We study system design problems stated as parameterized stochastic programs with a chance-constraint set. We adopt a Bayesian approach that requires the computation of a posterior predictive integral which is usually intractable. In addition, for the problem to be a well-defined convex program, we must retain the convexity of the feasible set. Consequently, we propose a variational Bayes-based method to approximately compute the posterior predictive integral that ensures tractability and retains the convexity of the feasible set. Under certain regularity conditions, we also show that the solution set obtained using variational Bayes converges to the true solution set as the number of observations tends to infinity. We also provide bounds on the probability of qualifying a true infeasible point (with respect to the true constraints) as feasible under the VB approximation for a given number of samples.

Its impact is drastic and real: Youtube's AIdriven recommendation system would present sports videos for days if one happens to watch a live baseball game on the platform [1]; email writing becomes much faster with machine learning (ML) based auto-completion [2]; many businesses have adopted natural language processing based chatbots as part of their customer services [3]. AI has also greatly advanced human capabilities in complex decision-making processes ranging from determining how to allocate security resources to protect airports [4] to games such as poker [5] and Go [6]. All such tangible and stunning progress suggests that an "AI summer" is happening. As some put it, "AI is the new electricity" [7]. Meanwhile, in the past decade, an emerging theme in the AI research community is the so-called "AI for social good" (AI4SG): researchers aim at developing AI methods and tools to address problems at the societal level and improve the wellbeing of the society.

Due to the steadily increasing relevance of machine learning for practical applications, many of which are coming with safety requirements, the notion of uncertainty has received increasing attention in machine learning research in the last couple of years. In particular, the idea of distinguishing between two important types of uncertainty, often refereed to as aleatoric and epistemic, has recently been studied in the setting of supervised learning. In this paper, we propose to quantify these uncertainties with random forests. More specifically, we show how two general approaches for measuring the learner's aleatoric and epistemic uncertainty in a prediction can be instantiated with decision trees and random forests as learning algorithms in a classification setting. In this regard, we also compare random forests with deep neural networks, which have been used for a similar purpose.

In this paper, we propose a new metric to measure goodness-of-fit for classifiers, the Real World Cost function. This metric factors in information about a real world problem, such as financial impact, that other measures like accuracy or F1 do not. This metric is also more directly interpretable for users. To optimize for this metric, we introduce the Real-World- Weight Crossentropy loss function, in both binary and single-label classification variants. Both variants allow direct input of real world costs as weights. For single-label, multicategory classification, our loss function also allows direct penalization of probabilistic false positives, weighted by label, during the training of a machine learning model. We compare the design of our loss function to the binary crossentropy and categorical crossentropy functions, as well as their weighted variants, to discuss the potential for improvement in handling a variety of known shortcomings of machine learning, ranging from imbalanced classes to medical diagnostic error to reinforcement of social bias. We create scenarios that emulate those issues using the MNIST data set and demonstrate empirical results of our new loss function. Finally, we sketch a proof of this function based on Maximum Likelihood Estimation and discuss future directions.

We describe a method for Bayesian optimization by which one may incorporate data from multiple systems whose quantitative interrelationships are unknown a priori. All general (nonreal-valued) features of the systems are associated with continuous latent variables that enter as inputs into a single metamodel that simultaneously learns the response surfaces of all of the systems. Bayesian inference is used to determine appropriate beliefs regarding the latent variables. We explain how the resulting probabilistic metamodel may be used for Bayesian optimization tasks and demonstrate its implementation on a variety of synthetic and real-world examples, comparing its performance under zero-, one-, and few-shot settings against traditional Bayesian optimization, which usually requires substantially more data from the system of interest.

Let's get the basic definition out of the way: Markov Chain Monte Carlo (MCMC) methods let us compute samples from a distribution even though we can't compute it. Let's back up and talk about Monte Carlo Sampling. What are Monte Carlo methods? "Monte Carlo methods, or Monte Carlo experiments, are a broad class of computational algorithms that rely on repeated random sampling to obtain numerical results." And you are tasked with determining the area enclosed by this shape.

Flow-based generative models parameterize probability distributions through an invertible transformation and can be trained by maximum likelihood. Invertible residual networks provide a flexible family of transformations where only Lipschitz conditions rather than strict architectural constraints are needed for enforcing invertibility. However, prior work trained invertible residual networks for density estimation by relying on biased log-density estimates whose bias increased with the network's expressiveness. We give a tractable unbiased estimate of the log density using a "Russian roulette" estimator, and reduce the memory required during training by using an alternative infinite series for the gradient. Furthermore, we improve invertible residual blocks by proposing the use of activation functions that avoid derivative saturation and generalizing the Lipschitz condition to induced mixed norms. The resulting approach, called Residual Flows, achieves state-of-theart performance on density estimation amongst flow-based models, and outperforms networks that use coupling blocks at joint generative and discriminative modeling.

Learning in Gaussian Process models occurs through the adaptation of hyperparameters of the mean and the covariance function. The classical approach entails maximizing the marginal likelihood yielding fixed point estimates (an approach called \textit{Type II maximum likelihood} or ML-II). An alternative learning procedure is to infer the posterior over hyperparameters in a hierarchical specification of GPs we call \textit{Fully Bayesian Gaussian Process Regression} (GPR). This work considers two approximation schemes for the intractable hyperparameter posterior: 1) Hamiltonian Monte Carlo (HMC) yielding a sampling-based approximation and 2) Variational Inference (VI) where the posterior over hyperparameters is approximated by a factorized Gaussian (mean-field) or a full-rank Gaussian accounting for correlations between hyperparameters. We analyze the predictive performance for fully Bayesian GPR on a range of benchmark data sets.

Robustness to out-of-distribution (OOD) data is an important goal in building reliable machine learning systems. Especially in autonomous systems, wrong predictions for OOD inputs can cause safety critical situations. As a first step towards a solution, we consider the problem of detecting such data in a value-based deep reinforcement learning (RL) setting. Modelling this problem as a one-class classification problem, we propose a framework for uncertainty-based OOD classification: UBOOD. It is based on the effect that an agent's epistemic uncertainty is reduced for situations encountered during training (in-distribution), and thus lower than for unencountered (OOD) situations. Being agnostic towards the approach used for estimating epistemic uncertainty, combinations with different uncertainty estimation methods, e.g. approximate Bayesian inference methods or ensembling techniques are possible. We further present a first viable solution for calculating a dynamic classification threshold, based on the uncertainty distribution of the training data. Evaluation shows that the framework produces reliable classification results when combined with ensemble-based estimators, while the combination with concrete dropout-based estimators fails to reliably detect OOD situations. In summary, UBOOD presents a viable approach for OOD classification in deep RL settings by leveraging the epistemic uncertainty of the agent's value function.

Sequence generation models are commonly refined with reinforcement learning over user-defined metrics. However, high gradient variance hinders the practical use of this method. To stabilize this method, we adapt to contextual generation of categorical sequences a policy gradient estimator, which evaluates a set of correlated Monte Carlo (MC) rollouts for variance control. Due to the correlation, the number of unique rollouts is random and adaptive to model uncertainty; those rollouts naturally become baselines for each other, and hence are combined to effectively reduce gradient variance. We also demonstrate the use of correlated MC rollouts for binary-tree softmax models, which reduce the high generation cost in large vocabulary scenarios by decomposing each categorical action into a sequence of binary actions. We evaluate our methods on both neural program synthesis and image captioning. The proposed methods yield lower gradient variance and consistent improvement over related baselines.