Risk-bounded motion planning is an important yet difficult problem for safety-critical tasks. While existing mathematical programming methods offer theoretical guarantees in the context of constrained Markov decision processes, they either lack scalability in solving larger problems or produce conservative plans. Recent advances in deep reinforcement learning improve scalability by learning policy networks as function approximators. In this paper, we propose an extension of soft actor critic model to estimate the execution risk of a plan through a risk critic and produce risk-bounded policies efficiently by adding an extra risk term in the loss function of the policy network. We define the execution risk in an accurate form, as opposed to approximating it through a summation of immediate risks at each time step that leads to conservative plans. Our proposed model is conditioned on a continuous spectrum of risk bounds, allowing the user to adjust the risk-averse level of the agent on the fly. Through a set of experiments, we show the advantage of our model in terms of both computational time and plan quality, compared to a state-of-the-art mathematical programming baseline, and validate its performance in more complicated scenarios, including nonlinear dynamics and larger state space.

In this work we continue studies of the uncertainty quantification problem in emission tomographies such as PET or SPECT. In particular, we consider a scenario when additional multimodal data (e.g., anatomical MRI images) are available. To solve the aforementioned problem we adapt the recently proposed nonparametric posterior learning technique to the context of Poisson-type data in emission tomography. Using this approach we derive sampling algorithms which are trivially parallelizable, scalable and very easy to implement. In addition, we prove conditional consistency and tightness for the distribution of produced samples in the small noise limit (i.e., when the acquisition time tends to infinity) and derive new geometrical and necessary condition on how MRI images must be used. This condition arises naturally in the context of misspecified generalized Poisson models. We also contrast our approach with bayesian MCMC sampling based one one data augmentation scheme which is very popular in the context of EM-type algorithms for PET or SPECT. We show theoretically and also numerically that such data augmentation significantly increases mixing times for the Markov chain. In view of this, our algorithms seem to give a reasonable trade-off between design complexity, scalability, numerical load and asessement for the uncertainty quantification.

Naive, Yet it is one of the very simple yet powerful and easy to implement algorithm used in Supervised learning mainly for classification problems. Through this blog, I intend to make y'all have a basic understanding of the Naive Bayes classifier and its applications and why is it called naive. Naive Bayes classifier is built upon three main fundamental theories which are Probababilty, Conditional Probability and Bayes theorem. I assume that my readers have knowledge of these if not you can find my blog on these over here. I will just try to give an overview of what is Baye's theorem because that is important to understand Naive Baye's theorem.

Tensor models play an increasingly prominent role in many fields, notably in machine learning. In several applications of such models, such as community detection, topic modeling and Gaussian mixture learning, one must estimate a low-rank signal from a noisy tensor. Hence, understanding the fundamental limits and the attainable performance of estimators of that signal inevitably calls for the study of random tensors. Substantial progress has been achieved on this subject thanks to recent efforts, under the assumption that the tensor dimensions grow large. Yet, some of the most significant among these results--in particular, a precise characterization of the abrupt phase transition (in terms of signal-to-noise ratio) that governs the performance of the maximum likelihood (ML) estimator of a symmetric rank-one model with Gaussian noise--were derived on the basis of statistical physics ideas, which are not easily accessible to non-experts. In this work, we develop a sharply distinct approach, relying instead on standard but powerful tools brought by years of advances in random matrix theory. The key idea is to study the spectra of random matrices arising from contractions of a given random tensor. We show how this gives access to spectral properties of the random tensor itself. In the specific case of a symmetric rank-one model with Gaussian noise, our technique yields a hitherto unknown characterization of the local maximum of the ML problem that is global above the phase transition threshold. This characterization is in terms of a fixed-point equation satisfied by a formula that had only been previously obtained via statistical physics methods. Moreover, our analysis sheds light on certain properties of the landscape of the ML problem in the large-dimensional setting. Our approach is versatile and can be extended to other models, such as asymmetric, non-Gaussian and higher-order ones.

This paper establishes non-asymptotic bounds on Wasserstein distances between the invariant probability measures of inexact MCMC methods and their target distribution. In particular, the results apply to the unadjusted Langevin algorithm and to unadjusted Hamiltonian Monte Carlo, but also to methods relying on other discretization schemes. Our focus is on understanding the precise dependence of the accuracy on both the dimension and the discretization step size. We show that the dimension dependence relies on some key quantities. As a consequence, the same dependence on the step size and the dimension as in the product case can be recovered for several important classes of models. On the other hand, for more general models, the dimension dependence of the asymptotic bias may be worse than in the product case even if the exact dynamics has dimension-free mixing properties.

