We explore a general framework in Markov chain Monte Carlo (MCMC) sampling where sequential proposals are tried as a candidate for the next state of the Markov chain. This sequential-proposal framework can be applied to various existing MCMC methods, including Metropolis-Hastings algorithms using random proposals and methods that use deterministic proposals such as Hamiltonian Monte Carlo or the bouncy particle sampler. Sequential-proposal MCMC methods construct the same Markov chains as those constructed by the delayed rejection method under certain circumstances. We demonstrate that applications of the sequential-proposal framework to Hamiltonian Monte Carlo (HMC) methods can lead to improved numerical efficiency compared to standard HMC methods and the No-U-Turn sampler. Finally, we show that the sequential-proposal bouncy particle sampler enables the constructed Markov chain to pass through regions of low target density and thus facilitates better mixing of the chain when the target density is multimodal.

We offer a graphical interpretation of unfairness in a dataset as the presence of an unfair causal path in the causal Bayesian network representing the data-generation mechanism. We use this viewpoint to revisit the recent debate surrounding the COMPAS pretrial risk assessment tool and, more generally, to point out that fairness evaluation on a model requires careful considerations on the patterns of unfairness underlying the training data. We show that causal Bayesian networks provide us with a powerful tool to measure unfairness in a dataset and to design fair models in complex unfairness scenarios.

In this paper, we consider sequential online prediction (SOP) for streaming data in the presence of outliers and change points. We propose an INstant TEmporal structure Learning (INTEL) algorithm to address this problem.Our INTEL algorithm is developed based on a full consideration to the duality between online prediction and anomaly detection. We first employ a mixture of weighted GP models (WGPs) to cover the expected possible temporal structures of the data. Then, on the basis of the rich modeling capacity of this WGP mixture, we develop an efficient technique to instantly learn (capture) the temporal structure of the data that follows a regime shift. This instant learning is achieved only by adjusting one hyper-parameter value of the mixture model. A weighted generalization of the product of experts (POE) model is used for fusing predictions yielded from multiple GP models. An outlier is declared once a real observation seriously deviates from the fused prediction. If a certain number of outliers are consecutively declared, then a change point is declared. Extensive experiments are performed using a diverse of real datasets. Results show that the proposed algorithm is significantly better than benchmark methods for SOP in the presence of outliers and change points.

Causal inference requires theory and prior knowledge to structure analyses, and is not usually thought of as an arena for the application of prediction modelling. However, contemporary causal inference methods, premised on counterfactual or potential outcomes approaches, often include processing steps before the final estimation step. The purposes of this paper are: (i) to overview the recent emergence of prediction underpinning steps in contemporary causal inference methods as a useful perspective on contemporary causal inference methods, and (ii) explore the role of machine learning (as one approach to'best prediction') in causal inference. Causal inference methods covered include propensity scores, inverse probability of treatment weights (IPTWs), G computation and targeted maximum likelihood estimation (TMLE). Machine learning has been used more for propensity scores and TMLE, and there is potential for increased use in G computation and estimation of IPTWs.

Mixtures-of-Experts (MoE) are conditional mixture models that have shown their performance in modeling heterogeneity in data in many statistical learning approaches for prediction, including regression and classification, as well as for clustering. Their estimation in high-dimensional problems is still however challenging. We consider the problem of parameter estimation and feature selection in MoE models with different generalized linear experts models, and propose a regularized maximum likelihood estimation that efficiently encourages sparse solutions for heterogeneous data with high-dimensional predictors. The developed proximal-Newton EM algorithm includes proximal Newton-type procedures to update the model parameter by monotonically maximizing the objective function and allows to perform efficient estimation and feature selection. An experimental study shows the good performance of the algorithms in terms of recovering the actual sparse solutions, parameter estimation, and clustering of heterogeneous regression data, compared to the main state-of-the art competitors.

