Complicated generative models often result in a situation where computing the likelihood of observed data is intractable, while simulating from the conditional density given a parameter value is relatively easy. Approximate Bayesian Computation (ABC) is a paradigm that enables simulation-based posterior inference in such cases by measuring the similarity between simulated and observed data in terms of a chosen set of summary statistics. However, there is no general rule to construct sufficient summary statistics for complex models. Insufficient summary statistics will "leak" information, which leads to ABC algorithms yielding samples from an incorrect (partial) posterior. In this paper, we propose a fully nonparametric ABC paradigm which circumvents the need for manually selecting summary statistics. Our approach, K2-ABC, uses maximum mean discrepancy (MMD) as a dissimilarity measure between the distributions over observed and simulated data. MMD is easily estimated as the squared difference between their empirical kernel embeddings. Experiments on a simulated scenario and a real-world biological problem illustrate the effectiveness of the proposed algorithm.

Vehicles are becoming more and more connected, this opens up a larger attack surface which not only affects the passengers inside vehicles, but also people around them. These vulnerabilities exist because modern systems are built on the comparatively less secure and old CAN bus framework which lacks even basic authentication. Since a new protocol can only help future vehicles and not older vehicles, our approach tries to solve the issue as a data analytics problem and use machine learning techniques to secure cars. We develop a Hidden Markov Model to detect anomalous states from real data collected from vehicles. Using this model, while a vehicle is in operation, we are able to detect and issue alerts. Our model could be integrated as a plug-n-play device in all new and old cars.

The histogram method is a powerful non-parametric approach for estimating the probability density function of a continuous variable. But the construction of a histogram, compared to the parametric approaches, demands a large number of observations to capture the underlying density function. Thus it is not suitable for analyzing a sparse data set, a collection of units with a small size of data. In this paper, by employing the probabilistic topic model, we develop a novel Bayesian approach to alleviating the sparsity problem in the conventional histogram estimation. Our method estimates a unit's density function as a mixture of basis histograms, in which the number of bins for each basis, as well as their heights, is determined automatically. The estimation procedure is performed by using the fast and easy-to-implement collapsed Gibbs sampling. We apply the proposed method to synthetic data, showing that it performs well.

This paper discusses real-time alignment of audio signals of music performance to the corresponding score (a.k.a. score following) which can handle tempo changes, errors and arbitrary repeats and/or skips (repeats/skips) in performances. This type of score following is particularly useful in automatic accompaniment for practices and rehearsals, where errors and repeats/skips are often made. Simple extensions of the algorithms previously proposed in the literature are not applicable in these situations for scores of practical length due to the problem of large computational complexity. To cope with this problem, we present two hidden Markov models of monophonic performance with errors and arbitrary repeats/skips, and derive efficient score-following algorithms with an assumption that the prior probability distributions of score positions before and after repeats/skips are independent from each other. We confirmed real-time operation of the algorithms with music scores of practical length (around 10000 notes) on a modern laptop and their tracking ability to the input performance within 0.7 s on average after repeats/skips in clarinet performance data. Further improvements and extension for polyphonic signals are also discussed.

The discovery of causal relationships from purely observational data is a fundamental problem in science. The most elementary form of such a causal discovery problem is to decide whether X causes Y or, alternatively, Y causes X, given joint observations of two variables X, Y. An example is to decide whether altitude causes temperature, or vice versa, given only joint measurements of both variables. Even under the simplifying assumptions of no confounding, no feedback loops, and no selection bias, such bivariate causal discovery problems are challenging. Nevertheless, several approaches for addressing those problems have been proposed in recent years. We review two families of such methods: Additive Noise Methods (ANM) and Information Geometric Causal Inference (IGCI). We present the benchmark CauseEffectPairs that consists of data for 100 different cause-effect pairs selected from 37 datasets from various domains (e.g., meteorology, biology, medicine, engineering, economy, etc.) and motivate our decisions regarding the "ground truth" causal directions of all pairs. We evaluate the performance of several bivariate causal discovery methods on these real-world benchmark data and in addition on artificially simulated data. Our empirical results on real-world data indicate that certain methods are indeed able to distinguish cause from effect using only purely observational data, although more benchmark data would be needed to obtain statistically significant conclusions. One of the best performing methods overall is the additive-noise method originally proposed by Hoyer et al. (2009), which obtains an accuracy of 63+-10 % and an AUC of 0.74+-0.05 on the real-world benchmark. As the main theoretical contribution of this work we prove the consistency of that method.

