A key challenge in reinforcement learning (RL) is how to bala nce exploration and exploitation in order to efficiently learn to make good sequences of decisions in a way that is both computationally tractable and statistically efficient. In the tabular case, the exploration-exploitation problem is well-understood for a number of settings (e.g., finite-hori zon, average reward, infinite horizon with discount), explorati on objectives (e.g., regret minimization and probably approximately correct), and for different algorithmic appro aches, where optimism-under-uncertainty [JOA10, FPLO18] and Thompson sampling (TS) [OBPVR16, Rus19] are the most pop ular principles. For instance, in the finite-horizon setting, [AOM17] and [ZB19] recently derived minimax optim al and structure adaptive regret bounds for optimistic exploration algorithms. TSbased algorithms have mainly b een analyzed in tabular MDPs in terms of Bayesian regret [OBPVR16, OR17, OGNJ17], which assumes that the MDP is s ampled from a known prior distribution. These bounds do not hold against a fixed MDP and algorithms with smal l Bayesian regret may still suffer high regret in some hard-to-learn MDPs within the chosen prior. In the tabu lar setting, frequentist (or worst-case) regret analysis h as been developed for TSbased algorithms both in the average r eward [GM15, AJ17] and finite-horizon case [Rus19]. Despite the fact that TSbased approaches have slightly wor se regret bounds compared to optimism-based algorithms, their empirical performance is often superior [CL11, OR17] . Unfortunately, the performance of tabular exploration met hods rapidly degrades with the number of states and actions, thus making them unfeasible in large or continuous MD Ps.

The framework of cognitively bounded rationality treats problem solving as fundamentally rational, but emphasises that it is constrained by cognitive architecture and the task environment. This paper investigates a simple decision making heuristic, Take The Best (TTB), within that framework. We formulate TTB as a likelihood-based probabilistic model, where the decision strategy arises by probabilistic inference based on the training data and the model constraints. The strengths of the probabilistic formulation, in addition to providing a bounded rational account of the learning of the heuristic, include natural extensibility with additional cognitively plausible constraints and prior information, and the possibility to embed the heuristic as a subpart of a larger probabilistic model. We extend the model to learn cue discrimination thresholds for continuous-valued cues and experiment with using the model to account for biased preference feedback from a boundedly rational agent in a simulated interactive machine learning task.

We consider the fusion of two aerodynamic data sets originating from differing fidelity physical or computer experiments. We specifically address the fusion of: 1) noisy and in-complete fields from wind tunnel measurements and 2) deterministic but biased fields from numerical simulations. These two data sources are fused in order to estimate the \emph{true} field that best matches measured quantities that serves as the ground truth. For example, two sources of pressure fields about an aircraft are fused based on measured forces and moments from a wind-tunnel experiment. A fundamental challenge in this problem is that the true field is unknown and can not be estimated with 100\% certainty. We employ a Bayesian framework to infer the true fields conditioned on measured quantities of interest; essentially we perform a \emph{statistical correction} to the data. The fused data may then be used to construct more accurate surrogate models suitable for early stages of aerospace design. We also introduce an extension of the Proper Orthogonal Decomposition with constraints to solve the same problem. Both methods are demonstrated on fusing the pressure distributions for flow past the RAE2822 airfoil and the Common Research Model wing at transonic conditions. Comparison of both methods reveal that the Bayesian method is more robust when data is scarce while capable of also accounting for uncertainties in the data. Furthermore, given adequate data, the POD based and Bayesian approaches lead to \emph{similar} results.

In this paper we offer a method and algorithm, which make possible fully autonomous (unsupervised) detection of new classes, and learning following a very parsimonious training priming (few labeled data samples only). Moreover, new unknown classes may appear at a later stage and the proposed xClass method and algorithm are able to successfully discover this and learn from the data autonomously. Furthermore, the features (inputs to the classifier) are automatically sub-selected by the algorithm based on the accumulated data density per feature per class. As a result, a highly efficient, lean, human-understandable, autonomously self-learning model (which only needs an extremely parsimonious priming) emerges from the data. To validate our proposal we tested it on two challenging problems, including imbalanced Caltech-101 data set and iRoads dataset. Not only we achieved higher precision, but, more significantly, we only used a single class beforehand, while other methods used all the available classes) and we generated interpretable models with smaller number of features used, through extremely weak and weak supervision.

