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Raghavendra Addanki, David Arbour, Tung Mai, Cameron Musco, Anup Rao

Treatment effect estimation is a fundamental problem in causal inference. We focus on designing efficient randomized controlled trials, to accurately estimate the effect of some treatment on a population of $n$ individuals. In particular, we study sample-constrained treatment effect estimation, where we must select a subset of $s \ll n$ individuals from the population to experiment on. This subset must be further partitioned into treatment and control groups. Algorithms for partitioning the entire population into treatment and control groups, or for choosing a single representative subset, have been well-studied. The key challenge in our setting is jointly choosing a representative subset and a partition for that set. We focus on both individual and average treatment effect estimation, under a linear effects model. We give provably efficient experimental designs and corresponding estimators, by identifying connections to discrepancy minimization and leverage-score-based sampling used in randomized numerical linear algebra. Our theoretical results obtain a smooth transition to known guarantees when $s$ equals the population size. We also empirically demonstrate the performance of our algorithms.

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Nikhil Sheoran, Subrata Mitra, Vibhor Porwal, Siddharth Ghetia, Jatin Varshney, Tung Mai, Anup Rao, Vikas Maddukuri

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.

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Aravind Reddy, Ryan A. Rossi, Zhao Song, Anup Rao, Tung Mai, Nedim Lipka, Gang Wu, Eunyee Koh, Nesreen Ahmed

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.

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Sudhanshu Chanpuriya, Ryan A. Rossi, Anup Rao, Tung Mai, Nedim Lipka, Zhao Song, Cameron Musco

Many models for graphs fall under the framework of edge-independent dot product models. These models output the probabilities of edges existing between all pairs of nodes, and the probability of a link between two nodes increases with the dot product of vectors associated with the nodes. Recent work has shown that these models are unable to capture key structures in real-world graphs, particularly heterophilous structures, wherein links occur between dissimilar nodes. We propose the first edge-independent graph generative model that is a) expressive enough to capture heterophily, b) produces nonnegative embeddings, which allow link predictions to be interpreted in terms of communities, and c) optimizes effectively on real-world graphs with gradient descent on a cross-entropy loss. Our theoretical results demonstrate the expressiveness of our model in its ability to exactly reconstruct a graph using a number of clusters that is linear in the maximum degree, along with its ability to capture both heterophily and homophily in the data. Further, our experiments demonstrate the effectiveness of our model for a variety of important application tasks such as multi-label clustering and link prediction.

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Sridhar Mahadevan, Anup Rao, Georgios Theocharous, Jennifer Healey

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.

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Mojtaba Sahraee-Ardakan, Tung Mai, Anup Rao, Ryan Rossi, Sundeep Rangan, Alyson K. Fletcher

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.

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Enayat Ullah, Tung Mai, Anup Rao, Ryan Rossi, Raman Arora

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.

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Mohammad Mehrabi, Adel Javanmard, Ryan A. Rossi, Anup Rao, Tung Mai

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.

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Ryan A. Rossi, Nesreen K. Ahmed, Aldo Carranza, David Arbour, Anup Rao, Sungchul Kim, Eunyee Koh

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.

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David Arbour, Drew Dimmery, Anup Rao

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.

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