arXiv subjects

Anshumali Shrivastava

Publications and source records attributed to Anshumali Shrivastava.

At least 91 records · Page 5Linked to original sources

arXiv2020

FourierSAT: A Fourier Expansion-Based Algebraic Framework for Solving Hybrid Boolean Constraints

The Boolean SATisfiability problem (SAT) is of central importance in computer science. Although SAT is known to be NP-complete, progress on the engineering side, especially that of Conflict-Driven Clause Learning (CDCL) and Local Search SAT solvers, has been remarkable. Yet, while SAT solvers aimed at solving industrial-scale benchmarks in Conjunctive Normal Form (CNF) have become quite mature, SAT solvers that are effective on other types of constraints, e.g., cardinality constraints and XORs, are less well studied; a general approach to handling non-CNF constraints is still lacking. In addition, previous work indicated that for specific classes of benchmarks, the running time of extant SAT solvers depends heavily on properties of the formula and details of encoding, instead of the scale of the benchmarks, which adds uncertainty to expectations of running time. To address the issues above, we design FourierSAT, an incomplete SAT solver based on Fourier analysis of Boolean functions, a technique to represent Boolean functions by multilinear polynomials. By such a reduction to continuous optimization, we propose an algebraic framework for solving systems consisting of different types of constraints. The idea is to leverage gradient information to guide the search process in the direction of local improvements. Empirical results demonstrate that FourierSAT is more robust than other solvers on certain classes of benchmarks.

cs.LO↗

arXiv2019

Sub-linear RACE Sketches for Approximate Kernel Density Estimation on Streaming Data

Kernel density estimation is a simple and effective method that lies at the heart of many important machine learning applications. Unfortunately, kernel methods scale poorly for large, high dimensional datasets. Approximate kernel density estimation has a prohibitively high memory and computation cost, especially in the streaming setting. Recent sampling algorithms for high dimensional densities can reduce the computation cost but cannot operate online, while streaming algorithms cannot handle high dimensional datasets due to the curse of dimensionality. We propose RACE, an efficient sketching algorithm for kernel density estimation on high-dimensional streaming data. RACE compresses a set of N high dimensional vectors into a small array of integer counters. This array is sufficient to estimate the kernel density for a large class of kernels. Our sketch is practical to implement and comes with strong theoretical guarantees. We evaluate our method on real-world high-dimensional datasets and show that our sketch achieves 10x better compression compared to competing methods.

cs.DS↗

arXiv2019

Lsh-sampling Breaks the Computation Chicken-and-egg Loop in Adaptive Stochastic Gradient Estimation

Stochastic Gradient Descent or SGD is the most popular optimization algorithm for large-scale problems. SGD estimates the gradient by uniform sampling with sample size one. There have been several other works that suggest faster epoch-wise convergence by using weighted non-uniform sampling for better gradient estimates. Unfortunately, the per-iteration cost of maintaining this adaptive distribution for gradient estimation is more than calculating the full gradient itself, which we call the chicken-and-the-egg loop. As a result, the false impression of faster convergence in iterations, in reality, leads to slower convergence in time. In this paper, we break this barrier by providing the first demonstration of a scheme, Locality sensitive hashing (LSH) sampled Stochastic Gradient Descent (LGD), which leads to superior gradient estimation while keeping the sampling cost per iteration similar to that of the uniform sampling. Such an algorithm is possible due to the sampling view of LSH, which came to light recently. As a consequence of superior and fast estimation, we reduce the running time of all existing gradient descent algorithms, that relies on gradient estimates including Adam, Ada-grad, etc. We demonstrate the effectiveness of our proposal with experiments on linear models as well as the non-linear BERT, which is a recent popular deep learning based language representation model.

cs.LG↗

arXiv2019

Extreme Classification in Log Memory using Count-Min Sketch: A Case Study of Amazon Search with 50M Products