By and large the process of learning concepts that are embedded in time is regarded as quite a mature research topic. Hidden Markov models, recurrent neural networks are, amongst others, successful approaches to learning from temporal data. In this paper, we claim that the dominant approach minimizing appropriate risk functions defined over time by classic stochastic gradient might miss the deep interpretation of time given in other fields like physics. We show that a recent reformulation of learning according to the principle of Least Cognitive Action is better suited whenever time is involved in learning. The principle gives rise to a learning process that is driven by differential equations, that can somehow descrive the process within the same framework as other laws of nature.

Although deep neural networks have been widely applied in various domains [19, 25, 27], usually its parameters are learned via the principle of maximum likelihood, hence its success crucially hinges on the availability of large scale datasets. When training rich models on small datasets, explicit regularization techniques are crucial to alleviate overfitting. Previous works have explored various regularization [39] and data augmentation [19, 38] techniques to learn diversified representations. In this paper, we look into an alternative direction by proposing an adaptive and data-dependent regularization method to encourage neurons of the same layer to share statistical strength. The goal of our method is to prevent overfitting when training (large) networks on small dataset. Our key insight stems from the famous argument by Efron [8] in the literature of the empirical Bayes method: It is beneficial to learn from the experience of others. From an algorithmic perspective, we argue that the connection weights of neurons in the same layer (row/column vectors of the weight matrix) will be correlated with each other through the backpropagation learning. Hence, by learning the correlations of the weight matrix, a neuron can "borrow statistical strength" from other neurons in the same layer.

Compared with the classical policy gradient algorithm 1992), actor-critic tracks the action-value function (critic) in policy gradient in an online(Williams, manner, and alternatively updates the policy (actor) and the critic. On the one hand, the online update of critic significantly reduces the variance of policy gradient and hence leads to faster convergence. On the other hand, it also introduces algorithmic instability, which is often observed in practice (Islam et al., 2017) and parallels the notoriously unstable training of generative adversarial and Vinyals, 2016). Such instability of actor-critic originates from severalnetworks (Pfau intertwining challenges, including(i) function approximation of actor and critic, (ii) improper choice of stepsizes, (iii) the noise arising from stochastic approximation, (iv) the asynchrony between actor and critic, and (v) possibly off-policy data used in the update of critic. As a result, the convergence of actor-critic remains much less well understood than that of policy gradient, which itself is open. Consequently, the practical use of actor-critic often lacks theoretical guidance. In this paper, we aim to theoretically understand the algorithmic instability of actor-critic.

We present new techniques for automatically constructing probabilistic programs for data analysis, interpretation, and prediction. These techniques work with probabilistic domain-specific data modeling languages that capture key properties of a broad class of data generating processes, using Bayesian inference to synthesize probabilistic programs in these modeling languages given observed data. We provide a precise formulation of Bayesian synthesis for automatic data modeling that identifies sufficient conditions for the resulting synthesis procedure to be sound. We also derive a general class of synthesis algorithms for domain-specific languages specified by probabilistic context-free grammars and establish the soundness of our approach for these languages. We apply the techniques to automatically synthesize probabilistic programs for time series data and multivariate tabular data. We show how to analyze the structure of the synthesized programs to compute, for key qualitative properties of interest, the probability that the underlying data generating process exhibits each of these properties. Second, we translate probabilistic programs in the domain-specific language into probabilistic programs in Venture, a general-purpose probabilistic programming system. The translated Venture programs are then executed to obtain predictions of new time series data and new multivariate data records. Experimental results show that our techniques can accurately infer qualitative structure in multiple real-world data sets and outperform standard data analysis methods in forecasting and predicting new data.

Gaussian processes are used in machine learning to learn input-output mappings from observed data. Gaussian process regression is based on imposing a Gaussian process prior on the unknown regressor function and statistically conditioning it on the observed data. In system identification, Gaussian processes are used to form time series prediction models such as non-linear finite-impulse response (NFIR) models as well as non-linear autoregressive (NARX) models. Gaussian process state-space models (GPSS) can be used to learn the dynamic and measurement models for a state-space representation of the input-output data. Temporal and spatio-temporal Gaussian processes can be directly used to form regressor on the data in the time domain. The aim of this article is to briefly outline the main directions in system identification methods using Gaussian processes.