arXiv subjects

Zohar Karnin

Publications and source records attributed to Zohar Karnin.

36 records · Page 2Linked to original sources

arXiv2020

schuBERT: Optimizing Elements of BERT

Transformers \citep{vaswani2017attention} have gradually become a key component for many state-of-the-art natural language representation models. A recent Transformer based model- BERT \citep{devlin2018bert} achieved state-of-the-art results on various natural language processing tasks, including GLUE, SQuAD v1.1, and SQuAD v2.0. This model however is computationally prohibitive and has a huge number of parameters. In this work we revisit the architecture choices of BERT in efforts to obtain a lighter model. We focus on reducing the number of parameters yet our methods can be applied towards other objectives such FLOPs or latency. We show that much efficient light BERT models can be obtained by reducing algorithmically chosen correct architecture design dimensions rather than reducing the number of Transformer encoder layers. In particular, our schuBERT gives $6.6\%$ higher average accuracy on GLUE and SQuAD datasets as compared to BERT with three encoder layers while having the same number of parameters.

cs.CL↗

arXiv2019

Streaming Quantiles Algorithms with Small Space and Update Time

Approximating quantiles and distributions over streaming data has been studied for roughly two decades now. Recently, Karnin, Lang, and Liberty proposed the first asymptotically optimal algorithm for doing so. This manuscript complements their theoretical result by providing a practical variants of their algorithm with improved constants. For a given sketch size, our techniques provably reduce the upper bound on the sketch error by a factor of two. These improvements are verified experimentally. Our modified quantile sketch improves the latency as well by reducing the worst case update time from $O(1/\varepsilon)$ down to $O(\log (1/\varepsilon))$. We also suggest two algorithms for weighted item streams which offer improved asymptotic update times compared to naïve extensions. Finally, we provide a specialized data structure for these sketches which reduces both their memory footprints and update times.

cs.DS↗

arXiv2019

Asymmetric Random Projections

Random projections (RP) are a popular tool for reducing dimensionality while preserving local geometry. In many applications the data set to be projected is given to us in advance, yet the current RP techniques do not make use of information about the data. In this paper, we provide a computationally light way to extract statistics from the data that allows designing a data dependent RP with superior performance compared to data-oblivious RP. We tackle scenarios such as matrix multiplication and linear regression/classification in which we wish to estimate inner products between pairs of vectors from two possibly different sources. Our technique takes advantage of the difference between the sources and is provably superior to oblivious RPs. Additionally, we provide extensive experiments comparing RPs with our approach showing significant performance lifts in fast matrix multiplication, regression and classification problems.

cs.LG↗

arXiv2019

Discrepancy, Coresets, and Sketches in Machine Learning

This paper defines the notion of class discrepancy for families of functions. It shows that low discrepancy classes admit small offline and streaming coresets. We provide general techniques for bounding the class discrepancy of machine learning problems. As corollaries of the general technique we bound the discrepancy (and therefore coreset complexity) of logistic regression, sigmoid activation loss, matrix covariance, kernel density and any analytic function of the dot product or the squared distance. Our results prove the existence of epsilon-approximation O(sqrt{d}/epsilon) sized coresets for the above problems. This resolves the long-standing open problem regarding the coreset complexity of Gaussian kernel density estimation. We provide two more related but independent results. First, an exponential improvement of the widely used merge-and-reduce trick which gives improved streaming sketches for any low discrepancy problem. Second, an extremely simple deterministic algorithm for finding low discrepancy sequences (and therefore coresets) for any positive semi-definite kernel. This paper establishes some explicit connections between class discrepancy, coreset complexity, learnability, and streaming algorithms.

cs.LG↗

arXiv2019

DARC: Differentiable ARchitecture Compression

In many learning situations, resources at inference time are significantly more constrained than resources at training time. This paper studies a general paradigm, called Differentiable ARchitecture Compression (DARC), that combines model compression and architecture search to learn models that are resource-efficient at inference time. Given a resource-intensive base architecture, DARC utilizes the training data to learn which sub-components can be replaced by cheaper alternatives. The high-level technique can be applied to any neural architecture, and we report experiments on state-of-the-art convolutional neural networks for image classification. For a WideResNet with $97.2\%$ accuracy on CIFAR-10, we improve single-sample inference speed by $2.28\times$ and memory footprint by $5.64\times$, with no accuracy loss. For a ResNet with $79.15\%$ Top1 accuracy on ImageNet, we improve batch inference speed by $1.29\times$ and memory footprint by $3.57\times$ with $1\%$ accuracy loss. We also give theoretical Rademacher complexity bounds in simplified cases, showing how DARC avoids overfitting despite over-parameterization.

