-- Coordinated defensive escorts can aid a navigating payload by positioning themselves in order to maintain the safety of the payload from obstacles. In this paper, we present a novel, end-to-end solution for coordinating an escort team for protecting high-value payloads. Our solution employs deep reinforcement learning (RL) in order to train a team of escorts to maintain payload safety while navigating alongside the payload. This is done in a distributed fashion, relying only on limited range positional information of other escorts, the payload, and the obstacles. When compared to a state-of-art algorithm for obstacle avoidance, our solution with a single escort increases navigation success up to 31%. Additionally, escort teams increase success rate by up to 75% percent over escorts in static formations. We also show that this learned solution is general to several adaptations in the scenario including: a changing number of escorts in the team, changing obstacle density, and changes in payload conformation. Successful navigation in crowded scenarios often requires assuming a nonzero collision probability between the agent and stochastic obstacles [1]. This required assumption of risk is potentially frightening given the value of cargo that modern autonomous agents will be transporting, e.g., human life.

Continual learning models allow to learn and adapt to new changes and tasks over time. However, in continual and sequential learning scenarios in which the models are trained using different data with various distributions, neural networks tend to forget the previously learned knowledge. This phenomenon is often referred to as catastrophic forgetting. The catastrophic forgetting is an inevitable problem in continual learning models for dynamic environments. To address this issue, we propose a method, called Continual Bayesian Learning Networks (CBLN), which enables the networks to allocate additional resources to adapt to new tasks without forgetting the previously learned tasks. Using a Bayesian Neural Network, CBLN maintains a mixture of Gaussian posterior distributions that are associated with different tasks. The proposed method tries to optimise the number of resources that are needed to learn each task and avoids an exponential increase in the number of resources that are involved in learning multiple tasks. The proposed method does not need to access the past training data and can choose suitable weights to classify the data points during the test time automatically based on an uncertainty criterion. We have evaluated our method on the MNIST and UCR time-series datasets. The evaluation results show that our method can address the catastrophic forgetting problem at a promising rate compared to the state-of-the-art models.

We focus on kernel methods for set-valued inputs and their application to Bayesian set optimization, notably combinatorial optimization. We introduce a class of (strictly) positive definite kernels that relies on Reproducing Kernel Hilbert Space embeddings, and successfully generalizes "double sum" set kernels recently considered in Bayesian set optimization, which turn out to be unsuitable for combinatorial optimization. The proposed class of kernels, for which we provide theoretical guarantees, essentially consists in applying an outer kernel on top of the canonical distance induced by a double sum kernel. Proofs of theoretical results about considered kernels are complemented by a few practicalities regarding hyperparameter fitting. We furthermore demonstrate the applicability of our approach in prediction and optimization tasks, relying both on toy examples and on two test cases from mechanical engineering and hydrogeology, respectively. Experimental results illustrate the added value of the approach and open new perspectives in prediction and sequential design with set inputs.

We study the problem of causal discovery through targeted interventions. Starting from few observational measurements, we follow a Bayesian active learning approach to perform those experiments which, in expectation with respect to the current model, are maximally informative about the underlying causal structure. Unlike previous work, we consider the setting of continuous random variables with non-linear functional relationships, modelled with Gaussian process priors. To address the arising problem of choosing from an uncountable set of possible interventions, we propose to use Bayesian optimisation to efficiently maximise a Monte Carlo estimate of the expected information gain.

We introduce the probabilistic sequential matrix factorization (PSMF) method for factorizing time-varying and non-stationary datasets consisting of high-dimensional time-series. In particular, we consider nonlinear-Gaussian state-space models in which sequential approximate inference results in the factorization of a data matrix into a dictionary and time-varying coefficients with (possibly nonlinear) Markovian dependencies. The assumed Markovian structure on the coefficients enables us to encode temporal dependencies into a low-dimensional feature space. The proposed inference method is solely based on an approximate extended Kalman filtering scheme which makes the resulting method particularly efficient. The PSMF can account for temporal nonlinearities and, more importantly, can be used to calibrate and estimate generic differentiable nonlinear subspace models. We show that the PSMF can be used in multiple contexts: modelling time series with a periodic subspace, robustifying changepoint detection methods, and imputing missing-data in high-dimensional time-series of air pollutants measured across London.

Truncated densities are probability density functions defined on truncated input domains. These densities share the same parametric form with their non-truncated counterparts up to a normalization term. However, normalization terms usually cannot be obtained in closed form for these distributions, due to complicated truncation domains. Score Matching is a powerful tool for fitting parameters in unnormalized models. However, it cannot be straightforwardly applied here as boundary conditions used to derive a tractable objective are usually not satisfied by truncated distributions. In this paper, we propose a maximally weighted Score Matching objective function which takes the geometry of the truncation boundary into account when fitting unnor-malized density models. We show the weighting function that maximizes the objective function can be constructed easily and the boundary conditions for deriving a tradable objective are satisfied.

We present Natural Gradient Boosting (NGBoost), an algorithm which brings probabilistic prediction capability to gradient boosting in a generic way. Predictive uncertainty estimation is crucial in many applications such as healthcare and weather forecasting. Probabilistic prediction, which is the approach where the model outputs a full probability distribution over the entire outcome space, is a natural way to quantify those uncertainties. Gradient Boosting Machines have been widely successful in prediction tasks on structured input data, but a simple boosting solution for probabilistic prediction of real valued outputs is yet to be made. NGBoost is a gradient boosting approach which uses the \emph{Natural Gradient} to address technical challenges that makes generic probabilistic prediction hard with existing gradient boosting methods. Our approach is modular with respect to the choice of base learner, probability distribution, and scoring rule. We show empirically on several regression datasets that NGBoost provides competitive predictive performance of both uncertainty estimates and traditional metrics.

Many methods exist for function optimization, such as randomly sampling the variable search space, called random search, or systematically evaluating samples in a grid across the search space, called grid search. More principled methods are able to learn from sampling the space so that future samples are directed toward the parts of the search space that are most likely to contain the extrema. A directed approach to global optimization that uses probability is called Bayesian Optimization. Take my free 7-day email crash course now (with sample code). Click to sign-up and also get a free PDF Ebook version of the course.

Machine Learning engineers work around bias or the offsets in a model by drawing insights from the output, gauging the losses, going through tonnes of data and repeating till agreeable results have been obtained. This is a traditional process which takes time but works decently. An alternative to this approach is the Lagrangian approach, a mathematical method to find the local maxima and local minima of a function when provided with equality constraints. This too, comes with its own set of complexities. The unfairness of machine learning algorithms was exposed when they were deployed for manual tasks like hiring, surveillance and other such critical tasks, where the damages can be irreversible.

I'm trying to write a Kernel Density Estimation algorithm in Tensorflow. Later, when trying to predict the likelihood of a data point with respect to the model fitted above, for each data point I am evaluating, I am summing together the probability given by each of the kernels above: tf.reduce_sum([kernel._prob(X) for kernel in self.kernels], This approach only works when X is a numpy array, as TF doesn't let you iterate over a Tensor. My question is whether or not there is a way to make the algorithm above work with X as a tf.Tensor or tf.Variable?