vector from $\mathcal{M}$ (nearest neighbor) is provided as output, preferably via a fast iterative algorithm.

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