We present a new experiment demonstrating destructive interference in customers' estimates of conditional probabilities of product failure. We take the perspective of a manufacturer of consumer products, and consider two situations of cause and effect. Whereas individually the effect of the causes is similar, it is observed that when combined, the two causes produce the opposite effect. Such negative interference of two or more reasons may be exploited for better modeling the cognitive processes taking place in the customers' mind. Doing so can enhance the likelihood that a manufacturer will be able to design a better product, or a feature within it. Quantum probability has been used to explain some commonly observed deviations such as question order and response replicability effects, as well as in explaining paradoxes such as violations of the sure-thing principle, and Machina and Ellsberg paradoxes. In this work, we present results from a survey conducted regarding the effect of multiple observed symptoms on the drivability of a vehicle. We demonstrate that the set of responses cannot be explained using classical probability, but quantum formulation easily models it, as it allows for both positive and negative "interference" between events. Since quantum formulism also accounts for classical probability's predictions, it serves as a richer paradigm for modeling decision making behavior in engineering design and behavioral economics.

We propose a fully Bayesian framework for learning ground truth labels from noisy annotators. Our framework ensures scalability by factoring a generative, Bayesian soft clustering model over label distributions into the classic David and Skene joint annotator-data model. Earlier research along these lines has neither fully incorporated label distributions nor explored clustering by annotators only or data only. Our framework incorporates all of these properties as: (1) a graphical model designed to provide better ground truth estimates of annotator responses as input to \emph{any} black box supervised learning algorithm, and (2) a standalone neural model whose internal structure captures many of the properties of the graphical model. We conduct supervised learning experiments using both models and compare them to the performance of one baseline and a state-of-the-art model.

Despite their compelling theoretical properties, Bayesian neural networks (BNNs) tend to perform worse than frequentist methods in classification-based uncertainty quantification (UQ) tasks such as out-of-distribution (OOD) detection and dataset-shift robustness. In this work, based on empirical findings in prior works, we hypothesize that this issue is due to the avoidance of Bayesian methods in the so-called "OOD training" -- a family of techniques for incorporating OOD data during training process, which has since been an integral part of state-of-the-art frequentist UQ methods. To validate this, we treat OOD data as a first-class citizen in BNN training by exploring four different ways of incorporating OOD data in Bayesian inference. We show in extensive experiments that OOD-trained BNNs are competitive to, if not better than recent frequentist baselines. This work thus provides strong baselines for future work in both Bayesian and frequentist UQ.

Inductive program synthesis, or inferring programs from examples of desired behavior, offers a general paradigm for building interpretable, robust, and generalizable machine learning systems. Effective program synthesis depends on two key ingredients: a strong library of functions from which to build programs, and an efficient search strategy for finding programs that solve a given task. We introduce LAPS (Language for Abstraction and Program Search), a technique for using natural language annotations to guide joint learning of libraries and neurally-guided search models for synthesis. When integrated into a state-of-the-art library learning system (DreamCoder), LAPS produces higher-quality libraries and improves search efficiency and generalization on three domains -- string editing, image composition, and abstract reasoning about scenes -- even when no natural language hints are available at test time.

We advocate for a practical Maximum Likelihood Estimation (MLE) approach for regression and forecasting, as an alternative to the typical approach of Empirical Risk Minimization (ERM) for a specific target metric. This approach is better suited to capture inductive biases such as prior domain knowledge in datasets, and can output post-hoc estimators at inference time that can optimize different types of target metrics. We present theoretical results to demonstrate that our approach is always competitive with any estimator for the target metric under some general conditions, and in many practical settings (such as Poisson Regression) can actually be much superior to ERM. We demonstrate empirically that our method instantiated with a well-designed general purpose mixture likelihood family can obtain superior performance over ERM for a variety of tasks across time-series forecasting and regression datasets with different data distributions.

