Random binning features, introduced in the seminal paper of Rahimi and Recht (2007), are an efficient method for approximating a kernel matrix using locality sensitive hashing. Random binning features provide a very simple and efficient way of approximating the Laplace kernel but unfortunately do not apply to many important classes of kernels, notably ones that generate smooth Gaussian processes, such as the Gaussian kernel and Matern kernel. In this paper, we introduce a simple weighted version of random binning features and show that the corresponding kernel function generates Gaussian processes of any desired smoothness. We show that our weighted random binning features provide a spectral approximation to the corresponding kernel matrix, leading to efficient algorithms for kernel ridge regression. Experiments on large scale regression datasets show that our method outperforms the accuracy of random Fourier features method.
The analysis of the compression effects in generative adversarial networks (GANs) after training, i.e. without any fine-tuning, remains an unstudied, albeit important, topic with the increasing trend of their computation and memory requirements. While existing works discuss the difficulty of compressing GANs during training, requiring novel methods designed with the instability of GANs training in mind, we show that existing compression methods (namely clipping and quantization) may be directly applied to compress GANs post-training, without any additional changes. High compression levels may …
Department of Applied Mathematics, University of Colorado, Boulder（科罗拉多大学博尔德分校应用数学系）
We discuss the problem of performing similarity search over function spaces. To perform search over such spaces in a reasonable amount of time, we use {\it locality-sensitive hashing} (LSH). We present two methods that allow LSH functions on $\mathbb{R}^N$ to be extended to $L^p$ spaces: one using function approximation in an orthonormal basis, and another using (quasi-)Monte Carlo-style techniques. We use the presented hashing schemes to construct an LSH family for Wasserstein distance over one-dimensional, continuous probability distributions.
Large scale agglomerative clustering is hindered by computational burdens. We propose a novel scheme where exact inter-instance distance calculation is replaced by the Hamming distance between Kernelized Locality-Sensitive Hashing (KLSH) hashed values. This results in a method that drastically decreases computation time. Additionally, we take advantage of certain labeled data points via distance metric learning to achieve a competitive precision and recall comparing to K-Means but in much less computation time.
Recently it was shown that the problem of Maximum Inner Product Search (MIPS) is efficient and it admits provably sub-linear hashing algorithms. Asymmetric transformations before hashing were the key in solving MIPS which was otherwise hard. In the prior work, the authors use asymmetric transformations which convert the problem of approximate MIPS into the problem of approximate near neighbor search which can be efficiently solved using hashing. In this work, we provide a different transformation which converts the problem of approximate MIPS into the problem of approximate cosine similarity s…
Rice University（莱斯大学）；Institute for Advanced Study（高等研究院）；Princeton University（普林斯顿大学）
We present the first provable Least-Squares Value Iteration (LSVI) algorithms that have runtime complexity sublinear in the number of actions. We formulate the value function estimation procedure in value iteration as an approximate maximum inner product search problem and propose a locality sensitive hashing (LSH) [Indyk and Motwani STOC'98, Andoni and Razenshteyn STOC'15, Andoni, Laarhoven, Razenshteyn and Waingarten SODA'17] type data structure to solve this problem with sublinear time complexity. Moreover, we build the connections between the theory of approximate maximum inner product sea…
We propose a new class of data-independent locality-sensitive hashing (LSH) algorithms based on the fruit fly olfactory circuit. The fundamental difference of this approach is that, instead of assigning hashes as dense points in a low dimensional space, hashes are assigned in a high dimensional space, which enhances their separability. We show theoretically and empirically that this new family of hash functions is locality-sensitive and preserves rank similarity for inputs in any `p space. We then analyze different variations on this strategy and show empirically that they outperform existing …
Kernel based methods including Gaussian process regression (GPR) and generally kernel ridge regression (KRR) have been finding increasing use in computational chemistry, including the fitting of potential energy surfaces and density functionals in high-dimensional feature spaces. Kernels of the Matern family such as Gaussian-like kernels (basis functions) are often used, which allows imparting them the meaning of covariance functions and formulating GPR as an estimator of the mean of a Gaussian distribution. The notion of locality of the kernel is critical for this interpretation. It is also c…
We present a simple but powerful reinterpretation of kernelized locality-sensitive hashing (KLSH), a general and popular method developed in the vision community for performing approximate nearest-neighbor searches in an arbitrary reproducing kernel Hilbert space (RKHS). Our new perspective is based on viewing the steps of the KLSH algorithm in an appropriately projected space, and has several key theoretical and practical benefits. First, it eliminates the problematic conceptual difficulties that are present in the existing motivation of KLSH. Second, it yields the first formal retrieval perf…
Locality-sensitive hashing converts high-dimensional feature vectors, such as image and speech, into bit arrays and allows high-speed similarity calculation with the Hamming distance. There is a hashing scheme that maps feature vectors to bit arrays depending on the signs of the inner products between feature vectors and the normal vectors of hyperplanes placed in the feature space. This hashing can be seen as a discretization of the feature space by hyperplanes. If labels for data are given, one can determine the hyperplanes by using learning algorithms. However, many proposed learning method…