cs.LG↗

arXiv2017

Adaptive Feature Selection: Computationally Efficient Online Sparse Linear Regression under RIP

Online sparse linear regression is an online problem where an algorithm repeatedly chooses a subset of coordinates to observe in an adversarially chosen feature vector, makes a real-valued prediction, receives the true label, and incurs the squared loss. The goal is to design an online learning algorithm with sublinear regret to the best sparse linear predictor in hindsight. Without any assumptions, this problem is known to be computationally intractable. In this paper, we make the assumption that data matrix satisfies restricted isometry property, and show that this assumption leads to computationally efficient algorithms with sublinear regret for two variants of the problem. In the first variant, the true label is generated according to a sparse linear model with additive Gaussian noise. In the second, the true label is chosen adversarially.

cs.LG↗

arXiv2016

Budget-Constrained Item Cold-Start Handling in Collaborative Filtering Recommenders via Optimal Design

It is well known that collaborative filtering (CF) based recommender systems provide better modeling of users and items associated with considerable rating history. The lack of historical ratings results in the user and the item cold-start problems. The latter is the main focus of this work. Most of the current literature addresses this problem by integrating content-based recommendation techniques to model the new item. However, in many cases such content is not available, and the question arises is whether this problem can be mitigated using CF techniques only. We formalize this problem as an optimization problem: given a new item, a pool of available users, and a budget constraint, select which users to assign with the task of rating the new item in order to minimize the prediction error of our model. We show that the objective function is monotone-supermodular, and propose efficient optimal design based algorithms that attain an approximation to its optimum. Our findings are verified by an empirical study using the Netflix dataset, where the proposed algorithms outperform several baselines for the problem at hand.

cs.IR↗

arXiv2016

One-Shot Session Recommendation Systems with Combinatorial Items

In recent years, content recommendation systems in large websites (or \emph{content providers}) capture an increased focus. While the type of content varies, e.g.\ movies, articles, music, advertisements, etc., the high level problem remains the same. Based on knowledge obtained so far on the user, recommend the most desired content. In this paper we present a method to handle the well known user-cold-start problem in recommendation systems. In this scenario, a recommendation system encounters a new user and the objective is to present items as relevant as possible with the hope of keeping the user's session as long as possible. We formulate an optimization problem aimed to maximize the length of this initial session, as this is believed to be the key to have the user come back and perhaps register to the system. In particular, our model captures the fact that a single round with low quality recommendation is likely to terminate the session. In such a case, we do not proceed to the next round as the user leaves the system, possibly never to seen again. We denote this phenomenon a \emph{One-Shot Session}. Our optimization problem is formulated as an MDP where the action space is of a combinatorial nature as we recommend in each round, multiple items. This huge action space presents a computational challenge making the straightforward solution intractable. We analyze the structure of the MDP to prove monotone and submodular like properties that allow a computationally efficient solution via a method denoted by \emph{Greedy Value Iteration} (G-VI).

stat.ML↗

arXiv2016

How Many Folders Do You Really Need?

Email classification is still a mostly manual task. Consequently, most Web mail users never define a single folder. Recently however, automatic classification offering the same categories to all users has started to appear in some Web mail clients, such as AOL or Gmail. We adopt this approach, rather than previous (unsuccessful) personalized approaches because of the change in the nature of consumer email traffic, which is now dominated by (non-spam) machine-generated email. We propose here a novel approach for (1) automatically distinguishing between personal and machine-generated email and (2) classifying messages into latent categories, without requiring users to have defined any folder. We report how we have discovered that a set of 6 "latent" categories (one for human- and the others for machine-generated messages) can explain a significant portion of email traffic. We describe in details the steps involved in building a Web-scale email categorization system, from the collection of ground-truth labels, the selection of features to the training of models. Experimental evaluation was performed on more than 500 billion messages received during a period of six months by users of Yahoo mail service, who elected to be part of such research studies. Our system achieved precision and recall rates close to 90% and the latent categories we discovered were shown to cover 70% of both email traffic and email search queries. We believe that these results pave the way for a change of approach in the Web mail industry, and could support the invention of new large-scale email discovery paradigms that had not been possible before.

