arXiv subjects

Ali Jalali

Publications and source records attributed to Ali Jalali.

At least 19 recordsLinked to original sources

arXiv2021

Not All Features Are Equal: Discovering Essential Features for Preserving Prediction Privacy

When receiving machine learning services from the cloud, the provider does not need to receive all features; in fact, only a subset of the features are necessary for the target prediction task. Discerning this subset is the key problem of this work. We formulate this problem as a gradient-based perturbation maximization method that discovers this subset in the input feature space with respect to the functionality of the prediction model used by the provider. After identifying the subset, our framework, Cloak, suppresses the rest of the features using utility-preserving constant values that are discovered through a separate gradient-based optimization process. We show that Cloak does not necessarily require collaboration from the service provider beyond its normal service, and can be applied in scenarios where we only have black-box access to the service provider's model. We theoretically guarantee that Cloak's optimizations reduce the upper bound of the Mutual Information (MI) between the data and the sifted representations that are sent out. Experimental results show that Cloak reduces the mutual information between the input and the sifted representations by 85.01% with only a negligible reduction in utility (1.42%). In addition, we show that Cloak greatly diminishes adversaries' ability to learn and infer non-conducive features.

cs.LG↗

arXiv2017

Dilaton Black Hole Entropy from Entropy Function Formalism

It has been shown that the entropy function formalism is an efficient way to calculate the entropy of black holes in string theory. We check this formalism for the extremal charged dilaton black hole. We find the general four-derivative correction on the black hole entropy from the value of the entropy function at its extremum point.

hep-th↗

arXiv2016

On Chern-Simons Couplings at order $O(α'^2)$

Using the explicit string scattering calculation and the linear T-dual ward identity, we evaluate the string theory disc amplitude of one Ramond-Ramond field $C^{(p+1)}$ and two Neveu-Schwarz B-fields in the presence of a single $D_p$-brane in type $IIB$ string theory. From this amplitude we extract the $O(α'^2)$ (or equivalently four-derivative) part of the $D_p$-brane couplings involving these fields.

hep-th↗

arXiv2016

Higher derivative corrections to DBI action at $ α'^2$ order

We use the compatibility of D-brane action with linear off-shell T-duality and linear on-shell S-duality as guiding principles to find all world volume couplings of one massless closed and three massless open strings at order $α'^2$ in type II superstring theories in flat space-time.

hep-th↗

arXiv2016

Higher derivative corrections to WZ action: One RR, one NSNS and one NS couplings

In the first part of this paper, we calculate the disk-level S-matrix elements of one RR, one NSNS and one NS vertex operators, and show that they are consistent with the amplitudes that have been recently found by applying various Ward identities. We show that the massless poles of the amplitude at low energy are fully consistent with the known D-brane couplings at order $α'^2$ which involve one RR or NSNS and two NS fields. Subtracting the massless poles, we then find the contact terms of one RR, one NSNS and one NS fields at order $α'^2$. Some of these terms are reproduced by the Taylor expansion and the pull-back of two closed string couplings, some other couplings are reproduced by linear graviton in the second fundamental form and by the B-field in the gauge field extension $F\rightarrow F+B$, in one closed and two open string couplings. In the second part, we write all independent covariant contractions of one RR, one NSNS and one NS fields with unknown coefficients. We then constrain the couplings to be consistent with the linear T-duality and with the above contact terms. Interestingly, we have found that up to total derivative terms and Bianchi identities, these constraints uniquely fix all the unknown coefficients.

hep-th↗

arXiv2015

On D-brane action at order $ α'^2$

We use compatibility of D-brane action with linear T-duality, S-duality and with S-matrix elements as guiding principles to find all world volume couplings of one massless closed and two open strings at order $α'^2$ in type II superstring theories. In particular, we find that the squares of second fundamental form appear only in world volume curvatures, and confirm the observation that dilaton appears in string frame action via the transformation $\hat{R}_{μν}\rightarrow \hat{R}_{μν}+\nabla_μ\nabla_νΦ$.

