Deep generative models trained by maximum likelihood remain very popular methods for reasoning about data probabilistically. However, it has been observed that they can assign higher likelihoods to out-of-distribution (OOD) data than in-distribution data, thus calling into question the meaning of these likelihood values. In this work we provide a novel perspective on this phenomenon, decomposing the average likelihood into a KL divergence term and an entropy term. We argue that the latter can explain the curious OOD behaviour mentioned above, suppressing likelihood values on datasets with higher entropy. Although our idea is simple, we have not seen it explored yet in the literature. This analysis provides further explanation for the success of OOD detection methods based on likelihood ratios, as the problematic entropy term cancels out in expectation. Finally, we discuss how this observation relates to recent success in OOD detection with manifold-supported models, for which the above decomposition does not hold.

Supervised learning is the machine learning task of learning a function that maps an input to an output based on example input-output pairs. A supervised learning algorithm analyzes the training data and produces an inferred function, which can be used later for mapping new examples. The most popular supervised learning tasks are: Regression and Classification. The result of solving the regression task is a model that can make numerical predictions. The result of solving the classification task is a model that can make classes predictions.

Active inference, a corollary of the free energy principle, is a formal way of describing the behavior of certain kinds of random dynamical systems that have the appearance of sentience. In this chapter, we describe how active inference combines Bayesian decision theory and optimal Bayesian design principles under a single imperative to minimize expected free energy. It is this aspect of active inference that allows for the natural emergence of information-seeking behavior. When removing prior outcomes preferences from expected free energy, active inference reduces to optimal Bayesian design, i.e., information gain maximization. Conversely, active inference reduces to Bayesian decision theory in the absence of ambiguity and relative risk, i.e., expected utility maximization. Using these limiting cases, we illustrate how behaviors differ when agents select actions that optimize expected utility, expected information gain, and expected free energy. Our T-maze simulations show optimizing expected free energy produces goal-directed information-seeking behavior while optimizing expected utility induces purely exploitive behavior and maximizing information gain engenders intrinsically motivated behavior.

In many fields of science and engineering, models with different fidelities are available. Physical experiments or detailed simulations that accurately capture the behavior of the system are regarded as high-fidelity models with low model uncertainty, however, they are expensive to run. On the other hand, simplified physical experiments or numerical models are seen as low-fidelity models that are cheaper to evaluate. Although low-fidelity models are often not suitable for direct use in reliability analysis due to their low accuracy, they can offer information about the trend of the high-fidelity model thus providing the opportunity to explore the design space at a low cost. This study presents a new approach called adaptive multi-fidelity Gaussian process for reliability analysis (AMGPRA). Contrary to selecting training points and information sources in two separate stages as done in state-of-the-art mfEGRA method, the proposed approach finds the optimal training point and information source simultaneously using the novel collective learning function (CLF). CLF is able to assess the global impact of a candidate training point from an information source and it accommodates any learning function that satisfies a certain profile. In this context, CLF provides a new direction for quantifying the impact of new training points and can be easily extended with new learning functions to adapt to different reliability problems. The performance of the proposed method is demonstrated by three mathematical examples and one engineering problem concerning the wind reliability of transmission towers. It is shown that the proposed method achieves similar or higher accuracy with reduced computational costs compared to state-of-the-art single and multi-fidelity methods. A key application of AMGPRA is high-fidelity fragility modeling using complex and costly physics-based computational models.

Deep Learning is a specialized form of machine learning which utilizes supervised, unsupervised and semi-supervised learning to learn data representations. It is similar to the structure and function of the human nervous system, where a complex network of interconnected computing units works in a coordinated way to process complex information. An artificial neural network is a computer system made up of several simple and highly interconnected processing elements which process information by their dynamic state response to external inputs. Feature of Neural Network - Cluster and classify the raw input. Naive Bayes - Is a simple but surprisingly powerful algorithm for predictive modeling.

Causal effect estimation for dynamic treatment regimes (DTRs) contributes to sequential decision making. However, censoring and time-dependent confounding under DTRs are challenging as the amount of observational data declines over time due to a reducing sample size but the feature dimension increases over time. Long-term follow-up compounds these challenges. Another challenge is the highly complex relationships between confounders, treatments, and outcomes, which causes the traditional and commonly used linear methods to fail. We combine outcome regression models with treatment models for high dimensional features using uncensored subjects that are small in sample size and we fit deep Bayesian models for outcome regression models to reveal the complex relationships between confounders, treatments, and outcomes. Also, the developed deep Bayesian models can model uncertainty and output the prediction variance which is essential for the safety-aware applications, such as self-driving cars and medical treatment design. The experimental results on medical simulations of HIV treatment show the ability of the proposed method to obtain stable and accurate dynamic causal effect estimation from observational data, especially with long-term follow-up. Our technique provides practical guidance for sequential decision making, and policy-making.