cs.AI↗

arXiv2016

Optimal Quantile Approximation in Streams

This paper resolves one of the longest standing basic problems in the streaming computational model. Namely, optimal construction of quantile sketches. An $\varepsilon$ approximate quantile sketch receives a stream of items $x_1,\ldots,x_n$ and allows one to approximate the rank of any query up to additive error $\varepsilon n$ with probability at least $1-δ$. The rank of a query $x$ is the number of stream items such that $x_i \le x$. The minimal sketch size required for this task is trivially at least $1/\varepsilon$. Felber and Ostrovsky obtain a $O((1/\varepsilon)\log(1/\varepsilon))$ space sketch for a fixed $δ$. To date, no better upper or lower bounds were known even for randomly permuted streams or for approximating a specific quantile, e.g.,\ the median. This paper obtains an $O((1/\varepsilon)\log \log (1/δ))$ space sketch and a matching lower bound. This resolves the open problem and proves a qualitative gap between randomized and deterministic quantile sketching. One of our contributions is a novel representation and modification of the widely used merge-and-reduce construction. This subtle modification allows for an analysis which is both tight and extremely simple. Similar techniques should be useful for improving other sketching objectives and geometric coreset constructions.

cs.DS↗

arXiv2015

Optimal Dynamic Distributed MIS

Finding a maximal independent set (MIS) in a graph is a cornerstone task in distributed computing. The local nature of an MIS allows for fast solutions in a static distributed setting, which are logarithmic in the number of nodes or in their degrees. The result trivially applies for the dynamic distributed model, in which edges or nodes may be inserted or deleted. In this paper, we take a different approach which exploits locality to the extreme, and show how to update an MIS in a dynamic distributed setting, either \emph{synchronous} or \emph{asynchronous}, with only \emph{a single adjustment} and in a single round, in expectation. These strong guarantees hold for the \emph{complete fully dynamic} setting: Insertions and deletions, of edges as well as nodes, gracefully and abruptly. This strongly separates the static and dynamic distributed models, as super-constant lower bounds exist for computing an MIS in the former. Our results are obtained by a novel analysis of the surprisingly simple solution of carefully simulating the greedy \emph{sequential} MIS algorithm with a random ordering of the nodes. As such, our algorithm has a direct application as a $3$-approximation algorithm for correlation clustering. This adds to the important toolbox of distributed graph decompositions, which are widely used as crucial building blocks in distributed computing. Finally, our algorithm enjoys a useful \emph{history-independence} property, meaning the output is independent of the history of topology changes that constructed that graph. This means the output cannot be chosen, or even biased, by the adversary in case its goal is to prevent us from optimizing some objective function.

cs.DC↗

arXiv2015

Copeland Dueling Bandits

A version of the dueling bandit problem is addressed in which a Condorcet winner may not exist. Two algorithms are proposed that instead seek to minimize regret with respect to the Copeland winner, which, unlike the Condorcet winner, is guaranteed to exist. The first, Copeland Confidence Bound (CCB), is designed for small numbers of arms, while the second, Scalable Copeland Bandits (SCB), works better for large-scale problems. We provide theoretical results bounding the regret accumulated by CCB and SCB, both substantially improving existing results. Such existing results either offer bounds of the form $O(K \log T)$ but require restrictive assumptions, or offer bounds of the form $O(K^2 \log T)$ without requiring such assumptions. Our results offer the best of both worlds: $O(K \log T)$ bounds without restrictive assumptions.

cs.LG↗

arXiv2014

Volumetric Spanners: an Efficient Exploration Basis for Learning

Numerous machine learning problems require an exploration basis - a mechanism to explore the action space. We define a novel geometric notion of exploration basis with low variance, called volumetric spanners, and give efficient algorithms to construct such a basis. We show how efficient volumetric spanners give rise to the first efficient and optimal regret algorithm for bandit linear optimization over general convex sets. Previously such results were known only for specific convex sets, or under special conditions such as the existence of an efficient self-concordant barrier for the underlying set.

cs.LG↗

arXiv2014

Reducing Dueling Bandits to Cardinal Bandits

We present algorithms for reducing the Dueling Bandits problem to the conventional (stochastic) Multi-Armed Bandits problem. The Dueling Bandits problem is an online model of learning with ordinal feedback of the form "A is preferred to B" (as opposed to cardinal feedback like "A has value 2.5"), giving it wide applicability in learning from implicit user feedback and revealed and stated preferences. In contrast to existing algorithms for the Dueling Bandits problem, our reductions -- named $\Doubler$, $\MultiSbm$ and $\DoubleSbm$ -- provide a generic schema for translating the extensive body of known results about conventional Multi-Armed Bandit algorithms to the Dueling Bandits setting. For $\Doubler$ and $\MultiSbm$ we prove regret upper bounds in both finite and infinite settings, and conjecture about the performance of $\DoubleSbm$ which empirically outperforms the other two as well as previous algorithms in our experiments. In addition, we provide the first almost optimal regret bound in terms of second order terms, such as the differences between the values of the arms.

