There is an increasing conflict between business incentives to hide models and data as trade secrets, and the societal need for algorithmic transparency. For example, a rightsholder who currently wishes to know whether their copyrighted works have been used during training must convince the model provider to allow a third party to audit the model and data. Finding a mutually agreeable third party is difficult, and the associated costs often make this approach impractical. In this work, we show that it is possible to simultaneously allow model providers to keep their models and data secret while allowing other parties to trustlessly audit properties of the model and data. We do this by designing a protocol called ZkAudit in which model providers publish cryptographic commitments of datasets and model weights, alongside a zero-knowledge proof (ZKP) certifying that published commitments are derived from training the model. Model providers can then respond to audit requests by privately computing any function F of the dataset (or model) and releasing the output of F alongside another ZKP certifying the correct execution of F. To enable ZkAudit, we develop new methods of computing ZKPs for SGD on modern neural nets for recommender systems and image classification models capable of high accuracies on ImageNet. Empirically, we show it is possible to provide trustless audits of DNNs, including copyright, censorship, and counterfactual audits with little to no loss in accuracy.

Analysts and scientists are interested in querying streams of video, audio, and text to extract quantitative insights. For example, an urban planner may wish to measure congestion by querying the live feed from a traffic camera. Prior work has used deep neural networks (DNNs) to answer such queries in the batch setting. However, much of this work is not suited for the streaming setting because it requires access to the entire dataset before a query can be submitted or is specific to video. Thus, to the best of our knowledge, no prior work addresses the problem of efficiently answering queries over multiple modalities of streams. In this work we propose InQuest, a system for accelerating aggregation queries on unstructured streams of data with statistical guarantees on query accuracy. InQuest leverages inexpensive approximation models ("proxies") and sampling techniques to limit the execution of an expensive high-precision model (an "oracle") to a subset of the stream. It then uses the oracle predictions to compute an approximate query answer in real-time. We theoretically analyzed InQuest and show that the expected error of its query estimates converges on stationary streams at a rate inversely proportional to the oracle budget. We evaluated our algorithm on six real-world video and text datasets and show that InQuest achieves the same root mean squared error (RMSE) as two streaming baselines with up to 5.0x fewer oracle invocations. We further show that InQuest can achieve up to 1.9x lower RMSE at a fixed number of oracle invocations than a state-of-the-art batch setting algorithm.

Though data augmentation has rapidly emerged as a key tool for optimization in modern machine learning, a clear picture of how augmentation schedules affect optimization and interact with optimization hyperparameters such as learning rate is nascent. In the spirit of classical convex optimization and recent work on implicit bias, the present work analyzes the effect of augmentation on optimization in the simple convex setting of linear regression with MSE loss.We find joint schedules for learning rate and data augmentation scheme under which augmented gradient descent provably converges and characterize the resulting minimum. Our results apply to arbitrary augmentation schemes, revealing complex interactions between learning rates and augmentations even in the convex setting. Our approach interprets augmented (S)GD as a stochastic optimization method for a time-varying sequence of proxy losses. This gives a unified way to analyze learning rate, batch size, and augmentations ranging from additive noise to random projections. From this perspective, our results, which also give rates of convergence, can be viewed as Monro-Robbins type conditions for augmented (S)GD.

Researchers and industry analysts are increasingly interested in computing aggregation queries over large, unstructured datasets with selective predicates that are computed using expensive deep neural networks (DNNs). As these DNNs are expensive and because many applications can tolerate approximate answers, analysts are interested in accelerating these queries via approximations. Unfortunately, standard approximate query processing techniques to accelerate such queries are not applicable because they assume the result of the predicates are available ahead of time. Furthermore, recent work using cheap approximations (i.e., proxies) do not support aggregation queries with predicates. To accelerate aggregation queries with expensive predicates, we develop and analyze a query processing algorithm that leverages proxies (ABAE). ABAE must account for the key challenge that it may sample records that do not satisfy the predicate. To address this challenge, we first use the proxy to group records into strata so that records satisfying the predicate are ideally grouped into few strata. Given these strata, ABAE uses pilot sampling and plugin estimates to sample according to the optimal allocation. We show that ABAE converges at an optimal rate in a novel analysis of stratified sampling with draws that may not satisfy the predicate. We further show that ABAE outperforms on baselines on six real-world datasets, reducing labeling costs by up to 2.3X.

We analyze directed, unweighted graphs obtained from x_i∈\RR^d by connecting vertex i to j iff |x_i - x_j| < ε(x_i). Examples of such graphs include k-nearest neighbor graphs, where ε(x_i) varies from point to point, and, arguably, many real world graphs such as co-purchasing graphs. We ask whether we can recover the underlying Euclidean metric ε(x_i) and the associated density p(x_i) given only the directed graph and d. We show that consistent recovery is possible up to isometric scaling when the vertex degree is at least ω(n^2/(2+d)\log(n)^d/(d+2)). Our estimator is based on a careful characterization of a random walk over the directed graph and the associated continuum limit. As an algorithm, it resembles the PageRank centrality metric. We demonstrate empirically that the estimator performs well on simulated examples as well as on real-world co-purchasing graphs even with a small number of points and degree scaling as low as \log(n).

Large unweighted directed graphs are commonly used to capture relations between entities. A fundamental problem in the analysis of such networks is to properly define the similarity or dissimilarity between any two vertices. Despite the significance of this problem, statistical characterization of the proposed metrics has been limited.We introduce and develop a class of techniques for analyzing random walks on graphs using stochastic calculus. Using these techniques we generalize results on the degeneracy of hitting times and analyze a metric based on the Laplace transformed hitting time (LTHT). The metric serves as a natural, provably well-behaved alternative to the expected hitting time. We establish a general correspondence between hitting times of the Brownian motion and analogous hitting times on the graph. We show that the LTHT is consistent with respect to the underlying metric of a geometric graph, preserves clustering tendency, and remains robust against random addition of non-geometric edges. Tests on simulated and real-world data show that the LTHT matches theoretical predictions and outperforms alternatives.

We study the attribution problem. That is, given a real-valued characteristic function f of n variables and initial and final values r and s for its independent variables, our objective is to divide the responsibility for the change f(s) - f(r) in the characteristic function among each of its independent variables. We call these assigned responsibilities attributions, and we would like the attributions to form a complete partition of the total change. When r=0, the attribution problem coincides with a standard cost sharing model from the social choice literature (cf. Moulin [2]), where the characteristic function is the cost function, the independent variables are the demands of the agents, and the attributions are cost shares for the agents. We follow the cost sharing literature in identifying good attribution methods axiomatically (for a classical example, see Friedman and Moulin [1]). We consider: Additivity -- attributions are additive in the characteristic function, Dummy -- if the characteristic function does not depend on a variable, then its attribution is zero, and Affine Scale Invariance -- attributions are invariant under simultaneous affine transformation of the characteristic function and the variables.