Variational inference has experienced a recent surge in popularity owing to stochastic approaches, which have yielded practical tools for a wide range of model classes. A key benefit is that stochastic variational inference obviates the tedious process of deriving analytical expressions for closed-form variable updates. Instead, one simply needs to derive the gradient of the log-posterior, which is often much easier. Yet for certain model classes, the log-posterior itself is difficult to optimize using standard gradient techniques. One such example are random field models, where optimization based on gradient linearization has proven popular, since it speeds up convergence significantly and can avoid poor local optima. In this paper we propose stochastic variational inference with gradient linearization (SVIGL). It is similarly convenient as standard stochastic variational inference - all that is required is a local linearization of the energy gradient. Its benefit over stochastic variational inference with conventional gradient methods is a clear improvement in convergence speed, while yielding comparable or even better variational approximations in terms of KL divergence. We demonstrate the benefits of SVIGL in three applications: Optical flow estimation, Poisson-Gaussian denoising, and 3D surface reconstruction.

Recently, the intervention calculus when the DAG is absent (IDA) method was developed to estimate lower bounds of causal effects from observational high-dimensional data. Originally it was introduced to assess the effect of baseline biomarkers which do not vary over time. However, in many clinical settings, measurements of biomarkers are repeated at fixed time points during treatment exposure and, therefore, this method need to be extended. The purpose of this paper is then to extend the first step of the IDA, the Peter Clarks (PC)-algorithm, to a time-dependent exposure in the context of a binary outcome. We generalised the PC-algorithm for taking into account the chronological order of repeated measurements of the exposure and propose to apply the IDA with our new version, the chronologically ordered PC-algorithm (COPC-algorithm). A simulation study has been performed before applying the method for estimating causal effects of time-dependent immunological biomarkers on toxicity, death and progression in patients with metastatic melanoma. The simulation study showed that the completed partially directed acyclic graphs (CPDAGs) obtained using COPC-algorithm were structurally closer to the true CPDAG than CPDAGs obtained using PC-algorithm. Also, causal effects were more accurate when they were estimated based on CPDAGs obtained using COPC-algorithm. Moreover, CPDAGs obtained by COPC-algorithm allowed removing non-chronologic arrows with a variable measured at a time t pointing to a variable measured at a time t' where t'< t. Bidirected edges were less present in CPDAGs obtained with the COPC-algorithm, supporting the fact that there was less variability in causal effects estimated from these CPDAGs. The COPC-algorithm provided CPDAGs that keep the chronological structure present in the data, thus allowed to estimate lower bounds of the causal effect of time-dependent biomarkers.

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Across diverse fields, investigators face problems and opportunities involving data. Scientists, scholars, engineers, and other analysts seek new methods to ingest data, extract salient patterns, and then use the results for prediction and understanding. These methods come from machine learning (ML), which is quickly becoming core to modern technological systems, modern scientific workflow, and modern approaches to understanding data. The classical approach to solving a problem with ML follows the "cookbook" approach, one where the scientist shoehorns her data and problem to match the inputs and outputs of a reliable ML method. This strategy has been successful in many domains--examples include spam filtering, speech recognition, and movie recommendation--but it can only take us so far.

Abstract-- We propose the use of Bayesian networks, which provide both a mean value and an uncertainty estimate as output, to enhance the safety of learned control policies under circumstances in which a test-time input differs significantly from the training set. Our algorithm combines reinforcement learning and end-to-end imitation learning to simultaneously learn a control policy as well as a threshold over the predictive uncertainty of the learned model, with no hand-tuning required. Corrective action, such as a return of control to the model predictive controller or human expert, is taken when the uncertainty threshold is exceeded. We demonstrate that our method is robust to uncertainty resulting from varying system dynamics as well as from partial state observability. As the deployment of deep neural networks as controllers for physical robotic systems becomes more prevalent, the issue of safety within artificial intelligence becomes an increasingly important concern. Recently the use of end-to-end imitation learning to develop neural network control policies has surged in popularity, due in large part to the ease with which deep models can learn complex dynamics and infer global state from local data while bypassing the need for significant parameter tuning. In contrast, traditional approaches to vision-based control rely on methods such image segmentation and object detection, classification, labeling, and filtering; often, these methods require significant engineering and tuning.