In the last decade, it has been shown that many hard AI tasks, especially in NLP, can be naturally modeled as extreme classification problems leading to improved precision. However, such models are prohibitively expensive to train due to the memory blow-up in the last layer. For example, a reasonable softmax layer for the dataset of interest in this paper can easily reach well beyond 100 billion parameters (>400 GB memory). To alleviate this problem, we present Merged-Average Classifiers via Hashing (MACH), a generic K-classification algorithm where memory provably scales at O(logK) without any strong assumption on the classes. MACH is subtly a count-min sketch structure in disguise, which uses universal hashing to reduce classification with a large number of classes to few embarrassingly parallel and independent classification tasks with a small (constant) number of classes. MACH naturally provides a technique for zero communication model parallelism. We experiment with 6 datasets; some multiclass and some multilabel, and show consistent improvement over respective state-of-the-art baselines. In particular, we train an end-to-end deep classifier on a private product search dataset sampled from Amazon Search Engine with 70 million queries and 49.46 million products. MACH outperforms, by a significant margin,the state-of-the-art extreme classification models deployed on commercial search engines: Parabel and dense embedding models. Our largest model has 6.4 billion parameters and trains in less than 35 hours on a single p3.16x machine. Our training times are 7-10x faster, and our memory footprints are 2-4x smaller than the best baselines. This training time is also significantly lower than the one reported by Google's mixture of experts (MoE) language model on a comparable model size and hardware.

cs.LG↗

arXiv2019

Adaptive Learned Bloom Filter (Ada-BF): Efficient Utilization of the Classifier

Recent work suggests improving the performance of Bloom filter by incorporating a machine learning model as a binary classifier. However, such learned Bloom filter does not take full advantage of the predicted probability scores. We proposed new algorithms that generalize the learned Bloom filter by using the complete spectrum of the scores regions. We proved our algorithms have lower False Positive Rate (FPR) and memory usage compared with the existing approaches to learned Bloom filter. We also demonstrated the improved performance of our algorithms on real-world datasets.

cs.DS↗

arXiv2019

Sub-Linear Privacy-Preserving Near-Neighbor Search

In Near-Neighbor Search (NNS), a new client queries a database (held by a server) for the most similar data (near-neighbors) given a certain similarity metric. The Privacy-Preserving variant (PP-NNS) requires that neither server nor the client shall learn information about the other party's data except what can be inferred from the outcome of NNS. The overwhelming growth in the size of current datasets and the lack of a truly secure server in the online world render the existing solutions impractical; either due to their high computational requirements or non-realistic assumptions which potentially compromise privacy. PP-NNS having query time {\it sub-linear} in the size of the database has been suggested as an open research direction by Li et al. (CCSW'15). In this paper, we provide the first such algorithm, called Secure Locality Sensitive Indexing (SLSI) which has a sub-linear query time and the ability to handle honest-but-curious parties. At the heart of our proposal lies a secure binary embedding scheme generated from a novel probabilistic transformation over locality sensitive hashing family. We provide information theoretic bound for the privacy guarantees and support our theoretical claims using substantial empirical evidence on real-world datasets.

cs.CR↗

arXiv2019

Using Local Experiences for Global Motion Planning

Sampling-based planners are effective in many real-world applications such as robotics manipulation, navigation, and even protein modeling. However, it is often challenging to generate a collision-free path in environments where key areas are hard to sample. In the absence of any prior information, sampling-based planners are forced to explore uniformly or heuristically, which can lead to degraded performance. One way to improve performance is to use prior knowledge of environments to adapt the sampling strategy to the problem at hand. In this work, we decompose the workspace into local primitives, memorizing local experiences by these primitives in the form of local samplers, and store them in a database. We synthesize an efficient global sampler by retrieving local experiences relevant to the given situation. Our method transfers knowledge effectively between diverse environments that share local primitives and speeds up the performance dramatically. Our results show, in terms of solution time, an improvement of multiple orders of magnitude in two traditionally challenging high-dimensional problems compared to state-of-the-art approaches.

