arXiv subjects

Anup Rao

Publications and source records attributed to Anup Rao.

At least 37 records · Page 2Linked to original sources

arXiv2022

Electra: Conditional Generative Model based Predicate-Aware Query Approximation

The goal of Approximate Query Processing (AQP) is to provide very fast but "accurate enough" results for costly aggregate queries thereby improving user experience in interactive exploration of large datasets. Recently proposed Machine-Learning based AQP techniques can provide very low latency as query execution only involves model inference as compared to traditional query processing on database clusters. However, with increase in the number of filtering predicates(WHERE clauses), the approximation error significantly increases for these methods. Analysts often use queries with a large number of predicates for insights discovery. Thus, maintaining low approximation error is important to prevent analysts from drawing misleading conclusions. In this paper, we propose ELECTRA, a predicate-aware AQP system that can answer analytics-style queries with a large number of predicates with much smaller approximation errors. ELECTRA uses a conditional generative model that learns the conditional distribution of the data and at runtime generates a small (~1000 rows) but representative sample, on which the query is executed to compute the approximate result. Our evaluations with four different baselines on three real-world datasets show that ELECTRA provides lower AQP error for large number of predicates compared to baselines.

cs.DB↗

arXiv2022

Anti-concentration and the Exact Gap-Hamming Problem

We prove anti-concentration bounds for the inner product of two independent random vectors, and use these bounds to prove lower bounds in communication complexity. We show that if $A,B$ are subsets of the cube $\{\pm 1\}^n$ with $|A| \cdot |B| \geq 2^{1.01 n}$, and $X \in A$ and $Y \in B$ are sampled independently and uniformly, then the inner product $\langle X,Y \rangle$ takes on any fixed value with probability at most $O(1/\sqrt{n})$. In fact, we prove the following stronger "smoothness" statement: $$ \max_{k } \big| \Pr[\langle X,Y \rangle = k] - \Pr[\langle X,Y \rangle = k+4]\big| \leq O(1/n).$$ We use these results to prove that the exact gap-hamming problem requires linear communication, resolving an open problem in communication complexity. We also conclude anti-concentration for structured distributions with low entropy. If $x \in \mathcal{Z}^n$ has no zero coordinates, and $B \subseteq \{\pm 1\}^n$ corresponds to a subspace of $\mathcal{F}_2^n$ of dimension $0.51n$, then $\max_k \Pr[\langle x,Y \rangle = k] \leq O(\sqrt{\ln (n)/n})$.

math.PR↗

arXiv2021

Online MAP Inference and Learning for Nonsymmetric Determinantal Point Processes

In this paper, we introduce the online and streaming MAP inference and learning problems for Non-symmetric Determinantal Point Processes (NDPPs) where data points arrive in an arbitrary order and the algorithms are constrained to use a single-pass over the data as well as sub-linear memory. The online setting has an additional requirement of maintaining a valid solution at any point in time. For solving these new problems, we propose algorithms with theoretical guarantees, evaluate them on several real-world datasets, and show that they give comparable performance to state-of-the-art offline algorithms that store the entire data in memory and take multiple passes over it.

cs.LG↗

arXiv2021

Multiscale Manifold Warping

Many real-world applications require aligning two temporal sequences, including bioinformatics, handwriting recognition, activity recognition, and human-robot coordination. Dynamic Time Warping (DTW) is a popular alignment method, but can fail on high-dimensional real-world data where the dimensions of aligned sequences are often unequal. In this paper, we show that exploiting the multiscale manifold latent structure of real-world data can yield improved alignment. We introduce a novel framework called Warping on Wavelets (WOW) that integrates DTW with a a multi-scale manifold learning framework called Diffusion Wavelets. We present a theoretical analysis of the WOW family of algorithms and show that it outperforms previous state of the art methods, such as canonical time warping (CTW) and manifold warping, on several real-world datasets.

