The attribution problem, that is the problem of attributing a model’s prediction to its base features, is well-studied. We extend the notion of attribution to also apply to feature interactions. The Shapley value is a commonly used method to attribute a model’s prediction to its base features. We propose a generalization of the Shapley value called Shapley-Taylor index that attributes the model’s prediction to interactions of subsets of features up to some size $k$. The method is analogous to how the truncated Taylor Series decomposes the function value at a certain point using its derivatives at a different point. In fact, we show that the Shapley Taylor index is equal to the Taylor Series of the multilinear extension of the set-theoretic behavior of the model. We axiomatize this method using the standard Shapley axioms—linearity, dummy, symmetry and efficiency—and an additional axiom that we call the interaction distribution axiom. This new axiom explicitly characterizes how interactions are distributed for a class of functions that model pure interaction. We contrast the Shapley-Taylor index against the previously proposed Shapley Interaction index from the cooperative game theory literature. We also apply the Shapley Taylor index to three models and identify interesting qualitative insights.

We present several approximation algorithms for the problem of embedding metric spaces into a line, and into the 2-dimensional plane. Among other results, we give an $O(\sqrt{n})$-approximation algorithm for the problem of finding a line embedding of a metric induced by a given unweighted graph, that minimizes the (standard) multiplicative distortion. We give an improved $\tilde{O}(n^{1/3})$ approximation for the case of metrics induced by unweighted trees.

We analyze state-of-the-art deep learning models for three tasks: question answering on (1) images, (2) tables, and (3) passages of text.Using the notion of attribution (word importance), we find that these deep networks often ignore important question terms.Leveraging such behavior, we perturb questions to craft a variety of adversarial examples.Our strongest attacks drop the accuracy of a visual question answering model from 61.1% to 19%, and that of a tabular question answering model from 33.5% to 3.3%.Additionally, we show how attributions can strengthen attacks proposed by Jia and Liang (2017) on paragraph comprehension models.Our results demonstrate that attributions can augment standard measures of accuracy and empower investigation of model performance.When a model is accurate but for the wrong reasons, attributions can surface erroneous logic in the model that indicates inadequacies in the test data.

We describe Analyza, a system that helps lay users explore data. Analyza has been used within two large real world systems. The first is a question-and-answer feature in a spreadsheet product. The second provides convenient access to a revenue/inventory database for a large sales force. Both user bases consist of users who do not necessarily have coding skills, demonstrating Analyza's ability to democratize access to data. We discuss the key design decisions in implementing this system. For instance, how to mix structured and natural language modalities, how to use conversation to disambiguate and simplify querying, how to rely on the ``semantics' of the data to compensate for the lack of syntactic structure, and how to efficiently curate the data.

We consider the problem of embedding finite metrics with slack: We seek to produce embeddings with small dimension and distortion while allowing a (small) constant fraction of all distances to be arbitrarily distorted. This definition is motivated by recent research in the networking community, which achieved striking empirical success at embedding Internet latencies with low distortion into low-dimensional Euclidean space, provided that some small slack is allowed. Answering an open question of Kleinberg, Slivkins, and Wexler [in Proceedings of the 45th IEEE Symposium on Foundations of Computer Science, 2004], we show that provable guarantees of this type can in fact be achieved in general: Any finite metric space can be embedded, with constant slack and constant distortion, into constant-dimensional Euclidean space. We then show that there exist stronger embeddings into $\ell_1$ which exhibit gracefully degrading distortion: There is a single embedding into $\ell_1$ that achieves distortion at most $O(\log\frac{1}{\epsilon})$ on all but at most-1.5pt an $\epsilon$ fraction of distances simultaneously for all $\epsilon>0$. We extend this with distortion1pt $O(\log\frac{1}{\epsilon})^{1/p}$ to maps into general $\ell_p$, $p\geq1$, for several classes of metrics, including those with bounded doubling dimension and those arising from the shortest-path metric of a graph with an excluded minor. Finally, we show that many of our constructions are tight and give a general technique to obtain lower bounds for $\epsilon$-slack embeddings from lower bounds for low-distortion embeddings.