cs.LG↗

arXiv2013

Near-Optimal Entrywise Sampling for Data Matrices

We consider the problem of selecting non-zero entries of a matrix $A$ in order to produce a sparse sketch of it, $B$, that minimizes $\|A-B\|_2$. For large $m \times n$ matrices, such that $n \gg m$ (for example, representing $n$ observations over $m$ attributes) we give sampling distributions that exhibit four important properties. First, they have closed forms computable from minimal information regarding $A$. Second, they allow sketching of matrices whose non-zeros are presented to the algorithm in arbitrary order as a stream, with $O(1)$ computation per non-zero. Third, the resulting sketch matrices are not only sparse, but their non-zero entries are highly compressible. Lastly, and most importantly, under mild assumptions, our distributions are provably competitive with the optimal offline distribution. Note that the probabilities in the optimal offline distribution may be complex functions of all the entries in the matrix. Therefore, regardless of computational complexity, the optimal distribution might be impossible to compute in the streaming model.

cs.LG↗

arXiv2013

Distributed Exploration in Multi-Armed Bandits

We study exploration in Multi-Armed Bandits in a setting where $k$ players collaborate in order to identify an $ε$-optimal arm. Our motivation comes from recent employment of bandit algorithms in computationally intensive, large-scale applications. Our results demonstrate a non-trivial tradeoff between the number of arm pulls required by each of the players, and the amount of communication between them. In particular, our main result shows that by allowing the $k$ players to communicate only once, they are able to learn $\sqrt{k}$ times faster than a single player. That is, distributing learning to $k$ players gives rise to a factor $\sqrt{k}$ parallel speed-up. We complement this result with a lower bound showing this is in general the best possible. On the other extreme, we present an algorithm that achieves the ideal factor $k$ speed-up in learning performance, with communication only logarithmic in $1/ε$.

cs.LG↗

arXiv2012

A note on: No need to choose: How to get both a PTAS and Sublinear Query Complexity

We revisit various PTAS's (Polynomial Time Approximation Schemes) for minimization versions of dense problems, and show that they can be performed with sublinear query complexity. This means that not only do we obtain a (1+eps)-approximation to the NP-Hard problems in polynomial time, but also avoid reading the entire input. This setting is particularly advantageous when the price of reading parts of the input is high, as is the case, for examples, where humans provide the input. Trading off query complexity with approximation is the raison d'etre of the field of learning theory, and of the ERM (Empirical Risk Minimization) setting in particular. A typical ERM result, however, does not deal with computational complexity. We discuss two particular problems for which (a) it has already been shown that sublinear querying is sufficient for obtaining a (1 + eps)-approximation using unlimited computational power (an ERM result), and (b) with full access to input, we could get a (1+eps)-approximation in polynomial time (a PTAS). Here we show that neither benefit need be sacrificed. We get a PTAS with efficient query complexity.

cs.CC↗

arXiv2012

On the Furthest Hyperplane Problem and Maximal Margin Clustering

This paper introduces the Furthest Hyperplane Problem (FHP), which is an unsupervised counterpart of Support Vector Machines. Given a set of n points in Rd, the objective is to produce the hyperplane (passing through the origin) which maximizes the separation margin, that is, the minimal distance between the hyperplane and any input point. To the best of our knowledge, this is the first paper achieving provable results regarding FHP. We provide both lower and upper bounds to this NP-hard problem. First, we give a simple randomized algorithm whose running time is n^O(1/θ^2) where θ is the optimal separation margin. We show that its exponential dependency on 1/θ^2 is tight, up to sub-polynomial factors, assuming SAT cannot be solved in sub-exponential time. Next, we give an efficient approxima- tion algorithm. For any α \in [0, 1], the algorithm produces a hyperplane whose distance from at least 1 - 5α fraction of the points is at least α times the optimal separation margin. Finally, we show that FHP does not admit a PTAS by presenting a gap preserving reduction from a particular version of the PCP theorem.

cs.CC↗