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no code implementations • 11 Mar 2023 • Abhishek Sinha, Ativ Joshi, Rajarshi Bhattacharjee, Cameron Musco, Mohammad Hajiesmaili

The objective is to allocate resources equitably among several agents in an online fashion so that the difference of the aggregate $\alpha$-fair utilities of the agents between an optimal static clairvoyant allocation and that of the online policy grows sub-linearly with time.

1 code implementation • 12 Oct 2022 • Raghavendra Addanki, David Arbour, Tung Mai, Cameron Musco, Anup Rao

In particular, we study sample-constrained treatment effect estimation, where we must select a subset of $s \ll n$ individuals from the population to experiment on.

no code implementations • 30 Sep 2022 • Sudhanshu Chanpuriya, Ryan A. Rossi, Sungchul Kim, Tong Yu, Jane Hoffswell, Nedim Lipka, Shunan Guo, Cameron Musco

We present a simple method that avoids both shortcomings: construct the line graph of the network, which includes a node for each interaction, and weigh the edges of this graph based on the difference in time between interactions.

no code implementations • 8 Feb 2022 • Sudhanshu Chanpuriya, Cameron Musco

Like SGC, ASGC is not a deep model, and hence is fast, scalable, and interpretable; further, we can prove performance guarantees on natural synthetic data models.

1 code implementation • 17 Dec 2021 • Archan Ray, Nicholas Monath, Andrew McCallum, Cameron Musco

Approximation methods reduce this quadratic complexity, often by using a small subset of exactly computed similarities to approximate the remainder of the complete pairwise similarity matrix.

no code implementations • 9 Nov 2021 • Cameron Musco, Christopher Musco, David P. Woodruff, Taisuke Yasuda

By combining this with our techniques for $\ell_p$ regression, we obtain an active regression algorithm making $\tilde O(d^{1+\max\{1, p/2\}}/\mathrm{poly}(\epsilon))$ queries for such loss functions, including the Tukey and Huber losses, answering another question of [CD21].

no code implementations • 4 Nov 2021 • Sudhanshu Chanpuriya, Ryan A. Rossi, Anup Rao, Tung Mai, Nedim Lipka, Zhao Song, Cameron Musco

Many models for undirected graphs are based on factorizing the graph's adjacency matrix; these models find a vector representation of each node such that the predicted probability of a link between two nodes increases with the similarity (dot product) of their associated vectors.

1 code implementation • NeurIPS 2021 • Sudhanshu Chanpuriya, Cameron Musco, Konstantinos Sotiropoulos, Charalampos E. Tsourakakis

We prove that subject to a bounded overlap condition, which ensures that the model does not simply memorize a single graph, edge independent models are inherently limited in their ability to generate graphs with high triangle and other subgraph densities.

no code implementations • NeurIPS 2021 • Tung Mai, Anup B. Rao, Cameron Musco

It also does not depend on the specific loss function, so a single coreset can be used in multiple training scenarios.

1 code implementation • 17 Feb 2021 • Sudhanshu Chanpuriya, Cameron Musco, Konstantinos Sotiropoulos, Charalampos E. Tsourakakis

Our findings are a step towards a more rigorous understanding of exactly what information embeddings encode about the input graph, and why this information is useful for learning tasks.

no code implementations • 16 Feb 2021 • Arturs Backurs, Piotr Indyk, Cameron Musco, Tal Wagner

In particular, we consider estimating the sum of kernel matrix entries, along with its top eigenvalue and eigenvector.

no code implementations • 28 Jan 2021 • Mohit Yadav, Daniel Sheldon, Cameron Musco

Structured kernel interpolation (SKI) is among the most scalable methods: by placing inducing points on a dense grid and using structured matrix algebra, SKI achieves per-iteration time of O(n + m log m) for approximate inference.

no code implementations • 27 Dec 2020 • Raghavendra Addanki, Andrew Mcgregor, Cameron Musco

Our goal is to recover the directions of all causal or ancestral relations in $G$, via a minimum cost set of interventions.

no code implementations • 19 Nov 2020 • Raj Kumar Maity, Cameron Musco

Such matrices generalize Toeplitz and circulant covariance matrices and are widely applied in signal processing applications, where the covariance between two measurements depends on the (shortest path) distance between them in time or space.

no code implementations • 20 Oct 2020 • Anant Raj, Cameron Musco, Lester Mackey, Nicolo Fusi

Model selection requires repeatedly evaluating models on a given dataset and measuring their relative performances.

1 code implementation • 19 Oct 2020 • Raphael A. Meyer, Cameron Musco, Christopher Musco, David P. Woodruff

This improves on the ubiquitous Hutchinson's estimator, which requires $O(1/\epsilon^2)$ matrix-vector products.

no code implementations • 5 Oct 2020 • Aarshvi Gajjar, Cameron Musco

We consider low-distortion embeddings for subspaces under \emph{entrywise nonlinear transformations}.

no code implementations • NeurIPS 2020 • Tamás Erdélyi, Cameron Musco, Christopher Musco

Bounding Fourier sparse leverage scores under various measures is of pure mathematical interest in approximation theory, and our work extends existing results for the uniform measure [Erd17, CP19a].

