Conditional randomization tests (CRTs) assess whether a variable $x$ is predictive of another variable $y$, having observed covariates $z$. CRTs require fitting a large number of predictive models, which is often computationally intractable. Existing solutions to reduce the cost of CRTs typically split the dataset into a train and test portion, or rely on heuristics for interactions, both of which lead to a loss in power. We propose the decoupled independence test (DIET), an algorithm that avoids both of these issues by leveraging marginal independence statistics to test conditional independence relationships. DIET tests the marginal independence of two random variables: $F_{x\vert z}(x \vert z)$ and $F_{y\vert z}(y \vert z)$ where $F_{\cdot \vert z}(\cdot \vert z)$ is a conditional cumulative distribution function (CDF) for the distribution $p(\cdot \vert z)$. These variables are termed “information residuals.” We give sufficient conditions for DIET to achieve finite sample type-1 error control and power greater than the type-1 error rate. We then prove that when using the mutual information between the information residuals as a test statistic, DIET yields the most powerful conditionally valid test. Finally, we show DIET achieves higher power than other tractable CRTs on several synthetic and real benchmarks.

Quantile regression is the task of estimating a specified percentile response, such as the median (50th percentile), from a collection of known covariates. We study quantile regression with rectified linear unit (ReLU) neural networks as the chosen model class. We derive an upper bound on the expected mean squared error of a ReLU network used to estimate any quantile conditioning on a set of covariates. This upper bound only depends on the best possible approximation error, the number of layers in the network, and the number of nodes per layer. We further show upper bounds that are tight for two large classes of functions: compositions of Hölder functions and members of a Besov space. These tight bounds imply ReLU networks with quantile regression achieve minimax rates for broad collections of function types. Unlike existing work, the theoretical results hold under minimal assumptions and apply to general error distributions, including heavy-tailed distributions. Empirical simulations on a suite of synthetic response functions demonstrate the theoretical results translate to practical implementations of ReLU networks. Overall, the theoretical and empirical results provide insight into the strong performance of ReLU neural networks for quantile regression across a broad range of function classes and error distributions. All code for this paper is publicly available at https://github.com/tansey/quantile-regression.

Predictive modeling often uses black box machine learning methods, such as deep neural networks, to achieve state-of-the-art performance. In scientific domains, the scientist often wishes to discover which features are actually important for making the predictions. These discoveries may lead to costly follow-up experiments and as such it is important that the error rate on discoveries is not too high. Model-X knockoffs enable important features to be discovered with control of the false discovery rate (FDR). However, knockoffs require rich generative models capable of accurately modeling the knockoff features while ensuring they obey the so-called "swap" property. We develop Deep Direct Likelihood Knockoffs (DDLK), which directly minimizes the KL divergence implied by the knockoff swap property. DDLK consists of two stages: it first maximizes the explicit likelihood of the features, then minimizes the KL divergence between the joint distribution of features and knockoffs and any swap between them. To ensure that the generated knockoffs are valid under any possible swap, DDLK uses the Gumbel-Softmax trick to optimize the knockoff generator under the worst-case swap. We find DDLK has higher power than baselines while controlling the false discovery rate on a variety of synthetic and real benchmarks including a task involving the largest COVID-19 health record dataset in the United States.

Analyzing large-scale, multi-experiment studies requires scientists to test each experimental outcome for statistical significance and then assess the results as a whole. We present Black Box FDR (BB-FDR), an empirical-Bayes method for analyzing multi-experiment studies when many covariates are gathered per experiment. BB-FDR learns a series of black box predictive models to boost power and control the false discovery rate (FDR) at two stages of study analysis. In Stage 1, it uses a deep neural network prior to report which experiments yielded significant outcomes. In Stage 2, a separate black box model of each covariate is used to select features that have significant predictive power across all experiments. In benchmarks, BB-FDR outperforms competing state-of-the-art methods in both stages of analysis. We apply BB-FDR to two real studies on cancer drug efficacy. For both studies, BB-FDR increases the proportion of significant outcomes discovered and selects variables that reveal key genomic drivers of drug sensitivity and resistance in cancer.

We present Vector-Space Markov Random Fields (VS-MRFs), a novel class of undirected graphical models where each variable can belong to an arbitrary vector space. VS-MRFs generalize a recent line of work on scalar-valued, uni-parameter exponential family and mixed graphical models, thereby greatly broadening the class of exponential families available (e.g., allowing multinomial and Dirichlet distributions). Specifically, VS-MRFs are the joint graphical model distributions where the node-conditional distributions belong to generic exponential families with general vector space domains. We also present a sparsistent M-estimator for learning our class of MRFs that recovers the correct set of edges with high probability. We validate our approach via a set of synthetic data experiments as well as a real-world case study of over four million foods from the popular diet tracking app MyFitnessPal. Our results demonstrate that our algorithm performs well empirically and that VS-MRFs are capable of capturing and highlighting interesting structure in complex, real-world data. All code for our algorithm is open source and publicly available.

Social learning is an extension to evolutionary algorithms that enables agents to learn from observations of others in the population. Historically, social learning algorithms have employed a student-teacher model where the behavior of one or more high-fitness agents is used to train a subset of the remaining agents in the population. This paper presents ESL, an egalitarian model of social learning in which agents are not labeled as teachers or students, instead allowing any individual receiving a sufficiently high reward to teach other agents to mimic its recent behavior. We validate our approach through a series of experiments in a robot foraging domain, including comparisons of egalitarian social learning with baseline neuroevolution and a variant of student-teacher social learning. In a complex foraging task, ESL converges to near-optimal strategies faster than either benchmark approach, outperforming both by more than an order of magnitude. The results indicate that egalitarian social learning is a promising new paradigm for social learning in intelligent agents.

We present an automated approach for marshaling C++ data structures in high performance computing (HPC) applications. Our approach utilizes a graphical editor through which the user can express a subset of an object's state to be marshaled and sent across a network. Our tool, MPI serializer, then automatically generates efficient marshaling and unmarshaling code for use with the message passing interface (MPI), the predominant communication middleware for HPC systems. Our approach provides a more comprehensive level of support for C++ language features than the existing state of the art, and does so in full compliance with the C++ language standard. Specifically, we can marshal effectively and efficiently non-trivial language constructs such as polymorphic pointers, dynamically allocated arrays, non-public member fields, inherited members, and STL container classes. Additionally, our marshaling approach is also applicable to third party libraries, as it does not require any modifications to the existing C++ source code. We validate our approach through two case studies of applying our tool to automatically generate the marshaling functionality of two realistic HPC applications. The case studies demonstrate that the automatically generated code matches the performance of typical hand-written implementations and surpasses current state-of-the-art C++ marshaling libraries, in some cases by more than an order of magnitude. The results of our case studies indicate that our approach can be beneficial for both the initial construction of HPC applications as well as for the refactoring of sequential applications for parallel execution.

Since annotations were added to the Java language, many frameworks have moved to using annotated Plain Old Java Objects (POJOs) in their newest releases. Legacy applications are thus forced to undergo extensive restructuring in order to migrate from old framework versions to new versions based on annotations (Version Lock-in). Additionally, because annotations are embedded in the application code, changing between framework vendors may also entail largescale manual changes (Vendor Lock-in).