For robots to operate in a three dimensional world and interact with humans, learning spatial relationships among objects in the surrounding is necessary. Reasoning about the state of the world requires inputs from many different sensory modalities including vision ($V$) and haptics ($H$). We examine the problem of desk organization: learning how humans spatially position different objects on a planar surface according to organizational ''preference''. We model this problem by examining how humans position objects given multiple features received from vision and haptic modalities. However, organizational habits vary greatly between people both in structure and adherence. To deal with user organizational preferences, we add an additional modality, ''utility'' ($U$), which informs on a particular human's perceived usefulness of a given object. Models were trained as generalized (over many different people) or tailored (per person). We use two types of models: random forests, which focus on precise multi-task classification, and Markov logic networks, which provide an easily interpretable insight into organizational habits. The models were applied to both synthetic data, which proved to be learnable when using fixed organizational constraints, and human-study data, on which the random forest achieved over 90% accuracy. Over all combinations of $\{H, U, V\}$ modalities, $UV$ and $HUV$ were the most informative for organization. In a follow-up study, we gauged participants preference of desk organizations by a generalized random forest organization vs. by a random model. On average, participants rated the random forest models as 4.15 on a 5-point Likert scale compared to 1.84 for the random model

This thesis explores the benefits machine learning algorithms can bring to online planning and scheduling for autonomous vehicles in off-road situations. Mainly, we focus on typical problems of interest which include computing itineraries that meet certain objectives, as well as computing scheduling strategies to execute synchronized maneuvers with other vehicles. We present a range of learning-based heuristics to assist different itinerary planners. We show that these heuristics allow a significant increase in performance for optimal planners. Furthermore, in the case of approximate planning, we show that not only does the running time decrease, the quality of the itinerary found also becomes almost always better. Finally, in order to synthesize strategies to execute synchronized maneuvers, we propose a novel type of scheduling controllability and a learning-assisted algorithm. The proposed framework achieves significant improvement on known benchmarks in this controllability type over the performance of state-of-the-art works in a related controllability type. Moreover, it is able to find strategies on complex scheduling problems for which previous works fail to do so.

This survey gives an overview of Monte Carlo methodologies using surrogate models, for dealing with densities which are intractable, costly, and/or noisy. This type of problem can be found in numerous real-world scenarios, including stochastic optimization and reinforcement learning, where each evaluation of a density function may incur some computationally-expensive or even physical (real-world activity) cost, likely to give different results each time. The surrogate model does not incur this cost, but there are important trade-offs and considerations involved in the choice and design of such methodologies. We classify the different methodologies into three main classes and describe specific instances of algorithms under a unified notation. A modular scheme which encompasses the considered methods is also presented. A range of application scenarios is discussed, with special attention to the likelihood-free setting and reinforcement learning. Several numerical comparisons are also provided.

Energy disaggregation, also known as non-intrusive load monitoring (NILM), challenges the problem of separating the whole-home electricity usage into appliance-specific individual consumptions, which is a typical application of data analysis. {NILM aims to help households understand how the energy is used and consequently tell them how to effectively manage the energy, thus allowing energy efficiency which is considered as one of the twin pillars of sustainable energy policy (i.e., energy efficiency and renewable energy).} Although NILM is unidentifiable, it is widely believed that the NILM problem can be addressed by data science. Most of the existing approaches address the energy disaggregation problem by conventional techniques such as sparse coding, non-negative matrix factorization, and hidden Markov model. Recent advances reveal that deep neural networks (DNNs) can get favorable performance for NILM since DNNs can inherently learn the discriminative signatures of the different appliances. In this paper, we propose a novel method named adversarial energy disaggregation (AED) based on DNNs. We introduce the idea of adversarial learning into NILM, which is new for the energy disaggregation task. Our method trains a generator and multiple discriminators via an adversarial fashion. The proposed method not only learns shard representations for different appliances, but captures the specific multimode structures of each appliance. Extensive experiments on real-world datasets verify that our method can achieve new state-of-the-art performance.

Autonomous systems often operate in environments where the behavior of multiple agents is coordinated by a shared global state. Reliable estimation of the global state is thus critical for successfully operating in a multi-agent setting. We introduce agent-aware state estimation -- a framework for calculating indirect estimations of state given observations of the behavior of other agents in the environment. We also introduce transition-independent agent-aware state estimation -- a tractable class of agent-aware state estimation -- and show that it allows the speed of inference to scale linearly with the number of agents in the environment. As an example, we model traffic light classification in instances of complete loss of direct observation. By taking into account observations of vehicular behavior from multiple directions of traffic, our approach exhibits accuracy higher than that of existing traffic light-only HMM methods on a real-world autonomous vehicle data set under a variety of simulated occlusion scenarios.