Computing approximate nearest neighbors in high dimensional spaces is a central problem in large-scale data mining with a wide range of applications in machine learning and data science. A popular and effective technique in computing nearest neighbors approximately is the locality-sensitive hashing (LSH) scheme. In this paper, we aim to develop LSH schemes for distance functions that measure the distance between two probability distributions, particularly for f-divergences as well as a generalization to capture mutual information loss. First, we provide a general framework to design LHS scheme…
Web application security has become a major concern in recent years, as more and more content and services are available online. A useful method for identifying security vulnerabilities is black-box testing, which relies on an automated crawling of web applications. However, crawling Rich Internet Applications (RIAs) is a very challenging task. One of the key obstacles crawlers face is the state similarity problem: how to determine if two client-side states are equivalent. As current methods do not completely solve this problem, a successful scan of many real-world RIAs is still not possible. …
Sister Nibedita Govt. General Degree College for Girls（尼贝迪塔修女女子政府普通学位学院）；Indian Statistical Institute（印度统计研究所）
Single Molecule Real-Time (SMRT) sequencing is a recent advancement of Next Gen technology developed by Pacific Bio (PacBio). It comes with an explosion of long and noisy reads demanding cutting edge research to get most out of it. To deal with the high error probability of SMRT data, a novel contextual Locality Sensitive Hashing (conLSH) based algorithm is proposed in this article, which can effectively align the noisy SMRT reads to the reference genome. Here, sequences are hashed together based not only on their closeness, but also on similarity of context. The algorithm has $\mathcal{O}(n^{…
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 bidirectional LSTM for sequence modeling as an approach to perform locality-sensitive hashing (LSH)-based sequence alignment. In particular, we use the deep bidirectional LSTM to learn features of LSH. The obtained LSH is then can be utilized to perform sequence alignment. We demonstrate the feasibility of the modeling sequences using the proposed LSTM-based m…
We present PSEUDo, an adaptive feature learning technique for exploring visual patterns in multi-track sequential data. Our approach is designed with the primary focus to overcome the uneconomic retraining requirements and inflexible representation learning in current deep learning-based systems. Multi-track time series data are generated on an unprecedented scale due to increased sensors and data storage. These datasets hold valuable patterns, like in neuromarketing, where researchers try to link patterns in multivariate sequential data from physiological sensors to the purchase behavior of p…
Rochester Institute of Technology（罗切斯特理工学院）；Massachusetts Institute of Technology（麻省理工学院）；Philips Research North America（飞利浦北美研究院）
Timely prediction of clinically critical events in Intensive Care Unit (ICU) is important for improving care and survival rate. Most of the existing approaches are based on the application of various classification methods on explicitly extracted statistical features from vital signals. In this work, we propose to eliminate the high cost of engineering hand-crafted features from multivariate time-series of physiologic signals by learning their representation with a sequence-to-sequence auto-encoder. We then propose to hash the learned representations to enable signal similarity assessment for …
Institute of Physics（物理研究所）；École Polytechnique Fédérale de Lausanne（洛桑联邦理工学院）
Convolutional neural networks perform a local and translationally-invariant treatment of the data: quantifying which of these two aspects is central to their success remains a challenge. We study this problem within a teacher-student framework for kernel regression, using `convolutional' kernels inspired by the neural tangent kernel of simple convolutional architectures of given filter size. Using heuristic methods from physics, we find in the ridgeless case that locality is key in determining the learning curve exponent $β$ (that relates the test error $ε_t\sim P^{-β}$ to the size of the trai…
Entity resolution seeks to merge databases as to remove duplicate entries where unique identifiers are typically unknown. We review modern blocking approaches for entity resolution, focusing on those based upon locality sensitive hashing (LSH). First, we introduce $k$-means locality sensitive hashing (KLSH), which is based upon the information retrieval literature and clusters similar records into blocks using a vector-space representation and projections. Second, we introduce a subquadratic variant of LSH to the literature, known as Densified One Permutation Hashing (DOPH). Third, we propose …
The probability Jaccard similarity was recently proposed as a natural generalization of the Jaccard similarity to measure the proximity of sets whose elements are associated with relative frequencies or probabilities. In combination with a hash algorithm that maps those weighted sets to compact signatures which allow fast estimation of pairwise similarities, it constitutes a valuable method for big data applications such as near-duplicate detection, nearest neighbor search, or clustering. This paper introduces a class of one-pass locality-sensitive hash algorithms that are orders of magnitude …
Anomaly detection is one of the frequent and important subroutines deployed in large-scale data processing systems. Even being a well-studied topic, existing techniques for unsupervised anomaly detection require storing significant amounts of data, which is prohibitive from memory and latency perspective. In the big-data world existing methods fail to address the new set of memory and latency constraints. In this paper, we propose ACE (Arrays of (locality-sensitive) Count Estimators) algorithm that can be 60x faster than the ELKI package~\cite{DBLP:conf/ssd/AchtertBKSZ09}, which has the fastes…
Large-scale regression problems where both the number of variables, $p$, and the number of observations, $n$, may be large and in the order of millions or more, are becoming increasingly more common. Typically the data are sparse: only a fraction of a percent of the entries in the design matrix are non-zero. Nevertheless, often the only computationally feasible approach is to perform dimension reduction to obtain a new design matrix with far fewer columns and then work with this compressed data. $b$-bit min-wise hashing (Li and Konig, 2011) is a promising dimension reduction scheme for sparse …