cs.RO↗

arXiv2019

Compressing Gradient Optimizers via Count-Sketches

Many popular first-order optimization methods (e.g., Momentum, AdaGrad, Adam) accelerate the convergence rate of deep learning models. However, these algorithms require auxiliary parameters, which cost additional memory proportional to the number of parameters in the model. The problem is becoming more severe as deep learning models continue to grow larger in order to learn from complex, large-scale datasets. Our proposed solution is to maintain a linear sketch to compress the auxiliary variables. We demonstrate that our technique has the same performance as the full-sized baseline, while using significantly less space for the auxiliary variables. Theoretically, we prove that count-sketch optimization maintains the SGD convergence rate, while gracefully reducing memory usage for large-models. On the large-scale 1-Billion Word dataset, we save 25% of the memory used during training (8.6 GB instead of 11.7 GB) by compressing the Adam optimizer in the Embedding and Softmax layers with negligible accuracy and performance loss. For an Amazon extreme classification task with over 49.5 million classes, we also reduce the training time by 38%, by increasing the mini-batch size 3.5x using our count-sketch optimizer.

cs.LG↗

arXiv2019

Better accuracy with quantified privacy: representations learned via reconstructive adversarial network

The remarkable success of machine learning, especially deep learning, has produced a variety of cloud-based services for mobile users. Such services require an end user to send data to the service provider, which presents a serious challenge to end-user privacy. To address this concern, prior works either add noise to the data or send features extracted from the raw data. They struggle to balance between the utility and privacy because added noise reduces utility and raw data can be reconstructed from extracted features. This work represents a methodical departure from prior works: we balance between a measure of privacy and another of utility by leveraging adversarial learning to find a sweeter tradeoff. We design an encoder that optimizes against the reconstruction error (a measure of privacy), adversarially by a Decoder, and the inference accuracy (a measure of utility) by a Classifier. The result is RAN, a novel deep model with a new training algorithm that automatically extracts features for classification that are both private and useful. It turns out that adversarially forcing the extracted features to only conveys the intended information required by classification leads to an implicit regularization leading to better classification accuracy than the original model which completely ignores privacy. Thus, we achieve better privacy with better utility, a surprising possibility in machine learning! We conducted extensive experiments on five popular datasets over four training schemes, and demonstrate the superiority of RAN compared with existing alternatives.

cs.LG↗

arXiv2018

Scaling-up Split-Merge MCMC with Locality Sensitive Sampling (LSS)

Split-Merge MCMC (Monte Carlo Markov Chain) is one of the essential and popular variants of MCMC for problems when an MCMC state consists of an unknown number of components. It is well known that state-of-the-art methods for split-merge MCMC do not scale well. Strategies for rapid mixing requires smart and informative proposals to reduce the rejection rate. However, all known smart proposals involve expensive operations to suggest informative transitions. As a result, the cost of each iteration is prohibitive for massive scale datasets. It is further known that uninformative but computationally efficient proposals, such as random split-merge, leads to extremely slow convergence. This tradeoff between mixing time and per update cost seems hard to get around. In this paper, we show a sweet spot. We leverage some unique properties of weighted MinHash, which is a popular LSH, to design a novel class of split-merge proposals which are significantly more informative than random sampling but at the same time efficient to compute. Overall, we obtain a superior tradeoff between convergence and per update cost. As a direct consequence, our proposals are around 6X faster than the state-of-the-art sampling methods on two large real datasets KDDCUP and PubMed with several millions of entities and thousands of clusters.

cs.LG↗

arXiv2018

Probabilistic Blocking with An Application to the Syrian Conflict

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 a weighted variant of DOPH. We illustrate each method on an application to a subset of the ongoing Syrian conflict, giving a discussion of each method.

