Abstract--In this paper we consider the problem of modelbased learningof turbulent flows using mobile robots. The key idea is to use empirical data to improve on numerical estimates of time-averaged flow properties that can be obtained using Reynolds-Averaged Navier Stokes (RANS) models. RANS models are computationally efficient and provide global knowledge of the flow but they also rely on simplifying assumptions and require experimental validation. In this paper, we instead construct statistical models of the flow properties using Gaussian Processes (GPs) and rely on the numerical solutions obtained from RANS models to inform their mean. We then utilize Bayesian inference to incorporate empirical measurements of the flow into these GPs, specifically, measurements of the time-averaged velocity and turbulent intensity fields. Moreover, it accounts for measurement noise by systematically incorporating it in the GP models. To obtain the velocity and turbulent intensity measurements, we design a cost-effective mobile robot sensor that collects and analyzes instantaneous velocity readings. We control this mobile robot through a sequence of waypoints that maximize the information content of the corresponding measurements. The end result is a posterior distribution of the flow field that better approximates the real flow and also quantifies the uncertainty in the flow properties. We present experimental results that demonstrate considerable improvement in the prediction of the flow properties compared to pure numerical simulations. I. INTRODUCTION Knowledge of turbulent flow properties, e.g., velocity and turbulent intensity, is of paramount importance for many engineering applications.At larger scales, these properties are used for the study of ocean currents and their effects on aquatic life, [1], [2], [3], meteorology, [4], bathymetry, [5], and localization of atmospheric pollutants, [6], to name a few. At smaller scales, knowledge of flow fields is important in applications ranging from optimal HVAC of residential buildings for human comfort, [7], to design of drag-efficient bodies in aerospace and automotive industries, [8]. At even smaller scales, the characteristics of velocity fluctuations in vessels are important for vascular pathology and diagnosis, [9] or for the control of bacteria-inspired uniflagellar robots, [10]. Another important application that requires global knowledge of the velocity field is chemical source identification in advection-diffusion transport systems, [11], [12], [13].

Phylogeny is the field of modelling the temporal discrete dynamics of speciation. Complex models can nowadays be studied using the Approximate Bayesian Computation approach which avoids likelihood calculations. The field's progression is hampered by the lack of robust software to estimate the numerous parameters of the speciation process. In this work we present an R package, pcmabc, based on Approximate Bayesian Computations, that implements three novel phylogenetic algorithms for trait-dependent speciation modelling. Our phylogenetic comparative methodology takes into account both the simulated traits and phylogeny, attempting to estimate the parameters of the processes generating the phenotype and the trait. The user is not restricted to a predefined set of models and can specify a variety of evolutionary and branching models. We illustrate the software with a simulation-reestimation study focused around the branching Ornstein-Uhlenbeck process, where the branching rate depends non-linearly on the value of the driving Ornstein-Uhlenbeck process. Included in this work is a tutorial on how to use the software.

Robots are increasingly used to carry out critical missions in extreme environments that are hazardous for humans. This requires a high degree of operational autonomy under uncertain conditions, and poses new challenges for assuring the robot's safety and reliability. In this paper, we develop a framework for probabilistic model checking on a layered Markov model to verify the safety and reliability requirements of such robots, both at pre-mission stage and during runtime. Two novel estimators based on conservative Bayesian inference and imprecise probability model with sets of priors are introduced to learn the unknown transition parameters from operational data. We demonstrate our approach using data from a real-world deployment of unmanned underwater vehicles in extreme environments.

Tasks such as social network analysis, human behavior recognition, or modeling biochemical reactions, can be solved elegantly by using the probabilistic inference framework. However, standard probabilistic inference algorithms work at a propositional level, and thus cannot capture the symmetries and redundancies that are present in these tasks. Algorithms that exploit those symmetries have been devised in different research fields, for example by the lifted inference-, multiple object tracking-, and modeling and simulation-communities. The common idea, that we call state space abstraction, is to perform inference over compact representations of sets of symmetric states. Although they are concerned with a similar topic, the relationship between these approaches has not been investigated systematically. This survey provides the following contributions. We perform a systematic literature review to outline the state of the art in probabilistic inference methods exploiting symmetries. From an initial set of more than 4,000 papers, we identify 116 relevant papers. Furthermore, we provide new high-level categories that classify the approaches, based on common properties of the approaches. The research areas underlying each of the categories are introduced concisely. Researchers from different fields that are confronted with a state space explosion problem in a probabilistic system can use this classification to identify possible solutions. Finally, based on this conceptualization, we identify potentials for future research, as some relevant application domains are not addressed by current approaches.

Traditional model-based RL relies on hand-specified or learned models of transition dynamics of the environment. These methods are sample efficient and facilitate learning in the real world but fail to generalize to subtle variations in the underlying dynamics, e.g., due to differences in mass, friction, or actuators across robotic agents or across time. We propose using variational inference to learn an explicit latent representation of unknown environment properties that accelerates learning and facilitates generalization on novel environments at test time. We use Online Bayesian Inference of these learned latents to rapidly adapt online to changes in environments without retaining large replay buffers of recent data. Combined with a neural network ensemble that models dynamics and captures uncertainty over dynamics, our approach demonstrates positive transfer during training and online adaptation on the continuous control task HalfCheetah.

