Nested sampling is an efficient algorithm for the calculation of the Bayesian evidence and posterior parameter probability distributions. It is based on the step-by-step exploration of the parameter space by Monte Carlo sampling with a series of values sets called live points that evolve towards the region of interest, i.e. where the likelihood function is maximal. In presence of several local likelihood maxima, the algorithm converges with difficulty. Some systematic errors can also be introduced by unexplored parameter volume regions. In order to avoid this, different methods are proposed in the literature for an efficient search of new live points, even in presence of local maxima. Here we present a new solution based on the mean shift cluster recognition method implemented in a random walk search algorithm. The clustering recognition is integrated within the Bayesian analysis program NestedFit. It is tested with the analysis of some difficult cases. Compared to the analysis results without cluster recognition, the computation time is considerably reduced. At the same time, the entire parameter space is efficiently explored, which translates into a smaller uncertainty of the extracted value of the Bayesian evidence.

Optimal Bayesian feature selection (OBFS) is a multivariat e supervised screening method designed from the ground up for bioma rker discovery. In this work, we prove that Gaussian OBFS is strongly consisten t under mild conditions, and provide rates of convergence for key posteriors i n the framework. These results are of enormous importance, since they identify pre cisely what features are selected by OBFS asymptotically, characterize the relativ e rates of convergence for posteriors on different types of features, provide condi tions that guarantee convergence, justify the use of OBFS when its internal assum ptions are invalid, and set the stage for understanding the asymptotic behavior of other algorithms based on the OBFS framework.

Controlling unknown discrete-time systems is a fundamenta l problem in adaptive control and reinforcement learning. In this problem, an agent interacts w ith an environment, with unknown dynamics, and aims to minimize the overall average regulati ng costs. To achieve this goal, the agent is required to explore the environment to gain a better understanding of the environment dynamics, which is often called system identification. The a gent then utilizes this understanding to design a set of improved controllers that simultaneously reduces the possible future costs and also enables the agent to explore the important and unknown a spects of the system. In recent decades, this challenging problem has been extensively stu died and resulted in a set of foundational steps to study the stability and asymptotic convergence to o ptimal controllers [Lai et al., 1982, Lai and Wei, 1987]. While asymptotic analyses set the ground for the design of optimal control, understanding the finite time behavior of adaptive algorith ms is critical for real-world applications. In practice, one might prefer an algorithm that guarantees b etter performance on a much shorter horizon. Recent developments in the fields of statistics and machine learning along with control theory [Van Der Vaart and Wellner, 1996, Peña et al., 2009, Lai et al., 1982] empowers us to not only advance the study of the asymptotic efficiency of algorithms b ut also to analyze their finite-time behavior [Fiechter, 1997, Abbasi-Yadkori and Szepesvári, 2011]. In partially observable linear quadratic control, if the ag ent, a priori, is handed the system dynamics, the optimal control/policy has a closed-form in t he presence of Gaussian disturbances.

We consider distributions arising from a mixture of causal models, where each model is represented by a directed acyclic graph (DAG). We provide a graphical representation of such mixture distributions and prove that this representation encodes the conditional independence relations of the mixture distribution. We then consider the problem of structure learning based on samples from such distributions. Since the mixing variable is latent, we consider causal structure discovery algorithms such as FCI that can deal with latent variables. We show that such algorithms recover a "union" of the component DAGs and can identify variables whose conditional distribution across the component DAGs vary. We demonstrate our results on synthetic and real data showing that the inferred graph identifies nodes that vary between the different mixture components. As an immediate application, we demonstrate how retrieval of this causal information can be used to cluster samples according to each mixture component.

Approximate Bayesian Computation is widely used in systems biology for inferring parameters in stochastic gene regulatory network models. Its performance hinges critically on the ability to summarize high-dimensional system responses such as time series into a few informative, low-dimensional summary statistics. The quality of those statistics critically affect the accuracy of the inference. Existing methods to select the best subset out of a pool of candidate statistics do not scale well with large pools. Since it is imperative for good performance this becomes a serious bottleneck when doing inference on complex and high-dimensional problems. This paper proposes a convolutional neural network architecture for automatically learning informative summary statistics of temporal responses. We show that the proposed network can effectively circumvent the statistics selection problem as a preprocessing step to ABC for a challenging inference problem learning parameters in a high-dimensional stochastic genetic oscillator. We also study the impact of experimental design on network performance by comparing different data richness and different data acquisition strategies.

