As an important Markov Chain Monte Carlo (MCMC) method, stochastic gradient Langevin dynamics (SGLD) algorithm has achieved great success in Bayesian learning and posterior sampling. However, SGLD typically suffers from slow convergence rate due to its large variance caused by the stochastic gradient. In order to alleviate these drawbacks, we leverage the recently developed Laplacian Smoothing (LS) technique and propose a Laplacian smoothing stochastic gradient Langevin dynamics (LS-SGLD) algorithm. We prove that for sampling from both log-concave and non-log-concave densities, LS-SGLD achieves strictly smaller discretization error in $2$-Wasserstein distance, although its mixing rate can be slightly slower. Experiments on both synthetic and real datasets verify our theoretical results, and demonstrate the superior performance of LS-SGLD on different machine learning tasks including posterior sampling, Bayesian logistic regression and training Bayesian convolutional neural networks. The code is available at \url{https://github.com/BaoWangMath/LS-MCMC}.

In statistical learning, a dataset is often partitioned into two parts: the training set and the holdout (i.e., testing) set. For instance, the training set is used to learn a predictor, and then the holdout set is used for estimating the accuracy of the predictor on the true distribution. However, often in practice, the holdout dataset is reused and the estimates tested on the holdout dataset are chosen adaptively based on the results of prior estimates, leading to that the predictor may become dependent of the holdout set. Hence, overfitting may occur, and the learned models may not generalize well to the unseen datasets. Prior studies have established connections between the stability of a learning algorithm and its ability to generalize, but the traditional generalization is not robust to adaptive composition. Recently, Dwork et al. in NIPS, STOC, and Science 2015 show that the holdout dataset from i.i.d. data samples can be reused in adaptive statistical learning, if the estimates are perturbed and coordinated using techniques developed for differential privacy, which is a widely used notion to quantify privacy. Yet, the results of Dwork et al. are applicable to only the case of i.i.d. samples. In contrast, correlations between data samples exist because of various behavioral, social, and genetic relationships between users. Our results in adaptive statistical learning generalize the results of Dwork et al. for i.i.d. data samples to arbitrarily correlated data. Specifically, we show that the holdout dataset from correlated samples can be reused in adaptive statistical learning, if the estimates are perturbed and coordinated using techniques developed for Bayesian differential privacy, which is a privacy notion recently introduced by Yang et al. in SIGMOD 2015 to broaden the application scenarios of differential privacy when data records are correlated.

Estimating hidden processes from non-linear noisy observations is particularly difficult when the parameters of these processes are not known. This paper adopts a machine learning approach to devise variational Bayesian inference for such scenarios. In particular, a random process generated by the autoregressive moving average (ARMA) linear model is inferred from non-linearity noise observations. The posterior distribution of hidden states are approximated by a set of weighted particles generated by the sequential Monte carlo (SMC) algorithm involving sampling with importance sampling resampling (SISR). Numerical efficiency and estimation accuracy of the proposed inference method are evaluated by computer simulations. Furthermore, the proposed inference method is demonstrated on a practical problem of estimating the missing values in the gene expression time series assuming vector autoregressive (VAR) data model.

Philip Becker-Ehmck philip.becker-ehmck@argmax.ai Patrick van der Smagt Disclosure: Parts of this work have been submitted in form of a Master's Thesis towards partial fulfillment of the requirements for a Masters program at the Technical University of Munich [4] Abstract Learning a model of dynamics from high-dimensional images can be a core ingredient for success in many applications across different domains, especially in sequential decision making. However, currently prevailing methods based on latent-variable models are limited to working with low resolution images only. In this work, we show that some of the issues with using high-dimensional observations arise from the discrepancy between the dimensionality of the latent and observable space, and propose solutions to overcome them. 1 Introduction Learning a probabilistic model for sequential data is a key step towards solving a lot of interesting problems, including analysis and deconstruction of auditory sequences [18], predicting the next piece of information given previously recorded data such as video frames [9] and text [20], and controlling an agent to perform specific tasks (model-based reinforcement learning [5]). While in this paper, we consider probabilistic models especially tuned for the needs of the last, i.e with control inputs, the approaches we discuss can be applied to control-less environments as well. A key feature required in control-based models is that they should be able to generate a feasible trajectory distribution given a control policy. To this end, one of the more successful solutions proposed in the past for modeling dynamical systems is Deep V ariational Bayes Filter ( DVBF) [10] - a framework for learning a State-Space Model given sequential observations from the environment in an unsupervised manner.

In this note, we study the minimax optimal rates for estimati ng the Integral Probability Metrics (IPMs) between probability measures based on samples. IPMs are widely used in both statistics and machine learning, with applications in nonparametric t wo-sample tests [ 23; 10 ], inferring the transportation cost (the Wasserstein-1 metric) from one se t of samples to another [ 22; 20 ], and with more recent appearances in rigorous investigations on the g enerative adversarial networks (GANs) [ 1; 17; 14; 21; 25; 3 ].