In recent years, machine learning (ML) algorithms have been deployed in safety-critical and high-stake decision-making, where the fairness of algorithms is of paramount importance. Fairness in ML centers on detecting bias towards certain demographic populations induced by an ML classifier and proposes algorithmic solutions to mitigate the bias with respect to different fairness definitions. To this end, several fairness verifiers have been proposed that compute the bias in the prediction of an ML classifier -- essentially beyond a finite dataset -- given the probability distribution of input features. In the context of verifying linear classifiers, existing fairness verifiers are limited by accuracy due to imprecise modelling of correlations among features and scalability due to restrictive formulations of the classifiers as SSAT or SMT formulas or by sampling. In this paper, we propose an efficient fairness verifier, called FVGM, that encodes the correlations among features as a Bayesian network. In contrast to existing verifiers, FVGM proposes a stochastic subset-sum based approach for verifying linear classifiers. Experimentally, we show that FVGM leads to an accurate and scalable assessment for more diverse families of fairness-enhancing algorithms, fairness attacks, and group/causal fairness metrics than the state-of-the-art. We also demonstrate that FVGM facilitates the computation of fairness influence functions as a stepping stone to detect the source of bias induced by subsets of features.

The deep learning approach to detecting malicious software (malware) is promising but has yet to tackle the problem of dataset shift, namely that the joint distribution of examples and their labels associated with the test set is different from that of the training set. This problem causes the degradation of deep learning models without users' notice. In order to alleviate the problem, one approach is to let a classifier not only predict the label on a given example but also present its uncertainty (or confidence) on the predicted label, whereby a defender can decide whether to use the predicted label or not. While intuitive and clearly important, the capabilities and limitations of this approach have not been well understood. In this paper, we conduct an empirical study to evaluate the quality of predictive uncertainties of malware detectors. Specifically, we re-design and build 24 Android malware detectors (by transforming four off-the-shelf detectors with six calibration methods) and quantify their uncertainties with nine metrics, including three metrics dealing with data imbalance. Our main findings are: (i) predictive uncertainty indeed helps achieve reliable malware detection in the presence of dataset shift, but cannot cope with adversarial evasion attacks; (ii) approximate Bayesian methods are promising to calibrate and generalize malware detectors to deal with dataset shift, but cannot cope with adversarial evasion attacks; (iii) adversarial evasion attacks can render calibration methods useless, and it is an open problem to quantify the uncertainty associated with the predicted labels of adversarial examples (i.e., it is not effective to use predictive uncertainty to detect adversarial examples).

We investigate novel parameter estimation and goodness-of-fit (GOF) assessment methods for large-scale confirmatory item factor analysis (IFA) with many respondents, items, and latent factors. For parameter estimation, we extend Urban and Bauer's (2021) deep learning algorithm for exploratory IFA to the confirmatory setting by showing how to handle user-defined constraints on loadings and factor correlations. For GOF assessment, we explore new simulation-based tests and indices. In particular, we consider extensions of the classifier two-sample test (C2ST), a method that tests whether a machine learning classifier can distinguish between observed data and synthetic data sampled from a fitted IFA model. The C2ST provides a flexible framework that integrates overall model fit, piece-wise fit, and person fit. Proposed extensions include a C2ST-based test of approximate fit in which the user specifies what percentage of observed data can be distinguished from synthetic data as well as a C2ST-based relative fit index that is similar in spirit to the relative fit indices used in structural equation modeling. Via simulation studies, we first show that the confirmatory extension of Urban and Bauer's (2021) algorithm produces more accurate parameter estimates as the sample size increases and obtains comparable estimates to a state-of-the-art confirmatory IFA estimation procedure in less time. We next show that the C2ST-based test of approximate fit controls the empirical type I error rate and detects when the number of latent factors is misspecified. Finally, we empirically investigate how the sampling distribution of the C2ST-based relative fit index depends on the sample size.

Intelligent robots are redefining a multitude of critical domains but are still far from being fully capable of assisting human peers in day-to-day tasks. An important requirement of collaboration is for each teammate to maintain and respect an understanding of the others' expectations of itself. Lack of which may lead to serious issues such as loose coordination between teammates, reduced situation awareness, and ultimately teaming failures. Hence, it is important for robots to behave explicably by meeting the human's expectations. One of the challenges here is that the expectations of the human are often hidden and can change dynamically as the human interacts with the robot. However, existing approaches to generating explicable plans often assume that the human's expectations are known and static. In this paper, we propose the idea of active explicable planning to relax this assumption. We apply a Bayesian approach to model and predict dynamic human belief and expectations to make explicable planning more anticipatory. We hypothesize that active explicable plans can be more efficient and explicable at the same time, when compared to explicable plans generated by the existing methods. In our experimental evaluation, we verify that our approach generates more efficient explicable plans while successfully capturing the dynamic belief change of the human teammate.