cs.DB↗

arXiv2018

Extreme Classification in Log Memory

We present Merged-Averaged Classifiers via Hashing (MACH) for K-classification with ultra-large values of K. Compared to traditional one-vs-all classifiers that require O(Kd) memory and inference cost, MACH only need O(d log K) (d is dimensionality )memory while only requiring O(K log K + d log K) operation for inference. MACH is a generic K-classification algorithm, with provably theoretical guarantees, which requires O(log K) memory without any assumption on the relationship between classes. MACH uses universal hashing to reduce classification with a large number of classes to few independent classification tasks with small (constant) number of classes. We provide theoretical quantification of discriminability-memory tradeoff. With MACH we can train ODP dataset with 100,000 classes and 400,000 features on a single Titan X GPU, with the classification accuracy of 19.28%, which is the best-reported accuracy on this dataset. Before this work, the best performing baseline is a one-vs-all classifier that requires 40 billion parameters (160 GB model size) and achieves 9% accuracy. In contrast, MACH can achieve 9% accuracy with 480x reduction in the model size (of mere 0.3GB). With MACH, we also demonstrate complete training of fine-grained imagenet dataset (compressed size 104GB), with 21,000 classes, on a single GPU. To the best of our knowledge, this is the first work to demonstrate complete training of these extreme-class datasets on a single Titan X.

cs.DC↗

arXiv2018

Want to bring a community together? Create more sub-communities

Understanding overlapping community structures is crucial for network analysis and prediction. AGM (Affiliation Graph Model) is one of the favorite models for explaining the densely overlapped community structures. In this paper, we thoroughly re-investigate the assumptions made by the AGM model on real datasets. We find that the AGM model is not sufficient to explain several empirical behaviors observed in popular real-world networks. To our surprise, all our experimental results can be explained by a parameter-free hypothesis, leading to more straightforward modeling than AGM which has many parameters. Based on these findings, we propose a parameter-free Jaccard-based Affiliation Graph (JAG) model which models the probability of edge as a network specific constant times the Jaccard similarity between community sets associated with the individuals. Our modeling is significantly simpler than AGM, and it eliminates the need of associating a parameter, the probability value, with each community. Furthermore, JAG model naturally explains why (and in fact when) overlapping communities are densely connected. Based on these observations, we propose a new community-driven friendship formation process, which mathematically recovers the JAG model. JAG is the first model that points towards a direct causal relationship between tight connections in the given community with the number of overlapping communities inside it. Thus, \emph{the most effective way to bring a community together is to form more sub-communities within it.} The community detection algorithm based on our modeling demonstrates a significantly simple algorithm with state-of-the-art accuracy on six real-world network datasets compared to the existing link analysis based methods.

cs.SI↗

arXiv2018

FLASH: Randomized Algorithms Accelerated over CPU-GPU for Ultra-High Dimensional Similarity Search

We present FLASH (\textbf{F}ast \textbf{L}SH \textbf{A}lgorithm for \textbf{S}imilarity search accelerated with \textbf{H}PC), a similarity search system for ultra-high dimensional datasets on a single machine, that does not require similarity computations and is tailored for high-performance computing platforms. By leveraging a LSH style randomized indexing procedure and combining it with several principled techniques, such as reservoir sampling, recent advances in one-pass minwise hashing, and count based estimations, we reduce the computational and parallelization costs of similarity search, while retaining sound theoretical guarantees. We evaluate FLASH on several real, high-dimensional datasets from different domains, including text, malicious URL, click-through prediction, social networks, etc. Our experiments shed new light on the difficulties associated with datasets having several million dimensions. Current state-of-the-art implementations either fail on the presented scale or are orders of magnitude slower than FLASH. FLASH is capable of computing an approximate k-NN graph, from scratch, over the full webspam dataset (1.3 billion nonzeros) in less than 10 seconds. Computing a full k-NN graph in less than 10 seconds on the webspam dataset, using brute-force ($n^2D$), will require at least 20 teraflops. We provide CPU and GPU implementations of FLASH for replicability of our results.

cs.DS↗

arXiv2018

MISSION: Ultra Large-Scale Feature Selection using Count-Sketches

Feature selection is an important challenge in machine learning. It plays a crucial role in the explainability of machine-driven decisions that are rapidly permeating throughout modern society. Unfortunately, the explosion in the size and dimensionality of real-world datasets poses a severe challenge to standard feature selection algorithms. Today, it is not uncommon for datasets to have billions of dimensions. At such scale, even storing the feature vector is impossible, causing most existing feature selection methods to fail. Workarounds like feature hashing, a standard approach to large-scale machine learning, helps with the computational feasibility, but at the cost of losing the interpretability of features. In this paper, we present MISSION, a novel framework for ultra large-scale feature selection that performs stochastic gradient descent while maintaining an efficient representation of the features in memory using a Count-Sketch data structure. MISSION retains the simplicity of feature hashing without sacrificing the interpretability of the features while using only O(log^2(p)) working memory. We demonstrate that MISSION accurately and efficiently performs feature selection on real-world, large-scale datasets with billions of dimensions.