1 code implementation • NeurIPS 2020 • Sudhanshu Chanpuriya, Cameron Musco, Konstantinos Sotiropoulos, Charalampos E. Tsourakakis

In this work we show that the results of Seshadhri et al. are intimately connected to the model they use rather than the low-dimensional structure of complex networks.

1 code implementation • 29 May 2020 • Sudhanshu Chanpuriya, Cameron Musco

We study the objective in the limit as T goes to infinity, which allows us to simplify the expression of Qiu et al. We prove that this limiting objective corresponds to factoring a simple transformation of the pseudoinverse of the graph Laplacian, linking DeepWalk to extensive prior work in spectral graph embeddings.

no code implementations • ICML 2020 • Raghavendra Addanki, Shiva Prasad Kasiviswanathan, Andrew Mcgregor, Cameron Musco

We consider recovering a causal graph in presence of latent variables, where we seek to minimize the cost of interventions used in the recovery process.

no code implementations • 17 Apr 2020 • Cameron Musco, Christopher Musco

In this note we illustrate how common matrix approximation methods, such as random projection and random sampling, yield projection-cost-preserving sketches, as introduced in [FSS13, CEM+15].

no code implementations • 4 Nov 2019 • Anant Raj, Cameron Musco, Lester Mackey

Unfortunately, sensitivity sampling is difficult to apply since (1) it is unclear how to efficiently compute the sensitivity scores and (2) the sample size required is often impractically large.

no code implementations • NeurIPS 2019 • Nika Haghtalab, Cameron Musco, Bo Waggoner

We aim to understand this fact, taking an axiomatic approach to the design of loss functions for learning distributions.

no code implementations • 14 May 2019 • Yonina C. Eldar, Jerry Li, Cameron Musco, Christopher Musco

In addition to results that hold for any Toeplitz $T$, we further study the important setting when $T$ is close to low-rank, which is often the case in practice.

no code implementations • 26 Apr 2019 • Daniel Alabi, Adam Tauman Kalai, Katrina Ligett, Cameron Musco, Christos Tzamos, Ellen Vitercik

We present an algorithm that learns to maximally prune the search space on repeated computations, thereby reducing runtime while provably outputting the correct solution each period with high probability.

no code implementations • 25 Apr 2019 • Nancy Lynch, Cameron Musco, Merav Parter

We provide efficient constructions of WTA circuits in our stochastic spiking neural network model, as well as lower bounds in terms of the number of auxiliary neurons required to drive convergence to WTA in a given number of steps.

no code implementations • 22 Apr 2019 • Cameron Musco, Christopher Musco, David P. Woodruff

In particular, for rank $k' > k$ depending on the $public\ coin\ partition\ number$ of $W$, the heuristic outputs rank-$k'$ $L$ with cost$(L) \leq OPT + \epsilon \|A\|_F^2$.

no code implementations • 20 Dec 2018 • Haim Avron, Michael Kapralov, Cameron Musco, Christopher Musco, Ameya Velingker, Amir Zandieh

We formalize this intuition by showing that, roughly, a continuous signal from a given class can be approximately reconstructed using a number of samples proportional to the *statistical dimension* of the allowed power spectrum of that class.

1 code implementation • NeurIPS 2018 • Jeremy Hoskins, Cameron Musco, Christopher Musco, Babis Tsourakakis

In this work we consider a privacy threat to a social network in which an attacker has access to a subset of random walk-based node similarities, such as effective resistances (i. e., commute times) or personalized PageRank scores.

no code implementations • 12 Aug 2018 • Nancy Lynch, Cameron Musco

We define two operators on SNNs: a $composition$ $operator$, which supports modeling of SNNs as combinations of smaller SNNs, and a $hiding$ $operator$, which reclassifies some output behavior of an SNN as internal.

no code implementations • ICML 2017 • Haim Avron, Michael Kapralov, Cameron Musco, Christopher Musco, Ameya Velingker, Amir Zandieh

Qualitatively, our results are twofold: on the one hand, we show that random Fourier feature approximation can provably speed up kernel ridge regression under reasonable assumptions.

1 code implementation • 23 Jan 2018 • Jeremy G. Hoskins, Cameron Musco, Christopher Musco, Charalampos E. Tsourakakis

In this work we consider a privacy threat to a social network in which an attacker has access to a subset of random walk-based node similarities, such as effective resistances (i. e., commute times) or personalized PageRank scores.

3 code implementations • 28 Dec 2017 • Cameron Musco, Christopher Musco, Charalampos E. Tsourakakis

We perform an empirical study of our proposed methods on synthetic and real-world data that verify their value as mining tools to better understand the trade-off between of disagreement and polarization.

no code implementations • NeurIPS 2017 • Cameron Musco, Christopher Musco

We give the first algorithm for kernel Nystrom approximation that runs in linear time in the number of training points and is provably accurate for all kernel matrices, without dependence on regularity or incoherence conditions.

no code implementations • NeurIPS 2017 • Cameron Musco, David P. Woodruff

Low-rank approximation is a common tool used to accelerate kernel methods: the $n \times n$ kernel matrix $K$ is approximated via a rank-$k$ matrix $\tilde K$ which can be stored in much less space and processed more quickly.