In many applications of machine learning, labeled data is scarce and obtaining additional labels is expensive. We introduce a new approach to supervising learning algorithms without labels by enforcing a small number of domain-specific constraints over the algorithms’ outputs. The constraints can be provided explicitly based on prior knowledge — e.g. we may require that objects detected in videos satisfy the laws of physics — or implicitly extracted from data using a novel framework inspired by adversarial training. We demonstrate the effectiveness of constraint-based learning on a variety of tasks — including tracking, object detection, and human pose estimation — and we find that algorithms supervised with constraints achieve high accuracies with only a small amount of labels, or with no labels at all in some cases.

In this paper, we develop a Bayesian evidence maximization framework to solve the sparse non-negative least squares (S-NNLS) problem. We introduce a family of probability densities referred to as the Rectified Gaussian Scale Mixture (R- GSM) to model the sparsity enforcing prior distribution for the solution. The R-GSM prior encompasses a variety of heavy-tailed densities such as the rectified Laplacian and rectified Student- t distributions with a proper choice of the mixing density. We utilize the hierarchical representation induced by the R-GSM prior and develop an evidence maximization framework based on the Expectation-Maximization (EM) algorithm. Using the EM based method, we estimate the hyper-parameters and obtain a point estimate for the solution. We refer to the proposed method as rectified sparse Bayesian learning (R-SBL). We provide four R- SBL variants that offer a range of options for computational complexity and the quality of the E-step computation. These methods include the Markov chain Monte Carlo EM, linear minimum mean-square-error estimation, approximate message passing and a diagonal approximation. Using numerical experiments, we show that the proposed R-SBL method outperforms existing S-NNLS solvers in terms of both signal and support recovery performance, and is also very robust against the structure of the design matrix.

Parametric images provide insight into the spatial distribution of physiological parameters, but they are often extremely noisy, due to low SNR of tomographic data. Direct estimation from projections allows accurate noise modeling, improving the results of post-reconstruction fitting. We propose a method, which we name kinetic compressive sensing (KCS), based on a hierarchical Bayesian model and on a novel reconstruction algorithm, that encodes sparsity of kinetic parameters. Parametric maps are reconstructed by maximizing the joint probability, with an Iterated Conditional Modes (ICM) approach, alternating the optimization of activity time series (OS-MAP-OSL), and kinetic parameters (MAP-LM). We evaluated the proposed algorithm on a simulated dynamic phantom: a bias/variance study confirmed how direct estimates can improve the quality of parametric maps over a post-reconstruction fitting, and showed how the novel sparsity prior can further reduce their variance, without affecting bias. Real FDG PET human brain data (Siemens mMR, 40min) images were also processed. Results enforced how the proposed KCS-regularized direct method can produce spatially coherent images and parametric maps, with lower spatial noise and better tissue contrast. A GPU-based open source implementation of the algorithm is provided.

Due to the intractable partition function, the exact likelihood function for a Markov random field (MRF), in many situations, can only be approximated. Major approximation approaches include pseudolikelihood and Laplace approximation. In this paper, we propose a novel way of approximating the likelihood function through first approximating the marginal likelihood functions of individual parameters and then reconstructing the joint likelihood function from these marginal likelihood functions. For approximating the marginal likelihood functions, we derive a particular likelihood function from a modified scenario of coin tossing which is useful for capturing how one parameter interacts with the remaining parameters in the likelihood function. For reconstructing the joint likelihood function, we use an appropriate copula to link up these marginal likelihood functions. Numerical investigation suggests the superior performance of our approach. Especially as the size of the MRF increases, both the numerical performance and the computational cost of our approach remain consistently satisfactory, whereas Laplace approximation deteriorates and pseudolikelihood becomes computationally unbearable.

We suggest a novel approach for the estimation of the posterior distribution of the weights of a neural network, using an online version of the variational Bayes method. Having a confidence measure of the weights allows to combat several shortcomings of neural networks, such as their parameter redundancy, and their notorious vulnerability to the change of input distribution ("catastrophic forgetting"). Specifically, We show that this approach helps alleviate the catastrophic forgetting phenomenon -- even without the knowledge of when the tasks are been switched. Furthermore, it improves the robustness of the network to weight pruning -- even without retraining.