cs.DS↗

arXiv2017

Unique Entity Estimation with Application to the Syrian Conflict

Entity resolution identifies and removes duplicate entities in large, noisy databases and has grown in both usage and new developments as a result of increased data availability. Nevertheless, entity resolution has tradeoffs regarding assumptions of the data generation process, error rates, and computational scalability that make it a difficult task for real applications. In this paper, we focus on a related problem of unique entity estimation, which is the task of estimating the unique number of entities and associated standard errors in a data set with duplicate entities. Unique entity estimation shares many fundamental challenges of entity resolution, namely, that the computational cost of all-to-all entity comparisons is intractable for large databases. To circumvent this computational barrier, we propose an efficient (near-linear time) estimation algorithm based on locality sensitive hashing. Our estimator, under realistic assumptions, is unbiased and has provably low variance compared to existing random sampling based approaches. In addition, we empirically show its superiority over the state-of-the-art estimators on three real applications. The motivation for our work is to derive an accurate estimate of the documented, identifiable deaths in the ongoing Syrian conflict. Our methodology, when applied to the Syrian data set, provides an estimate of $191,874 \pm 1772$ documented, identifiable deaths, which is very close to the Human Rights Data Analysis Group (HRDAG) estimate of 191,369. Our work provides an example of challenges and efforts involved in solving a real, noisy challenging problem where modeling assumptions may not hold.

stat.AP↗

arXiv2017

Accelerating Dependency Graph Learning from Heterogeneous Categorical Event Streams via Knowledge Transfer

Dependency graph, as a heterogeneous graph representing the intrinsic relationships between different pairs of system entities, is essential to many data analysis applications, such as root cause diagnosis, intrusion detection, etc. Given a well-trained dependency graph from a source domain and an immature dependency graph from a target domain, how can we extract the entity and dependency knowledge from the source to enhance the target? One way is to directly apply a mature dependency graph learned from a source domain to the target domain. But due to the domain variety problem, directly using the source dependency graph often can not achieve good performance. Traditional transfer learning methods mainly focus on numerical data and are not applicable. In this paper, we propose ACRET, a knowledge transfer based model for accelerating dependency graph learning from heterogeneous categorical event streams. In particular, we first propose an entity estimation model to filter out irrelevant entities from the source domain based on entity embedding and manifold learning. Only the entities with statistically high correlations are transferred to the target domain. On the surviving entities, we propose a dependency construction model for constructing the unbiased dependency relationships by solving a two-constraint optimization problem. The experimental results on synthetic and real-world datasets demonstrate the effectiveness and efficiency of ACRET. We also apply ACRET to a real enterprise security system for intrusion detection. Our method is able to achieve superior detection performance at least 20 days lead lag time in advance with more than 70% accuracy.

cs.AI↗

arXiv2017

Arrays of (locality-sensitive) Count Estimators (ACE): High-Speed Anomaly Detection via Cache Lookups

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 fastest implementation of the unsupervised anomaly detection algorithms. ACE algorithm requires less than $4MB$ memory, to dynamically compress the full data information into a set of count arrays. These tiny $4MB$ arrays of counts are sufficient for unsupervised anomaly detection. At the core of the ACE algorithm, there is a novel statistical estimator which is derived from the sampling view of Locality Sensitive Hashing(LSH). This view is significantly different and efficient than the widely popular view of LSH for near-neighbor search. We show the superiority of ACE algorithm over 11 popular baselines on 3 benchmark datasets, including the KDD-Cup99 data which is the largest available benchmark comprising of more than half a million entries with ground truth anomaly labels.

cs.DB↗