1 code implementation • 25 Aug 2017 • Cameron Musco, Christopher Musco, Aaron Sidford

In exact arithmetic, the method's error after $k$ iterations is bounded by the error of the best degree-$k$ polynomial uniformly approximating $f(x)$ on the range $[\lambda_{min}(A), \lambda_{max}(A)]$.

Data Structures and Algorithms Numerical Analysis

no code implementations • 5 Jun 2017 • Nancy Lynch, Cameron Musco, Merav Parter

Randomization allows us to solve this task with a very compact network, using $O \left (\frac{\sqrt{n}\log n}{\epsilon}\right)$ auxiliary neurons, which is sublinear in the input size.

no code implementations • 13 Apr 2017 • Cameron Musco, Praneeth Netrapalli, Aaron Sidford, Shashanka Ubaru, David P. Woodruff

We thus effectively compute a histogram of the spectrum, which can stand in for the true singular values in many applications.

no code implementations • 11 Apr 2017 • Cameron Musco, David P. Woodruff

We show how to compute a relative-error low-rank approximation to any positive semidefinite (PSD) matrix in sublinear time, i. e., for any $n \times n$ PSD matrix $A$, in $\tilde O(n \cdot poly(k/\epsilon))$ time we output a rank-$k$ matrix $B$, in factored form, for which $\|A-B\|_F^2 \leq (1+\epsilon)\|A-A_k\|_F^2$, where $A_k$ is the best rank-$k$ approximation to $A$.

no code implementations • 6 Oct 2016 • Nancy Lynch, Cameron Musco, Merav Parter

In this paper, we focus on the important `winner-take-all' (WTA) problem, which is analogous to a neural leader election unit: a network consisting of $n$ input neurons and $n$ corresponding output neurons must converge to a state in which a single output corresponding to a firing input (the `winner') fires, while all other outputs remain silent.

no code implementations • 26 May 2016 • Dan Garber, Elad Hazan, Chi Jin, Sham M. Kakade, Cameron Musco, Praneeth Netrapalli, Aaron Sidford

We give faster algorithms and improved sample complexities for estimating the top eigenvector of a matrix $\Sigma$ -- i. e. computing a unit vector $x$ such that $x^T \Sigma x \ge (1-\epsilon)\lambda_1(\Sigma)$: Offline Eigenvector Estimation: Given an explicit $A \in \mathbb{R}^{n \times d}$ with $\Sigma = A^TA$, we show how to compute an $\epsilon$ approximate top eigenvector in time $\tilde O([nnz(A) + \frac{d*sr(A)}{gap^2} ]* \log 1/\epsilon )$ and $\tilde O([\frac{nnz(A)^{3/4} (d*sr(A))^{1/4}}{\sqrt{gap}} ] * \log 1/\epsilon )$.

2 code implementations • 24 May 2016 • Cameron Musco, Christopher Musco

We give the first algorithm for kernel Nystr\"om approximation that runs in *linear time in the number of training points* and is provably accurate for all kernel matrices, without dependence on regularity or incoherence conditions.

no code implementations • 22 Feb 2016 • Roy Frostig, Cameron Musco, Christopher Musco, Aaron Sidford

To achieve our results, we first observe that ridge regression can be used to obtain a "smooth projection" onto the top principal components.

no code implementations • 23 Nov 2015 • Michael B. Cohen, Cameron Musco, Christopher Musco

Our method is based on a recursive sampling scheme for computing a representative subset of $A$'s columns, which is then used to find a low-rank approximation.

no code implementations • 29 Oct 2015 • Chi Jin, Sham M. Kakade, Cameron Musco, Praneeth Netrapalli, Aaron Sidford

Combining our algorithm with previous work to initialize $x_0$, we obtain a number of improved sample complexity and runtime results.

no code implementations • NeurIPS 2015 • Cameron Musco, Christopher Musco

We give the first provable runtime improvement on Simultaneous Iteration: a simple randomized block Krylov method, closely related to the classic Block Lanczos algorithm, gives the same guarantees in just $\tilde{O}(1/\sqrt{\epsilon})$ iterations and performs substantially better experimentally.

no code implementations • 24 Oct 2014 • Michael B. Cohen, Sam Elder, Cameron Musco, Christopher Musco, Madalina Persu

We show how to approximate a data matrix $\mathbf{A}$ with a much smaller sketch $\mathbf{\tilde A}$ that can be used to solve a general class of constrained k-rank approximation problems to within $(1+\epsilon)$ error.

no code implementations • 21 Aug 2014 • Michael B. Cohen, Yin Tat Lee, Cameron Musco, Christopher Musco, Richard Peng, Aaron Sidford

In addition to an improved understanding of uniform sampling, our main proof introduces a structural result of independent interest: we show that every matrix can be made to have low coherence by reweighting a small subset of its rows.

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