cs.LG↗

arXiv2021

Tight bounds on the Fourier growth of bounded functions on the hypercube

We give tight bounds on the degree $\ell$ homogenous parts $f_\ell$ of a bounded function $f$ on the cube. We show that if $f: \{\pm 1\}^n \rightarrow [-1,1]$ has degree $d$, then $\| f_\ell \|_\infty$ is bounded by $d^\ell/\ell!$, and $\| \hat{f}_\ell \|_1$ is bounded by $d^\ell e^{\binom{\ell+1}{2}} n^{\frac{\ell-1}{2}}$. We describe applications to pseudorandomness and learning theory. We use similar methods to generalize the classical Pisier's inequality from convex analysis. Our analysis involves properties of real-rooted polynomials that may be useful elsewhere.

cs.CC↗

arXiv2021

Optimal Space and Time for Streaming Pattern Matching

In this work, we study longest common substring, pattern matching, and wildcard pattern matching in the asymmetric streaming model. In this streaming model, we have random access to one string and streaming access to the other one. We present streaming algorithms with provable guarantees for these three fundamental problems. In particular, our algorithms for pattern matching improve the upper bound and beat the unconditional lower bounds on the memory of randomized and deterministic streaming algorithms. In addition to this, we present algorithms for wildcard pattern matching in the asymmetric streaming model that have optimal space and time.

cs.DS↗

arXiv2021

Graph Neural Networks with Heterophily

Graph Neural Networks (GNNs) have proven to be useful for many different practical applications. However, many existing GNN models have implicitly assumed homophily among the nodes connected in the graph, and therefore have largely overlooked the important setting of heterophily, where most connected nodes are from different classes. In this work, we propose a novel framework called CPGNN that generalizes GNNs for graphs with either homophily or heterophily. The proposed framework incorporates an interpretable compatibility matrix for modeling the heterophily or homophily level in the graph, which can be learned in an end-to-end fashion, enabling it to go beyond the assumption of strong homophily. Theoretically, we show that replacing the compatibility matrix in our framework with the identity (which represents pure homophily) reduces to GCN. Our extensive experiments demonstrate the effectiveness of our approach in more realistic and challenging experimental settings with significantly less training data compared to previous works: CPGNN variants achieve state-of-the-art results in heterophily settings with or without contextual node features, while maintaining comparable performance in homophily settings.

cs.LG↗

arXiv2021

Asymptotics of Ridge Regression in Convolutional Models

Understanding generalization and estimation error of estimators for simple models such as linear and generalized linear models has attracted a lot of attention recently. This is in part due to an interesting observation made in machine learning community that highly over-parameterized neural networks achieve zero training error, and yet they are able to generalize well over the test samples. This phenomenon is captured by the so called double descent curve, where the generalization error starts decreasing again after the interpolation threshold. A series of recent works tried to explain such phenomenon for simple models. In this work, we analyze the asymptotics of estimation error in ridge estimators for convolutional linear models. These convolutional inverse problems, also known as deconvolution, naturally arise in different fields such as seismology, imaging, and acoustics among others. Our results hold for a large class of input distributions that include i.i.d. features as a special case. We derive exact formulae for estimation error of ridge estimators that hold in a certain high-dimensional regime. We show the double descent phenomenon in our experiments for convolutional models and show that our theoretical results match the experiments.

stat.ML↗

arXiv2021

Machine Unlearning via Algorithmic Stability

We study the problem of machine unlearning and identify a notion of algorithmic stability, Total Variation (TV) stability, which we argue, is suitable for the goal of exact unlearning. For convex risk minimization problems, we design TV-stable algorithms based on noisy Stochastic Gradient Descent (SGD). Our key contribution is the design of corresponding efficient unlearning algorithms, which are based on constructing a (maximal) coupling of Markov chains for the noisy SGD procedure. To understand the trade-offs between accuracy and unlearning efficiency, we give upper and lower bounds on excess empirical and populations risk of TV stable algorithms for convex risk minimization. Our techniques generalize to arbitrary non-convex functions, and our algorithms are differentially private as well.