Deep neural networks(NNs) have achieved impressive performance, often exceed human performance on many computer vision tasks. However, one of the most challenging issues that still remains is that NNs are overconfident in their predictions, which can be very harmful when this arises in safety critical applications. In this paper, we show that predictive uncertainty can be efficiently estimated when we incorporate the concept of gradients uncertainty into posterior sampling. The proposed method is tested on two different datasets, MNIST for in-distribution confusing examples and notMNIST for out-of-distribution data. We show that our method is able to efficiently represent predictive uncertainty on both datasets.

As machine learning models continue to increase in complexity, collecting large hand-labeled training sets has become one of the biggest roadblocks in practice. Instead, weaker forms of supervision that provide noisier but cheaper labels are often used. However, these weak supervision sources have diverse and unknown accuracies, may output correlated labels, and may label different tasks or apply at different levels of granularity. We propose a framework for integrating and modeling such weak supervision sources by viewing them as labeling different related sub-tasks of a problem, which we refer to as the multi-task weak supervision setting. We show that by solving a matrix completion-style problem, we can recover the accuracies of these multi-task sources given their dependency structure, but without any labeled data, leading to higher-quality supervision for training an end model. Theoretically, we show that the generalization error of models trained with this approach improves with the number of unlabeled data points, and characterize the scaling with respect to the task and dependency structures. On three fine-grained classification problems, we show that our approach leads to average gains of 20.2 points in accuracy over a traditional supervised approach, 6.8 points over a majority vote baseline, and 4.1 points over a previously proposed weak supervision method that models tasks separately.

The wide adoption of machine learning approaches in the industry, government, medicine and science has renewed the interest in interpretable machine learning: many decisions are too important to be delegated to black-box techniques such as deep neural networks or kernel SVMs. Historically, problems of learning interpretable classifiers, including classification rules or decision trees, have been approached by greedy heuristic methods as essentially all the exact optimization formulations are NP-hard. Our primary contribution is a MaxSAT-based framework, called MLIC, which allows principled search for interpretable classification rules expressible in propositional logic. Our approach benefits from the revolutionary advances in the constraint satisfaction community to solve large-scale instances of such problems. In experimental evaluations over a collection of benchmarks arising from practical scenarios, we demonstrate its effectiveness: we show that the formulation can solve large classification problems with tens or hundreds of thousands of examples and thousands of features, and to provide a tunable balance of accuracy vs. interpretability. Furthermore, we show that in many problems interpretability can be obtained at only a minor cost in accuracy. The primary objective of the paper is to show that recent advances in the MaxSAT literature make it realistic to find optimal (or very high quality near-optimal) solutions to large-scale classification problems. The key goal of the paper is to excite researchers in both interpretable classification and in the CP community to take it further and propose richer formulations, and to develop bespoke solvers attuned to the problem of interpretable ML.

While machine learning is traditionally a resource intensive task, embedded systems, autonomous navigation and the vision of the Internet-of-Things fuel the interest in resource efficient approaches. These approaches require a carefully chosen trade-off between performance and resource consumption in terms of computation and energy. On top of this, it is crucial to treat uncertainty in a consistent manner in all but the simplest applications of machine learning systems. In particular, a desideratum for any real-world system is to be robust in the presence of outliers and corrupted data, as well as being `aware' of its limits, i.e.\ the system should maintain and provide an uncertainty estimate over its own predictions. These complex demands are among the major challenges in current machine learning research and key to ensure a smooth transition of machine learning technology into every day's applications. In this article, we provide an overview of the current state of the art of machine learning techniques facilitating these real-world requirements. First we provide a comprehensive review of resource-efficiency in deep neural networks with focus on techniques for model size reduction, compression and reduced precision. These techniques can be applied during training or as post-processing and are widely used to reduce both computational complexity and memory footprint. As most (practical) neural networks are limited in their ways to treat uncertainty, we contrast them with probabilistic graphical models, which readily serve these desiderata by means of probabilistic inference. In that way, we provide an extensive overview of the current state-of-the-art of robust and efficient machine learning for real-world systems.

It is now widely accepted that volatility models have to incorporate the so-called leverage effect in order to to model the dynamics of daily financial returns. We suggest a new class of multivariate power transformed asymmetric models. It includes several functional forms of multivariate GARCH models which are of great interest in financial modeling and time series literature. We provide an explicit necessary and sufficient condition to establish the strict stationarity of the model. We derive the asymptotic properties of the quasi-maximum likelihood estimator of the parameters. These properties are established both when the power of the transformation is known or is unknown. The asymptotic results are illustrated by Monte Carlo experiments. An application to real financial data is also proposed. Introduction The ARCH (AutoRegressive Conditional Heteroscedastic) model has been introduced by Engle (1982) in an univariate context. Since this work a lot of extensions have been proposed. A first one has been suggested four years latter, namely the GARCH (Generalised ARCH) model by Bollerslev (1986). This model had for goal to improve modeling by considering the past conditional variance (volatility). Their concept are based on the past conditional heteroscedasticity which depends on the past values of the return. A consequence is the volatility has the same magnitude for a negative or positive return. Financial series have their own characteristics which are usually difficult to reproduce artificially. An important characteristic is the leverage effect which consider negative returns differently than the positive returns. This is in contradiction with the construction of the GARCH model, because it cannot consider the asymmetry. The TGARCH (Threshold GARCH) model introduced by Rabemananjara and Zakoïan (1993) improve modeling because it considers the asymmetry since the volatility is determined by the past negative observations and the past positive observations with different weights. Various asymmetric GARCH processes are introduced in the econometric literature, for instance the EGARCH (Exponential GARCH) and the log GARCH models (see Francq et al. (2013) who studied the asymptotic properties of an EGARCH (1, 1) models).