We survey concepts at the frontier of research connecting artificial, animal and human cognition to computation and information processing---from the Turing test to Searle's Chinese Room argument, from Integrated Information Theory to computational and algorithmic complexity. We start by arguing that passing the Turing test is a trivial computational problem and that its pragmatic difficulty sheds light on the computational nature of the human mind more than it does on the challenge of artificial intelligence. We then review our proposed algorithmic information-theoretic measures for quantifying and characterizing cognition in various forms. These are capable of accounting for known biases in human behavior, thus vindicating a computational algorithmic view of cognition as first suggested by Turing, but this time rooted in the concept of algorithmic probability, which in turn is based on computational universality while being independent of computational model, and which has the virtue of being predictive and testable as a model theory of cognitive behavior.

Nowadays, hospitals are ubiquitous and integral to modern society. Patients flow in and out of a veritable whirlwind of paperwork, consultations, and potential inpatient admissions, through an abstracted system that is not without flaws. One of the biggest flaws in the medical system is perhaps an unexpected one: the patient alarm system. One longitudinal study reported an 88.8% rate of false alarms, with other studies reporting numbers of similar magnitudes. These false alarm rates lead to a number of deleterious effects that manifest in a significantly lower standard of care across clinics. This paper discusses a model-based probabilistic inference approach to identifying variables at a detection level. We design a generative model that complies with an overview of human physiology and perform approximate Bayesian inference. One primary goal of this paper is to justify a Bayesian modeling approach to increasing robustness in a physiological domain. We use three data sets provided by Physionet, a research resource for complex physiological signals, in the form of the Physionet 2014 Challenge set-p1 and set-p2, as well as the MGH/MF Waveform Database. On the extended data set our algorithm is on par with the other top six submissions to the Physionet 2014 challenge.

Mean field variational Bayes (MFVB) is a popular posterior approximation method due to its fast runtime on large-scale data sets. However, it is well known that a major failing of MFVB is that it underestimates the uncertainty of model variables (sometimes severely) and provides no information about model variable covariance. We generalize linear response methods from statistical physics to deliver accurate uncertainty estimates for model variables---both for individual variables and coherently across variables. We call our method linear response variational Bayes (LRVB). When the MFVB posterior approximation is in the exponential family, LRVB has a simple, analytic form, even for non-conjugate models. Indeed, we make no assumptions about the form of the true posterior. We demonstrate the accuracy and scalability of our method on a range of models for both simulated and real data.

Learning in deep models using Bayesian methods has generated significant attention recently. This is largely because of the feasibility of modern Bayesian methods to yield scalable learning and inference, while maintaining a measure of uncertainty in the model parameters. Stochastic gradient MCMC algorithms (SG-MCMC) are a family of diffusion-based sampling methods for large-scale Bayesian learning. In SG-MCMC, multivariate stochastic gradient thermostats (mSGNHT) augment each parameter of interest, with a momentum and a thermostat variable to maintain stationary distributions as target posterior distributions. As the number of variables in a continuous-time diffusion increases, its numerical approximation error becomes a practical bottleneck, so better use of a numerical integrator is desirable. To this end, we propose use of an efficient symmetric splitting integrator in mSGNHT, instead of the traditional Euler integrator. We demonstrate that the proposed scheme is more accurate, robust, and converges faster. These properties are demonstrated to be desirable in Bayesian deep learning. Extensive experiments on two canonical models and their deep extensions demonstrate that the proposed scheme improves general Bayesian posterior sampling, particularly for deep models.

Effective training of deep neural networks suffers from two main issues. The first is that the parameter spaces of these models exhibit pathological curvature. Recent methods address this problem by using adaptive preconditioning for Stochastic Gradient Descent (SGD). These methods improve convergence by adapting to the local geometry of parameter space. A second issue is overfitting, which is typically addressed by early stopping. However, recent work has demonstrated that Bayesian model averaging mitigates this problem. The posterior can be sampled by using Stochastic Gradient Langevin Dynamics (SGLD). However, the rapidly changing curvature renders default SGLD methods inefficient. Here, we propose combining adaptive preconditioners with SGLD. In support of this idea, we give theoretical properties on asymptotic convergence and predictive risk. We also provide empirical results for Logistic Regression, Feedforward Neural Nets, and Convolutional Neural Nets, demonstrating that our preconditioned SGLD method gives state-of-the-art performance on these models.