Brain-computer interfaces (BCIs) have enabled prosthetic device control by decoding motor movements from neural activities. Neural signals recorded from cortex exhibit nonstationary property due to abrupt noises and neuroplastic changes in brain activities during motor control. Current state-of-the-art neural signal decoders such as Kalman filter assume fixed relationship between neural activities and motor movements, thus will fail if this assumption is not satisfied. We propose a dynamic ensemble modeling (DyEnsemble) approach that is capable of adapting to changes in neural signals by employing a proper combination of decoding functions. The DyEnsemble method firstly learns a set of diverse candidate models. Then, it dynamically selects and combines these models online according to Bayesian updating mechanism. Our method can mitigate the effect of noises and cope with different task behaviors by automatic model switching, thus gives more accurate predictions. Experiments with neural data demonstrate that the DyEnsemble method outperforms Kalman filters remarkably, and its advantage is more obvious with noisy signals.

We propose a novel framework of the model specification test in regression using unlabeled test data. In many cases, we have conducted statistical inferences based on the assumption that we can correctly specify a model. However, it is difficult to confirm whether a model is correctly specified. To overcome this problem, existing works have devised statistical tests for model specification. Existing works have defined a correctly specified model in regression as a model with zero conditional mean of the error term over train data only. Extending the definition in conventional statistical tests, we define a correctly specified model as a model with zero conditional mean of the error term over any distribution of the explanatory variable. This definition is a natural consequence of the orthogonality of the explanatory variable and the error term. If a model does not satisfy this condition, the model might lack robustness with regards to the distribution shift. The proposed method would enable us to reject a misspecified model under our definition. By applying the proposed method, we can obtain a model that predicts the label for the unlabeled test data well without losing the interpretability of the model. In experiments, we show how the proposed method works for synthetic and real-world datasets.

Algorithms for Gaussian process, marginal likelihood methods or restricted maximum likelihood methods often require derivatives of log determinant terms. These log determinants are usually parametric with variance parameters of the underlying statistical models. This paper demonstrates that, when the underlying matrix is sparse, how to take the advantage of sparse inversion---selected inversion which share the same sparsity as the original matrix---to accelerate evaluating the derivative of log determinant.

Recent work on fair machine learning adds to a growing set of algorithmic safeguards required for deployment in high societal impact areas. A fundamental concern with model deployment is to guarantee stable performance under changes in data distribution. Extensive work in domain adaptation addresses this concern, albeit with the notion of stability limited to that of predictive performance. We provide conditions under which a stable model both in terms of prediction and fairness performance can be trained. Building on the problem setup of causal domain adaptation, we select a subset of features for training predictors with fairness constraints such that risk with respect to an unseen target data distribution is minimized. Advantages of the approach are demonstrated on synthetic datasets and on the task of diagnosing acute kidney injury in a real-world dataset under an instance of measurement policy shift and selection bias.

--Uncertainty of labels in clinical data resulting from intra-observer variability can have direct impact on the reliability of assessments made by deep neural networks. In this paper, we propose a method for modelling such uncertainty in the context of 2D echocardiography (echo), which is a routine procedure for detecting cardiovascular disease at point-of-care. Echo imaging quality and acquisition time is highly dependent on the operator's experience level. Recent developments have shown the possibility of automating echo image quality quantification by mapping an expert's assessment of quality to the echo image via deep learning techniques. Nevertheless, the observer variability in the expert's assessment can impact the quality quantification accuracy. Here, we aim to model the intra-observer variability in echo quality assessment as an aleatoric uncertainty modelling regression problem with the introduction of a novel method that handles the regression problem with categorical labels. A key feature of our design is that only a single forward pass is sufficient to estimate the level of uncertainty for the network output. Compared to the 0 .11 The simplicity of the proposed approach means that it could be generalized to other applications of deep learning in medical imaging, where there is often uncertainty in clinical labels. Z. Liao and H. Girgis have contributed equally to this work. Abolmaesumi have contributed equally to the manuscript (emails: t.tsang@ubc.ca, Z. Liao, A. Abdi, H. V aseli, and J. Hetherington are with the Department of Electrical and Computer Engineering, The University of British Columbia, V ancouver, BC V6T 1Z4, Canada. H. Girgis, T. Tsang, and K. Gin are with V ancouver General Hospital Echocardiography Laboratory, Division of Cardiology, Department of Medicine, The University of British Columbia, V ancouver, BC V5Z 1M9, Canada. R. Rohling is with the Department of Electrical and Computer Engineering and the Department of Mechanical Engineering, The University of British Columbia, V ancouver, BC V6T 1Z4, Canada T. Tsang is the Director of the V ancouver General Hospital and University of British Columbia Echocardiography Laboratories, and Principal Investigator of the CIHR-NSERC grant supporting this work. Abolmaesumi is Co-Principal Investigator for the grant supporting this work and is with the Department of Electrical and Computer Engineering, The University of British Columbia, V ancouver, BC V6T 1Z4, Canada.