Classifiers built with neural networks handle large-scale high dimensional data, such as facial images from computer vision, extremely well while traditional statistical methods often fail miserably. In this paper, we attempt to understand this empirical success in high dimensional classification by deriving the convergence rates of excess risk. In particular, a teacher-student framework is proposed that assumes the Bayes classifier to be expressed as ReLU neural networks. In this setup, we obtain a sharp rate of convergence, i.e., $\tilde{O}_d(n^{-2/3})$, for classifiers trained using either 0-1 loss or hinge loss. This rate can be further improved to $\tilde{O}_d(n^{-1})$ when the data distribution is separable. Here, $n$ denotes the sample size. An interesting observation is that the data dimension only contributes to the $\log(n)$ term in the above rates. This may provide one theoretical explanation for the empirical successes of deep neural networks in high dimensional classification, particularly for structured data.

State representation learning (SRL) in partially observable Markov decision processes has been studied to learn abstract features of data useful for robot control tasks. For SRL, acquiring domain-agnostic states is essential for achieving efficient imitation learning (IL). Without these states, IL is hampered by domain-dependent information useless for control. However, existing methods fail to remove such disturbances from the states when the data from experts and agents show large domain shifts. To overcome this issue, we propose a domain-adversarial and -conditional state space model (DAC-SSM) that enables control systems to obtain domain-agnostic and task- and dynamics-aware states. DAC-SSM jointly optimizes the state inference, observation reconstruction, forward dynamics, and reward models. To remove domain-dependent information from the states, the model is trained with domain discriminators in an adversarial manner, and the reconstruction is conditioned on domain labels. We experimentally evaluated the model predictive control performance via IL for continuous control of sparse reward tasks in simulators and compared it with the performance of the existing SRL method. The agents from DAC-SSM achieved performance comparable to experts and more than twice the baselines. We conclude domain-agnostic states are essential for IL that has large domain shifts and can be obtained using DAC-SSM.

Anna Sergeevna Bosman Department of Computer Science University of Pretoria Pretoria, South Africa anna.bosman@up.ac.za Abstract --Saliency maps are often used in computer vision to provide intuitive interpretations of what input regions a model has used to produce a specific prediction. A number of approaches to saliency map generation are available, but most require access to model parameters. This work proposes an approach for saliency map generation for black-box models, where no access to model parameters is available, using a Bayesian optimisation sampling method. The approach aims to find the global salient image region responsible for a particular (black-box) model's prediction. This is achieved by a sampling-based approach to model perturbations that seeks to localise salient regions of an image to the black-box model. Results show that the proposed approach to saliency map generation outperforms grid-based perturbation approaches, and performs similarly to gradient-based approaches which require access to model parameters. I NTRODUCTION Deep learning (DL) techniques have become a standard approach in computer vision. Specifically, the convolutional neural network (CNN) architecture has shown exceptional performance, achieving results comparable to human performance on image recognition tasks [1]-[3]. As a result, the CNN models are often deployed in real life as efficient black-box tools.

Predicting stochastic cellular dynamics as emerging from the mechanistic models of molecular interactions is a long-standing challenge in systems biology: low-level chemical reaction network (CRN) models give raise to a highly-dimensional continuous-time Markov chain (CTMC) which is computationally demanding and often prohibitive to analyse in practice. A recently proposed abstraction method uses deep learning to replace this CTMC with a discrete-time continuous-space process, by training a mixture density deep neural network with traces sampled at regular time intervals (which can obtained either by simulating a given CRN or as time-series data from experiment). The major advantage of such abstraction is that it produces a computational model that is dramatically cheaper to execute, while preserving the statistical features of the training data. In general, the abstraction accuracy improves with the amount of training data. However, depending on a CRN, the overall quality of the method -- the efficiency gain and abstraction accuracy -- will also depend on the choice of neural network architecture given by hyper-parameters such as the layer types and connections between them. As a consequence, in practice, the modeller would have to take care of finding the suitable architecture manually, for each given CRN, through a tedious and time-consuming trial-and-error cycle. In this paper, we propose to further automatise deep abstractions for stochastic CRNs, through learning the optimal neural network architecture along with learning the transition kernel of the abstract process. Automated search of the architecture makes the method applicable directly to any given CRN, which is time-saving for deep learning experts and crucial for non-specialists. We implement the method and demonstrate its performance on a number of representative CRNs with multi-modal emergent phenotypes.

Many classification applications require accurate probability estimates in addition to good class separation but often classifiers are designed focusing only on the latter. Calibration is the process of improving probability estimates by post-processing but commonly used calibration algorithms work poorly on small data sets and assume the classification task to be binary. Both of these restrictions limit their real-world applicability. Previously introduced Data Generation and Grouping algorithm alleviates the problem posed by small data sets and in this article, we will demonstrate that its application to multi-class problems is also possible which solves the other limitation. Our experiments show that calibration error can be decreased using the proposed approach and the additional computational cost is acceptable.