cs.LG↗

arXiv2021

Online Discrepancy Minimization via Persistent Self-Balancing Walks

We study the online discrepancy minimization problem for vectors in $\mathbb{R}^d$ in the oblivious setting where an adversary is allowed fix the vectors $x_1, x_2, \ldots, x_n$ in arbitrary order ahead of time. We give an algorithm that maintains $O(\sqrt{\log(nd/δ)})$ discrepancy with probability $1-δ$, matching the lower bound given in [Bansal et al. 2020] up to an $O(\sqrt{\log \log n})$ factor in the high-probability regime. We also provide results for the weighted and multi-color versions of the problem.

cs.DS↗

arXiv2021

Fundamental Tradeoffs in Distributionally Adversarial Training

Adversarial training is among the most effective techniques to improve the robustness of models against adversarial perturbations. However, the full effect of this approach on models is not well understood. For example, while adversarial training can reduce the adversarial risk (prediction error against an adversary), it sometimes increase standard risk (generalization error when there is no adversary). Even more, such behavior is impacted by various elements of the learning problem, including the size and quality of training data, specific forms of adversarial perturbations in the input, model overparameterization, and adversary's power, among others. In this paper, we focus on \emph{distribution perturbing} adversary framework wherein the adversary can change the test distribution within a neighborhood of the training data distribution. The neighborhood is defined via Wasserstein distance between distributions and the radius of the neighborhood is a measure of adversary's manipulative power. We study the tradeoff between standard risk and adversarial risk and derive the Pareto-optimal tradeoff, achievable over specific classes of models, in the infinite data limit with features dimension kept fixed. We consider three learning settings: 1) Regression with the class of linear models; 2) Binary classification under the Gaussian mixtures data model, with the class of linear classifiers; 3) Regression with the class of random features model (which can be equivalently represented as two-layer neural network with random first-layer weights). We show that a tradeoff between standard and adversarial risk is manifested in all three settings. We further characterize the Pareto-optimal tradeoff curves and discuss how a variety of factors, such as features correlation, adversary's power or the width of two-layer neural network would affect this tradeoff.

cs.LG↗

arXiv2020

Heterogeneous Graphlets

In this paper, we introduce a generalization of graphlets to heterogeneous networks called typed graphlets. Informally, typed graphlets are small typed induced subgraphs. Typed graphlets generalize graphlets to rich heterogeneous networks as they explicitly capture the higher-order typed connectivity patterns in such networks. To address this problem, we describe a general framework for counting the occurrences of such typed graphlets. The proposed algorithms leverage a number of combinatorial relationships for different typed graphlets. For each edge, we count a few typed graphlets, and with these counts along with the combinatorial relationships, we obtain the exact counts of the other typed graphlets in o(1) constant time. Notably, the worst-case time complexity of the proposed approach matches the time complexity of the best known untyped algorithm. In addition, the approach lends itself to an efficient lock-free and asynchronous parallel implementation. While there are no existing methods for typed graphlets, there has been some work that focused on computing a different and much simpler notion called colored graphlet. The experiments confirm that our proposed approach is orders of magnitude faster and more space-efficient than methods for computing the simpler notion of colored graphlet. Unlike these methods that take hours on small networks, the proposed approach takes only seconds on large networks with millions of edges. Notably, since typed graphlet is more general than colored graphlet (and untyped graphlets), the counts of various typed graphlets can be combined to obtain the counts of the much simpler notion of colored graphlets. The proposed methods give rise to new opportunities and applications for typed graphlets.

cs.SI↗

arXiv2020

Efficient Balanced Treatment Assignments for Experimentation

In this work, we reframe the problem of balanced treatment assignment as optimization of a two-sample test between test and control units. Using this lens we provide an assignment algorithm that is optimal with respect to the minimum spanning tree test of Friedman and Rafsky (1979). This assignment to treatment groups may be performed exactly in polynomial time. We provide a probabilistic interpretation of this process in terms of the most probable element of designs drawn from a determinantal point process which admits a probabilistic interpretation of the design. We provide a novel formulation of estimation as transductive inference and show how the tree structures used in design can also be used in an adjustment estimator. We conclude with a simulation study demonstrating the improved efficacy of our method.