hep-th↗

arXiv2014

Clustering Partially Observed Graphs via Convex Optimization

This paper considers the problem of clustering a partially observed unweighted graph---i.e., one where for some node pairs we know there is an edge between them, for some others we know there is no edge, and for the remaining we do not know whether or not there is an edge. We want to organize the nodes into disjoint clusters so that there is relatively dense (observed) connectivity within clusters, and sparse across clusters. We take a novel yet natural approach to this problem, by focusing on finding the clustering that minimizes the number of "disagreements"---i.e., the sum of the number of (observed) missing edges within clusters, and (observed) present edges across clusters. Our algorithm uses convex optimization; its basis is a reduction of disagreement minimization to the problem of recovering an (unknown) low-rank matrix and an (unknown) sparse matrix from their partially observed sum. We evaluate the performance of our algorithm on the classical Planted Partition/Stochastic Block Model. Our main theorem provides sufficient conditions for the success of our algorithm as a function of the minimum cluster size, edge density and observation probability; in particular, the results characterize the tradeoff between the observation probability and the edge density gap. When there are a constant number of clusters of equal size, our results are optimal up to logarithmic factors.

cs.LG↗

arXiv2013

A Lipschitz Exploration-Exploitation Scheme for Bayesian Optimization

The problem of optimizing unknown costly-to-evaluate functions has been studied for a long time in the context of Bayesian Optimization. Algorithms in this field aim to find the optimizer of the function by asking only a few function evaluations at locations carefully selected based on a posterior model. In this paper, we assume the unknown function is Lipschitz continuous. Leveraging the Lipschitz property, we propose an algorithm with a distinct exploration phase followed by an exploitation phase. The exploration phase aims to select samples that shrink the search space as much as possible. The exploitation phase then focuses on the reduced search space and selects samples closest to the optimizer. Considering the Expected Improvement (EI) as a baseline, we empirically show that the proposed algorithm significantly outperforms EI.

cs.LG↗

arXiv2013

Real Time Bid Optimization with Smooth Budget Delivery in Online Advertising

Today, billions of display ad impressions are purchased on a daily basis through a public auction hosted by real time bidding (RTB) exchanges. A decision has to be made for advertisers to submit a bid for each selected RTB ad request in milliseconds. Restricted by the budget, the goal is to buy a set of ad impressions to reach as many targeted users as possible. A desired action (conversion), advertiser specific, includes purchasing a product, filling out a form, signing up for emails, etc. In addition, advertisers typically prefer to spend their budget smoothly over the time in order to reach a wider range of audience accessible throughout a day and have a sustainable impact. However, since the conversions occur rarely and the occurrence feedback is normally delayed, it is very challenging to achieve both budget and performance goals at the same time. In this paper, we present an online approach to the smooth budget delivery while optimizing for the conversion performance. Our algorithm tries to select high quality impressions and adjust the bid price based on the prior performance distribution in an adaptive manner by distributing the budget optimally across time. Our experimental results from real advertising campaigns demonstrate the effectiveness of our proposed approach.

cs.GT↗

arXiv2013

Scalable Audience Reach Estimation in Real-time Online Advertising

Online advertising has been introduced as one of the most efficient methods of advertising throughout the recent years. Yet, advertisers are concerned about the efficiency of their online advertising campaigns and consequently, would like to restrict their ad impressions to certain websites and/or certain groups of audience. These restrictions, known as targeting criteria, limit the reachability for better performance. This trade-off between reachability and performance illustrates a need for a forecasting system that can quickly predict/estimate (with good accuracy) this trade-off. Designing such a system is challenging due to (a) the huge amount of data to process, and, (b) the need for fast and accurate estimates. In this paper, we propose a distributed fault tolerant system that can generate such estimates fast with good accuracy. The main idea is to keep a small representative sample in memory across multiple machines and formulate the forecasting problem as queries against the sample. The key challenge is to find the best strata across the past data, perform multivariate stratified sampling while ensuring fuzzy fall-back to cover the small minorities. Our results show a significant improvement over the uniform and simple stratified sampling strategies which are currently widely used in the industry.