Explaining the predictions of opaque machine learning algorithms is an important and challenging task, especially as complex models are increasingly used to assist in high-stakes decisions such as those arising in healthcare and finance. Most popular tools for post-hoc explainable artificial intelligence (XAI) are either insensitive to context (e.g., feature attributions) or difficult to summarize (e.g., counterfactuals). In this paper, I introduce \emph{rational Shapley values}, a novel XAI method that synthesizes and extends these seemingly incompatible approaches in a rigorous, flexible manner. I leverage tools from decision theory and causal modeling to formalize and implement a pragmatic approach that resolves a number of known challenges in XAI. By pairing the distribution of random variables with the appropriate reference class for a given explanation task, I illustrate through theory and experiments how user goals and knowledge can inform and constrain the solution set in an iterative fashion. The method compares favorably to state of the art XAI tools in a range of quantitative and qualitative comparisons.

This book develops an effective theory approach to understanding deep neural networks of practical relevance. Beginning from a first-principles component-level picture of networks, we explain how to determine an accurate description of the output of trained networks by solving layer-to-layer iteration equations and nonlinear learning dynamics. A main result is that the predictions of networks are described by nearly-Gaussian distributions, with the depth-to-width aspect ratio of the network controlling the deviations from the infinite-width Gaussian description. We explain how these effectively-deep networks learn nontrivial representations from training and more broadly analyze the mechanism of representation learning for nonlinear models. From a nearly-kernel-methods perspective, we find that the dependence of such models' predictions on the underlying learning algorithm can be expressed in a simple and universal way. To obtain these results, we develop the notion of representation group flow (RG flow) to characterize the propagation of signals through the network. By tuning networks to criticality, we give a practical solution to the exploding and vanishing gradient problem. We further explain how RG flow leads to near-universal behavior and lets us categorize networks built from different activation functions into universality classes. Altogether, we show that the depth-to-width ratio governs the effective model complexity of the ensemble of trained networks. By using information-theoretic techniques, we estimate the optimal aspect ratio at which we expect the network to be practically most useful and show how residual connections can be used to push this scale to arbitrary depths. With these tools, we can learn in detail about the inductive bias of architectures, hyperparameters, and optimizers.

The limit of infinite width allows for substantial simplifications in the analytical study of overparameterized neural networks. With a suitable random initialization, an extremely large network is well approximated by a Gaussian process, both before and during training. In the present work, we establish a similar result for a simple stochastic architecture whose parameters are random variables. The explicit evaluation of the output distribution allows for a PAC-Bayesian training procedure that directly optimizes the generalization bound. For a large but finite-width network, we show empirically on MNIST that this training approach can outperform standard PAC-Bayesian methods.

In this work we develop a novel characterization of marginal causal effect and causal bias in the continuous treatment setting. We show they can be expressed as an expectation with respect to a conditional probability distribution, which can be estimated via standard statistical and probabilistic methods. All terms in the expectations can be computed via automatic differentiation, also for highly non-linear models. We further develop a new complete criterion for identifiability of causal effects via covariate adjustment, showing the bias equals zero if the criterion is met. We study the effectiveness of our framework in three different scenarios: linear models under confounding, overcontrol and endogenous selection bias; a non-linear model where full identifiability cannot be achieved because of missing data; a simulated medical study of statins and atherosclerotic cardiovascular disease.

The Schr\"odinger bridge problem (SBP) finds the most likely stochastic evolution between two probability distributions given a prior stochastic evolution. As well as applications in the natural sciences, problems of this kind have important applications in machine learning such as dataset alignment and hypothesis testing. Whilst the theory behind this problem is relatively mature, scalable numerical recipes to estimate the Schr\"odinger bridge remain an active area of research. We prove an equivalence between the SBP and maximum likelihood estimation enabling direct application of successful machine learning techniques. We propose a numerical procedure to estimate SBPs using Gaussian process and demonstrate the practical usage of our approach in numerical simulations and experiments.