Related papers: Fast Cross-Polytope Locality-Sensitive Hashing
The current best practice for computing optimal transport (OT) is via entropy regularization and Sinkhorn iterations. This algorithm runs in quadratic time as it requires the full pairwise cost matrix, which is prohibitively expensive for…
Bidirectional Long Short-Term Memory (LSTM) is a special kind of Recurrent Neural Network (RNN) architecture which is designed to model sequences and their long-range dependencies more precisely than RNNs. This paper proposes to use deep…
We present SLASH (Sketched LocAlity Sensitive Hashing), an MPI (Message Passing Interface) based distributed system for approximate similarity search over terabyte scale datasets. SLASH provides a multi-node implementation of the popular…
The Johnson-Lindenstrauss (JL) lemma is a fundamental result in dimensionality reduction, ensuring that any finite set $X \subseteq \mathbb{R}^d$ can be embedded into a lower-dimensional space $\mathbb{R}^k$ while approximately preserving…
Hashing has been widely used for large-scale approximate nearest neighbor search because of its storage and search efficiency. Recent work has found that deep supervised hashing can significantly outperform non-deep supervised hashing in…
Consider the problem of minimizing an expected logarithmic loss over either the probability simplex or the set of quantum density matrices. This problem includes tasks such as solving the Poisson inverse problem, computing the…
It is well known that, using fast algorithms for polynomial multiplication and division, evaluation of a polynomial $F \in \mathbb{C}[x]$ of degree $n$ at $n$ complex-valued points can be done with $\tilde{O}(n)$ exact field operations in…
MinHash and SimHash are the two widely adopted Locality Sensitive Hashing (LSH) algorithms for large-scale data processing applications. Deciding which LSH to use for a particular problem at hand is an important question, which has no clear…
We give two different and simple constructions for dimensionality reduction in $\ell_2$ via linear mappings that are sparse: only an $O(\varepsilon)$-fraction of entries in each column of our embedding matrices are non-zero to achieve…
Recently, learning to hash has been widely studied for image retrieval thanks to the computation and storage efficiency of binary codes. For most existing learning to hash methods, sufficient training images are required and used to learn…
For every fixed constant $\alpha > 0$, we design an algorithm for computing the $k$-sparse Walsh-Hadamard transform of an $N$-dimensional vector $x \in \mathbb{R}^N$ in time $k^{1+\alpha} (\log N)^{O(1)}$. Specifically, the algorithm is…
This paper concerns the performance of the LASSO (also knows as basis pursuit denoising) for recovering sparse signals from undersampled, randomized, noisy measurements. We consider the recovery of the signal $x_o \in \mathbb{R}^N$ from $n$…
In Linear Programming (LP) decoding of a Low-Density-Parity-Check (LDPC) code one minimizes a linear functional, with coefficients related to log-likelihood ratios, over a relaxation of the polytope spanned by the codewords \cite{03FWK}. In…
We introduce an adaptive output-sensitive Metropolis-Hastings algorithm for probabilistic models expressed as programs, Adaptive Lightweight Metropolis-Hastings (AdLMH). The algorithm extends Lightweight Metropolis-Hastings (LMH) by…
For a set $X$ of $N$ points in $\mathbb{R}^D$, the Johnson-Lindenstrauss lemma provides random linear maps that approximately preserve all pairwise distances in $X$ -- up to multiplicative error $(1\pm \epsilon)$ with high probability --…
We propose a communication and computation efficient second-order method for distributed optimization. For each iteration, our method only requires $\mathcal{O}(d)$ communication complexity, where $d$ is the problem dimension. We also…
Approximate nearest neighbour (ANN) search is an essential component of search engines, recommendation systems, etc. Many recent works focus on learning-based data-distribution-dependent hashing and achieve good retrieval performance.…
A new, fast second-order method is proposed that achieves the optimal $\mathcal{O}\left(|\log(\epsilon)|\epsilon^{-3/2}\right)$ complexity to obtain first-order $\epsilon$-stationary points. Crucially, this is deduced without assuming the…
Non-asymptotic convergence analysis of quasi-Newton methods has gained attention with a landmark result establishing an explicit local superlinear rate of O$((1/\sqrt{t})^t)$. The methods that obtain this rate, however, exhibit a well-known…
We study the problem of computationally efficient robust estimation of the covariance/scatter matrix of elliptical distributions -- that is, affine transformations of spherically symmetric distributions -- under the strong contamination…