cs.LG↗

arXiv2012

A New Greedy Algorithm for Multiple Sparse Regression

This paper proposes a new algorithm for multiple sparse regression in high dimensions, where the task is to estimate the support and values of several (typically related) sparse vectors from a few noisy linear measurements. Our algorithm is a "forward-backward" greedy procedure that -- uniquely -- operates on two distinct classes of objects. In particular, we organize our target sparse vectors as a matrix; our algorithm involves iterative addition and removal of both (a) individual elements, and (b) entire rows (corresponding to shared features), of the matrix. Analytically, we establish that our algorithm manages to recover the supports (exactly) and values (approximately) of the sparse vectors, under assumptions similar to existing approaches based on convex optimization. However, our algorithm has a much smaller computational complexity. Perhaps most interestingly, it is seen empirically to require visibly fewer samples. Ours represents the first attempt to extend greedy algorithms to the class of models that can only/best be represented by a combination of component structural assumptions (sparse and group-sparse, in our case).

stat.ML↗

arXiv2012

Learning the Dependence Graph of Time Series with Latent Factors

This paper considers the problem of learning, from samples, the dependency structure of a system of linear stochastic differential equations, when some of the variables are latent. In particular, we observe the time evolution of some variables, and never observe other variables; from this, we would like to find the dependency structure between the observed variables - separating out the spurious interactions caused by the (marginalizing out of the) latent variables' time series. We develop a new method, based on convex optimization, to do so in the case when the number of latent variables is smaller than the number of observed ones. For the case when the dependency structure between the observed variables is sparse, we theoretically establish a high-dimensional scaling result for structure recovery. We verify our theoretical result with both synthetic and real data (from the stock market).

cs.LG↗

arXiv2012

Hybrid Batch Bayesian Optimization

Bayesian Optimization aims at optimizing an unknown non-convex/concave function that is costly to evaluate. We are interested in application scenarios where concurrent function evaluations are possible. Under such a setting, BO could choose to either sequentially evaluate the function, one input at a time and wait for the output of the function before making the next selection, or evaluate the function at a batch of multiple inputs at once. These two different settings are commonly referred to as the sequential and batch settings of Bayesian Optimization. In general, the sequential setting leads to better optimization performance as each function evaluation is selected with more information, whereas the batch setting has an advantage in terms of the total experimental time (the number of iterations). In this work, our goal is to combine the strength of both settings. Specifically, we systematically analyze Bayesian optimization using Gaussian process as the posterior estimator and provide a hybrid algorithm that, based on the current state, dynamically switches between a sequential policy and a batch policy with variable batch sizes. We provide theoretical justification for our algorithm and present experimental results on eight benchmark BO problems. The results show that our method achieves substantial speedup (up to %78) compared to a pure sequential policy, without suffering any significant performance loss.

cs.AI↗

arXiv2012

Clustering using Max-norm Constrained Optimization

We suggest using the max-norm as a convex surrogate constraint for clustering. We show how this yields a better exact cluster recovery guarantee than previously suggested nuclear-norm relaxation, and study the effectiveness of our method, and other related convex relaxations, compared to other clustering approaches.