stat.ME↗

arXiv2020

An Elementary Exposition of Pisier's Inequality

Pisier's inequality is central in the study of normed spaces and has important applications in geometry. We provide an elementary proof of this inequality, which avoids some non-constructive steps from previous proofs. Our goal is to make the inequality and its proof more accessible, because we think they will find additional applications. We demonstrate this with a new type of restriction on the Fourier spectrum of bounded functions on the discrete cube.

math.FA↗

arXiv2020

Sample Efficient Graph-Based Optimization with Noisy Observations

We study sample complexity of optimizing "hill-climbing friendly" functions defined on a graph under noisy observations. We define a notion of convexity, and we show that a variant of best-arm identification can find a near-optimal solution after a small number of queries that is independent of the size of the graph. For functions that have local minima and are nearly convex, we show a sample complexity for the classical simulated annealing under noisy observations. We show effectiveness of the greedy algorithm with restarts and the simulated annealing on problems of graph-based nearest neighbor classification as well as a web document re-ranking application.

cs.LG↗

arXiv2020

Coding for Sunflowers

A sunflower is a family of sets that have the same pairwise intersections. We simplify a recent result of Alweiss, Lovett, Wu and Zhang that gives an upper bound on the size of every family of sets of size $k$ that does not contain a sunflower. We show how to use the converse of Shannon's noiseless coding theorem to give a cleaner proof of their result.

math.CO↗

arXiv2019

Approximate Maximum Matching in Random Streams

In this paper, we study the problem of finding a maximum matching in the semi-streaming model when edges arrive in a random order. In the semi-streaming model, an algorithm receives a stream of edges and it is allowed to have a memory of $\tilde{O}(n)$ where $n$ is the number of vertices in the graph. A recent inspiring work by Assadi et al. shows that there exists a streaming algorithm with the approximation ratio of $\frac{2}{3}$ that uses $\tilde{O}(n^{1.5})$ memory. However, the memory of their algorithm is much larger than the memory constraint of the semi-streaming algorithms. In this work, we further investigate this problem in the semi-streaming model, and we present simple algorithms for approximating maximum matching in the semi-streaming model. Our main results are as follows. We show that there exists a single-pass deterministic semi-streaming algorithm that finds a $\frac{3}{5} (= 0.6)$ approximation of the maximum matching in bipartite graphs using $\tilde{O}(n)$ memory. This result significantly outperforms the state-of-the-art result of Konrad that finds a $0.539$ approximation of the maximum matching using $\tilde{O}(n)$ memory. By giving a black-box reduction from finding a matching in general graphs to finding a matching in bipartite graphs, we show there exists a single-pass deterministic semi-streaming algorithm that finds a $\frac{6}{11} (\approx 0.545)$ approximation of the maximum matching in general graphs, improving upon the state-of-art result $0.506$ approximation by Gamlath et al.

cs.DS↗

arXiv2019

Latent Network Summarization: Bridging Network Embedding and Summarization

Motivated by the computational and storage challenges that dense embeddings pose, we introduce the problem of latent network summarization that aims to learn a compact, latent representation of the graph structure with dimensionality that is independent of the input graph size (i.e., #nodes and #edges), while retaining the ability to derive node representations on the fly. We propose Multi-LENS, an inductive multi-level latent network summarization approach that leverages a set of relational operators and relational functions (compositions of operators) to capture the structure of egonets and higher-order subgraphs, respectively. The structure is stored in low-rank, size-independent structural feature matrices, which along with the relational functions comprise our latent network summary. Multi-LENS is general and naturally supports both homogeneous and heterogeneous graphs with or without directionality, weights, attributes or labels. Extensive experiments on real graphs show 3.5 - 34.3% improvement in AUC for link prediction, while requiring 80 - 2152x less output storage space than baseline embedding methods on large datasets. As application areas, we show the effectiveness of Multi-LENS in detecting anomalies and events in the Enron email communication graph and Twitter co-mention graph.

cs.SI↗