Truckload brokerages, a $100 billion/year industry in the U.S., plays the critical role of matching shippers with carriers, often to move loads several days into the future. Brokerages not only have to find companies that will agree to move a load, the brokerage often has to find a price that both the shipper and carrier will agree to. The price not only varies by shipper and carrier, but also by the traffic lanes and other variables such as commodity type. Brokerages have to learn about shipper and carrier response functions by offering a price and observing whether each accepts the quote. We propose a knowledge gradient policy with bootstrap aggregation for high-dimensional contextual settings to guide price experimentation by maximizing the value of information. The learning policy is tested using a newly developed, carefully calibrated fleet simulator that includes a stochastic lookahead policy that simulates fleet movements, as well as the stochastic modeling of driver assignments and the carrier's load commitment policies with advance booking.

A probability on its own is often an uninteresting thing. But when we can compare probabilities, that is when their full splendour is revealed. By comparing probabilities we are able form judgements; by comparing probabilities we can exploit the elements of our world that are probable; by comparing probabilities we can see the value of objects that are rare. In their own ways, all machine learning tricks help us make better probabilistic comparisons. Comparison is the theme of this post--not discussed in this series before--and the right start to this second sprint of machine learning tricks.

We call a learner super-teachable if a teacher can trim down an iid training set while making the learner learn even better. We provide sharp super-teaching guarantees on two learners: the maximum likelihood estimator for the mean of a Gaussian, and the large margin classifier in 1D. For general learners, we provide a mixed-integer nonlinear programming-based algorithm to find a super teaching set. Empirical experiments show that our algorithm is able to find good super-teaching sets for both regression and classification problems.

We propose a novel approach to parameter estimation for simulator-based statistical models with intractable likelihoods. The proposed method is recursive application of kernel ABC and kernel herding to the same observed data. We provide a theoretical explanation regarding why this approach works, showing (for the population setting) that the point estimate obtained with this method converges to the true parameter as recursion proceeds, under a certain assumption. We conduct a variety of numerical experiments, including parameter estimation for a real-world pedestrian flow simulator, and show that our method outperforms existing approaches in most cases.

Amortized inference allows latent-variable models trained via variational learning to scale to large datasets. The quality of approximate inference is determined by two factors: a) the capacity of the variational distribution to match the true posterior and b) the ability of the recognition network to produce good variational parameters for each datapoint. We examine approximate inference in variational autoencoders in terms of these factors. We find that divergence from the true posterior is often due to imperfect recognition networks, rather than the limited complexity of the approximating distribution. We show that this is due partly to the generator learning to accommodate the choice of approximation. Furthermore, we show that the parameters used to increase the expressiveness of the approximation play a role in generalizing inference rather than simply improving the complexity of the approximation.

Recent progress in variational inference has paid much attention to the flexibility of variational posteriors. One promising direction is to use implicit distributions, i.e., distributions without tractable densities as the variational posterior. However, existing methods on implicit posteriors still face challenges of noisy estimation and computational infeasibility when applied to models with high-dimensional latent variables. In this paper, we present a new approach named Kernel Implicit Variational Inference that addresses these challenges. As far as we know, for the first time implicit variational inference is successfully applied to Bayesian neural networks, which shows promising results on both regression and classification tasks.

Implicit models, which allow for the generation of samples but not for point-wise evaluation of probabilities, are omnipresent in real-world problems tackled by machine learning and a hot topic of current research. Some examples include data simulators that are widely used in engineering and scientific research, generative adversarial networks (GANs) for image synthesis, and hot-off-the-press approximate inference techniques relying on implicit distributions. The majority of existing approaches to learning implicit models rely on approximating the intractable distribution or optimisation objective for gradient-based optimisation, which is liable to produce inaccurate updates and thus poor models. This paper alleviates the need for such approximations by proposing the Stein gradient estimator, which directly estimates the score function of the implicitly defined distribution. The efficacy of the proposed estimator is empirically demonstrated by examples that include meta-learning for approximate inference, and entropy regularised GANs that provide improved sample diversity.

Visual analytics systems combine machine learning or other analytic techniques with interactive data visualization to promote sensemaking and analytical reasoning. It is through such techniques that people can make sense of large, complex data. While progress has been made, the tactful combination of machine learning and data visualization is still under-explored. This state-of-the-art report presents a summary of the progress that has been made by highlighting and synthesizing select research advances. Further, it presents opportunities and challenges to enhance the synergy between machine learning and visual analytics for impactful future research directions.

Causal discovery from empirical data is a fundamental problem in many scientific domains. Observational data allows for identifiability only up to Markov equivalence class. In this paper we first propose a polynomial time algorithm for learning the exact correctly-oriented structure of the transitive reduction of any causal Bayesian networks with high probability, by using interventional path queries. Each path query takes as input an origin node and a target node, and answers whether there is a directed path from the origin to the target. This is done by intervening the origin node and observing samples from the target node. We theoretically show the logarithmic sample complexity for the size of interventional data per path query, for continuous and discrete networks. We further extend our work to learn the transitive edges using logarithmic sample complexity (albeit in time exponential in the maximum number of parents for discrete networks). This allows us to learn the full network. We also provide an analysis of imperfect interventions.

Distribution regression has recently attracted much interest as a generic solution to the problem of supervised learning where labels are available at the group level, rather than at the individual level. Current approaches, however, do not propagate the uncertainty in observations due to sampling variability in the groups. This effectively assumes that small and large groups are estimated equally well, and should have equal weight in the final regression. We account for this uncertainty with a Bayesian distribution regression formalism, improving the robustness and performance of the model when group sizes vary. We frame our models in a neural network style, allowing for simple MAP inference using backpropagation to learn the parameters, as well as MCMC-based inference which can fully propagate uncertainty. We demonstrate our approach on illustrative toy datasets, as well as on a challenging problem of predicting age from images.