cs.LG↗

arXiv2011

High-dimensional Sparse Inverse Covariance Estimation using Greedy Methods

In this paper we consider the task of estimating the non-zero pattern of the sparse inverse covariance matrix of a zero-mean Gaussian random vector from a set of iid samples. Note that this is also equivalent to recovering the underlying graph structure of a sparse Gaussian Markov Random Field (GMRF). We present two novel greedy approaches to solving this problem. The first estimates the non-zero covariates of the overall inverse covariance matrix using a series of global forward and backward greedy steps. The second estimates the neighborhood of each node in the graph separately, again using greedy forward and backward steps, and combines the intermediate neighborhoods to form an overall estimate. The principal contribution of this paper is a rigorous analysis of the sparsistency, or consistency in recovering the sparsity pattern of the inverse covariance matrix. Surprisingly, we show that both the local and global greedy methods learn the full structure of the model with high probability given just $O(d\log(p))$ samples, which is a \emph{significant} improvement over state of the art $\ell_1$-regularized Gaussian MLE (Graphical Lasso) that requires $O(d^2\log(p))$ samples. Moreover, the restricted eigenvalue and smoothness conditions imposed by our greedy methods are much weaker than the strong irrepresentable conditions required by the $\ell_1$-regularization based methods. We corroborate our results with extensive simulations and examples, comparing our local and global greedy methods to the $\ell_1$-regularized Gaussian MLE as well as the Neighborhood Greedy method to that of nodewise $\ell_1$-regularized linear regression (Neighborhood Lasso).

cs.LG↗

arXiv2011

Dynamic Batch Bayesian Optimization

Bayesian optimization (BO) algorithms try to optimize an unknown function that is expensive to evaluate using minimum number of evaluations/experiments. Most of the proposed algorithms in BO are sequential, where only one experiment is selected at each iteration. This method can be time inefficient when each experiment takes a long time and more than one experiment can be ran concurrently. On the other hand, requesting a fix-sized batch of experiments at each iteration causes performance inefficiency in BO compared to the sequential policies. In this paper, we present an algorithm that asks a batch of experiments at each time step t where the batch size p_t is dynamically determined in each step. Our algorithm is based on the observation that the sequence of experiments selected by the sequential policy can sometimes be almost independent from each other. Our algorithm identifies such scenarios and request those experiments at the same time without degrading the performance. We evaluate our proposed method using the Expected Improvement policy and the results show substantial speedup with little impact on the performance in eight real and synthetic benchmarks.

cs.LG↗

arXiv2011

Low-rank Matrix Recovery from Errors and Erasures

This paper considers the recovery of a low-rank matrix from an observed version that simultaneously contains both (a) erasures: most entries are not observed, and (b) errors: values at a constant fraction of (unknown) locations are arbitrarily corrupted. We provide a new unified performance guarantee on when the natural convex relaxation of minimizing rank plus support succeeds in exact recovery. Our result allows for the simultaneous presence of random and deterministic components in both the error and erasure patterns. On the one hand, corollaries obtained by specializing this one single result in different ways recover (up to poly-log factors) all the existing works in matrix completion, and sparse and low-rank matrix recovery. On the other hand, our results also provide the first guarantees for (a) recovery when we observe a vanishing fraction of entries of a corrupted matrix, and (b) deterministic matrix completion.

cs.IT↗

arXiv2011

On Learning Discrete Graphical Models Using Greedy Methods

In this paper, we address the problem of learning the structure of a pairwise graphical model from samples in a high-dimensional setting. Our first main result studies the sparsistency, or consistency in sparsity pattern recovery, properties of a forward-backward greedy algorithm as applied to general statistical models. As a special case, we then apply this algorithm to learn the structure of a discrete graphical model via neighborhood estimation. As a corollary of our general result, we derive sufficient conditions on the number of samples n, the maximum node-degree d and the problem size p, as well as other conditions on the model parameters, so that the algorithm recovers all the edges with high probability. Our result guarantees graph selection for samples scaling as n = Omega(d^2 log(p)), in contrast to existing convex-optimization based algorithms that require a sample complexity of Ω(d^3 log(p)). Further, the greedy algorithm only requires a restricted strong convexity condition which is typically milder than irrepresentability assumptions. We corroborate these results using numerical simulations at the end.

cs.LG↗