We consider the problem of minimizing the total weighted flow time on a single machine with preemptions. We give an online algorithm that is O ( k )-competitive for k weight classes. This implies an O (log W )-competitive algorithm, where W is the maximum to minimum ratio of weights. This algorithm also implies an O (log n + log P )-approximation ratio for the problem, where P is the ratio of the maximum to minimum job size and n is the number of jobs. We also consider the nonclairvoyant setting where the size of a job is unknown upon its arrival and becomes known to the scheduler only when the job meets its service requirement. We consider the resource augmentation model, and give a (1 + ε)-speed, (1 +1/ε)-competitive online algorithm.

We consider the problem of reconstructing near-perfect phylogenetic trees using binary character states (referred to as BNPP). A perfect phylogeny assumes that every character mutates at most once in the evolutionary tree, yielding an algorithm for binary character states that is computationally efficient but not robust to imperfections in real data. A near-perfect phylogeny relaxes the perfect phylogeny assumption by allowing at most a constant number of additional mutations. We develop two algorithms for constructing optimal near-perfect phylogenies and provide empirical evidence of their performance. The first simple algorithm is fixed parameter tractable when the number of additional mutations and the number of characters that share four gametes with some other character are constants. The second, more involved algorithm for the problem is fixed parameter tractable when only the number of additional mutations is fixed. We have implemented both algorithms and shown them to be extremely efficient in practice on biologically significant data sets. This work proves the BNPP problem fixed parameter tractable and provides the first practical phylogenetic tree reconstruction algorithms that find guaranteed optimal solutions while being easily implemented and computationally feasible for data sets of biologically meaningful size and complexity.

We consider the problem of embedding finite metrics with slack: we seek to produce embeddings with small dimension and distortion while allowing a (small) constant fraction of all distances to be arbitrarily distorted. This definition is motivated by recent research in the networking community, which achieved striking empirical success at embedding Internet latencies with low distortion into low-dimensional Euclidean space, provided that some small slack is allowed. Answering an open question of Kleinberg, Slivkins, and Wexler (2004), we show that provable guarantees of this type can in fact be achieved in general: any finite metric can be embedded, with constant slack and constant distortion, into constant-dimensional Euclidean space. We then show that there exist stronger embeddings into /spl lscr//sub 1/ which exhibit gracefully degrading distortion: these is a single embedding into /spl lscr//sub 1/ that achieves distortion at most O(log 1//spl epsi/) on all but at most an /spl epsi/ fraction of distances, simultaneously for all /spl epsi/ > 0. We extend this with distortion O(log 1//spl epsi/)/sup 1/p/ to maps into general /spl lscr//sub p/, p /spl ges/ 1 for several classes of metrics, including those with bounded doubling dimension and those arising from the shortest-path metric of a graph with an excluded minor. Finally, we show that many of our constructions are tight, and give a general technique to obtain lower bounds for /spl epsi/-slack embeddings from lower bounds for low-distortion embeddings.

Robust optimization has traditionally focused on uncertainty in data and costs in optimization problems to formulate models whose solutions will be optimal in the worst-case among the various uncertain scenarios in the model. While these approaches may be thought of defining data- or cost-robust problems, we formulate a new "demand-robust" model motivated by recent work on two-stage stochastic optimization problems. We propose this in the framework of general covering problems and prove a general structural lemma about special types of first-stage solutions for such problems: there exists a first-stage solution that is a minimal feasible solution for the union of the demands for some subset of the scenarios and its objective function value is no more than twice the optimal. We then provide approximation algorithms for a variety of standard discrete covering problems in this setting, including minimum cut, minimum multi-cut, shortest paths, Steiner trees, vertex cover and un-capacitated facility location. While many of our results draw from rounding approaches recently developed for stochastic programming problems, we also show new applications of old metric rounding techniques for cut problems in this demand-robust setting.

We consider the problem of maintaining frequency counts for items occurring frequently in the union of multiple distributed data streams. Naive methods of combining approximate frequency counts from multiple nodes tend to result in excessively large data structures that are costly to transfer among nodes. To minimize communication requirements, the degree of precision maintained by each node while counting item frequencies must be managed carefully. We introduce the concept of a precision gradient for managing precision when nodes are arranged in a hierarchical communication structure. We then study the optimization problem of how to set the precision gradient so as to minimize communication, and provide optimal solutions that minimize worst-case communication load over all possible inputs. We then introduce a variant designed to perform well in practice, with input data that does not conform to worst-case characteristics. We verify the effectiveness of our approach empirically using real-world data, and show that our methods incur substantially less communication than naive approaches while providing the same error guarantees on answers.