Bayesian Neural Networks with Latent Variables (BNN+LV's) provide uncertainties in prediction estimates by explicitly modeling model uncertainty (via priors on network weights) and environmental stochasticity (via a latent input noise variable). In this work, we first show that BNN+LV suffers from a serious form of non-identifiability: explanatory power can be transferred between model parameters and input noise while fitting the data equally well. We demonstrate that, as a result, traditional inference methods may yield parameters that reconstruct observed data well but generalize poorly. Next, we develop a novel inference procedure that explicitly mitigates the effects of likelihood non-identifiability during training and yields high quality predictions as well as uncertainty estimates. We demonstrate that our inference method improves upon benchmark methods across a range of synthetic and real datasets.

Learning the causal-interaction network of multivariate Hawkes processes is a useful task in many applications. Maximum-likelihood estimation is the most common approach to solve the problem in the presence of long observation sequences. However, when only short sequences are available, the lack of data amplifies the risk of overfitting and regularization becomes critical. Due to the challenges of hyper-parameter tuning, state-of-the-art methods only parameterize regularizers by a single shared hyper-parameter, hence limiting the power of representation of the model. To solve both issues, we develop in this work an efficient algorithm based on variational expectation-maximization. Our approach is able to optimize over an extended set of hyper-parameters. It is also able to take into account the uncertainty in the model parameters by learning a posterior distribution over them. Experimental results on both synthetic and real datasets show that our approach significantly outperforms state-of-the-art methods under short observation sequences.

The usage of deep generative models for image compression has led to impressive performance gains over classical codecs while neural video compression is still in its infancy. Here, we propose an end-to-end, deep generative modeling approach to compress temporal sequences with a focus on video. Our approach builds upon variational autoencoder (VAE) models for sequential data and combines them with recent work on neural image compression. The approach jointly learns to transform the original sequence into a lower-dimensional representation as well as to discretize and entropy code this representation according to predictions of the sequential VAE. Rate-distortion evaluations on small videos from public data sets with varying complexity and diversity show that our model yields competitive results when trained on generic video content. Extreme compression performance is achieved when training the model on specialized content.

Probability is a measure of uncertainty. Probability applies to machine learning because in the real world, we need to make decisions with incomplete information. Hence, we need a mechanism to quantify uncertainty – which Probability provides us. Using probability, we can model elements of uncertainty such as risk in financial transactions and many other business processes. In contrast, in traditional programming, we work with deterministic problems i.e. the solution is not affected by uncertainty.

We address the problem of continual learning in multi-task Gaussian process (GP) models for handling sequential input-output observations. Our approach extends the existing prior-posterior recursion of online Bayesian inference, i.e.\ past posterior discoveries become future prior beliefs, to the infinite functional space setting of GP. For a reason of scalability, we introduce variational inference together with an sparse approximation based on inducing inputs. As a consequence, we obtain tractable continual lower-bounds where two novel Kullback-Leibler (KL) divergences intervene in a natural way. The key technical property of our method is the recursive reconstruction of conditional GP priors conditioned on the variational parameters learned so far. To achieve this goal, we introduce a novel factorization of past variational distributions, where the predictive GP equation propagates the posterior uncertainty forward. We then demonstrate that it is possible to derive GP models over many types of sequential observations, either discrete or continuous and amenable to stochastic optimization. The continual inference approach is also applicable to scenarios where potential multi-channel or heterogeneous observations might appear. Extensive experiments demonstrate that the method is fully scalable, shows a reliable performance and is robust to uncertainty error propagation over a plenty of synthetic and real-world datasets.

Learning exists in the context of data, yet notions of $\textit{confidence}$ typically focus on model predictions, not label quality. Confident learning (CL) has emerged as an approach for characterizing, identifying, and learning with noisy labels in datasets, based on the principles of pruning noisy data, counting to estimate noise, and ranking examples to train with confidence. Here, we generalize CL, building on the assumption of a classification noise process, to directly estimate the joint distribution between noisy (given) labels and uncorrupted (unknown) labels. This generalized CL, open-sourced as $\texttt{cleanlab}$, is provably consistent under reasonable conditions, and experimentally performant on ImageNet and CIFAR, outperforming recent approaches, e.g. MentorNet, by $30\%$ or more, when label noise is non-uniform. $\texttt{cleanlab}$ also quantifies ontological class overlap, and can increase model accuracy (e.g. ResNet) by providing clean data for training.