Modern reinforcement learning and planning algorithms have achieved tremendous successes on various tasks [Mnih et al., 2015, Silver et al., 2017]. However, most of these algorithms work in the standard Markov decision process (MDP) framework where the goal is to maximize the cumulative reward and thus it can be difficult to apply them to various practical sequential decision-making problems. In this paper, we study planning in generalized MDPs, where instead of maximizing the cumulative reward, the goal is to maximize the objective value induced by a submodular function. To motivate our approach, let us consider the following scenario: a company manufactures cars, and as part of its customer service, continuously monitors the status of all cars produced by the company. Each car is equipped with a number of sensors, each of which constantly produces noisy measurements of some attribute of the car, e.g., speed, location, temperature, etc. Due to bandwidth constraints, at any moment, each car may choose to transmit data generated by a single sensor to the company. The goal is to combine the statistics collected over a fixed period of time, presumably from multiple sensors, to gather as much information about the car as possible. Perhaps one seemingly natural strategy is to transmit only data generated by the most "informative" sensor. However, as the output of a sensor remains the same between two samples, it is pointless to transmit the same data multiple times. One may alternatively try to order sensors by their "informativity" and always choose the most informative sensor that has not yet transmitted data since the last sample was generated.

We present two methods to reduce the complexity of Bayesian network (BN) classifiers. First, we introduce quantization-aware training using the straight-through gradient estimator to quantize the parameters of BNs to few bits. Second, we extend a recently proposed differentiable tree-augmented naive Bayes (TAN) structure learning approach by also considering the model size. Both methods are motivated by recent developments in the deep learning community, and they provide effective means to trade off between model size and prediction accuracy, which is demonstrated in extensive experiments. Furthermore, we contrast quantized BN classifiers with quantized deep neural networks (DNNs) for small-scale scenarios which have hardly been investigated in the literature. We show Pareto optimal models with respect to model size, number of operations, and test error and find that both model classes are viable options.

We study reinforcement learning (RL) for text-based games, which are interactive simulations in the context of natural language. While different methods have been developed to represent the environment information and language actions, existing RL agents are not empowered with any reasoning capabilities to deal with textual games. In this work, we aim to conduct explicit reasoning with knowledge graphs for decision making, so that the actions of an agent are generated and supported by an interpretable inference procedure. We propose a stacked hierarchical attention mechanism to construct an explicit representation of the reasoning process by exploiting the structure of the knowledge graph. We extensively evaluate our method on a number of man-made benchmark games, and the experimental results demonstrate that our method performs better than existing text-based agents.

Discrete latent spaces in variational autoencoders have been shown to effectively capture the data distribution for many real-world problems such as natural language understanding, human intent prediction, and visual scene representation. However, discrete latent spaces need to be sufficiently large to capture the complexities of real-world data, rendering downstream tasks computationally challenging. For instance, performing motion planning in a high-dimensional latent representation of the environment could be intractable. We consider the problem of sparsifying the discrete latent space of a trained conditional variational autoencoder, while preserving its learned multimodality. As a post hoc latent space reduction technique, we use evidential theory to identify the latent classes that receive direct evidence from a particular input condition and filter out those that do not. Experiments on diverse tasks, such as image generation and human behavior prediction, demonstrate the effectiveness of our proposed technique at reducing the discrete latent sample space size of a model while maintaining its learned multimodality.

A support vector machine (SVM) is a supervised machine learning model that uses classification algorithms for two-group classification problems. After giving an SVM model sets of labeled training data for each category, they're able to categorize new text. You're refining your training data, and maybe you've even tried stuff out using Naive Bayes. But now you're feeling confident in your dataset, and want to take it one step further. Enter Support Vector Machines (SVM): a fast and dependable classification algorithm that performs very well with a limited amount of data to analyze.

Specifying a Bayesian prior is notoriously difficult for complex models such as neural networks. Reasoning about parameters is made challenging by the high-dimensionality and over-parameterization of the space. Priors that seem benign and uninformative can have unintuitive and detrimental effects on a model's predictions. For this reason, we propose predictive complexity priors: a functional prior that is defined by comparing the model's predictions to those of a reference model. Although originally defined on the model outputs, we transfer the prior to the model parameters via a change of variables. The traditional Bayesian workflow can then proceed as usual. We apply our predictive complexity prior to high-dimensional regression, reasoning over neural network depth, and sharing of statistical strength for few-shot learning.

Decision trees (DTs) epitomize what have become to be known as interpretable machine learning (ML) models. This is informally motivated by paths in DTs being often much smaller than the total number of features. This paper shows that in some settings DTs can hardly be deemed interpretable, with paths in a DT being arbitrarily larger than a PI-explanation, i.e. a subset-minimal set of feature values that entails the prediction. As a result, the paper proposes a novel model for computing PI-explanations of DTs, which enables computing one PI-explanation in polynomial time. Moreover, it is shown that enumeration of PI-explanations can be reduced to the enumeration of minimal hitting sets. Experimental results were obtained on a wide range of publicly available datasets with well-known DT-learning tools, and confirm that in most cases DTs have paths that are proper supersets of PI-explanations.

A decision tree is commonly restricted to use a single hyperplane to split the covariate space at each of its internal nodes. It often requires a large number of nodes to achieve high accuracy, hurting its interpretability. In this paper, we propose convex polytope trees (CPT) to expand the family of decision trees by an interpretable generalization of their decision boundary. The splitting function at each node of CPT is based on the logical disjunction of a community of differently weighted probabilistic linear decision-makers, which also geometrically corresponds to a convex polytope in the covariate space. We use a nonparametric Bayesian prior at each node to infer the community's size, encouraging simpler decision boundaries by shrinking the number of polytope facets. We develop a greedy method to efficiently construct CPT and scalable end-to-end training algorithms for the tree parameters when the tree structure is given. We empirically demonstrate the efficiency of CPT over existing state-of-the-art decision trees in several real-world classification and regression tasks from diverse domains.

The traditional binary classification framework constructs classifiers which may have good accuracy, but whose false positive and false negative error rates are not under users' control. In many cases, one of the errors is more severe and only the classifiers with the corresponding rate lower than the predefined threshold are acceptable. In this study, we combine binary classification with statistical hypothesis testing to control the target error rate of already trained classifiers. In particular, we show how to turn binary classifiers into statistical tests, calculate the classification p-values, and use them to limit the target error rate.

Domains where supervised models are deployed often come with task-specific constraints, such as prior expert knowledge on the ground-truth function, or desiderata like safety and fairness. We introduce a novel probabilistic framework for reasoning with such constraints and formulate a prior that enables us to effectively incorporate them into Bayesian neural networks (BNNs), including a variant that can be amortized over tasks. The resulting Output-Constrained BNN (OC-BNN) is fully consistent with the Bayesian framework for uncertainty quantification and is amenable to black-box inference. Unlike typical BNN inference in uninterpretable parameter space, OC-BNNs widen the range of functional knowledge that can be incorporated, especially for model users without expertise in machine learning. We demonstrate the efficacy of OC-BNNs on real-world datasets, spanning multiple domains such as healthcare, criminal justice, and credit scoring.