We propose a multiresolution Gaussian process (GP) model which assumes conditional independence among GPs across resolutions. We characterize each GP using a particular representation of the Karhunen-Lo\`eve expansion where each basis vector of the representation consists of an axis and a scale factor, referred to as the basis axis and the basis-axis scale. The basis axes have unique characteristics: They are zero-mean by construction and are on the unit sphere. The axes are modeled using Bingham distributions---a natural choice for modeling axial data. Given the axes, all GPs across resolutions are independent---this is in direct contrast to the common assumption of full independence between GPs. More specifically, all GPs are tied to the same set of axes but the basis-axis scales of each GP are specific to the resolution on which they are defined. Relaxing the full independence assumption helps in reducing overfitting which can be of a problem in an otherwise identical model architecture with full independence assumption. We consider a Bayesian treatment of the model using variational inference.

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.

This paper proposes an agent with particle swarm optimization (PSO) based on a Fuzzy Markup Language (FML) for students learning performance evaluation and educational applications, and the proposed agent is according to the response data from a conventional test and an item response theory. First, we apply a GS-based parameter estimation mechanism to estimate the items parameters according to the response data, and then to compare its results with those of an IRT-based Bayesian parameter estimation mechanism. In addition, we propose a static-IRT test assembly mechanism to assemble a form for the conventional test. The presented FML-based dynamic assessment mechanism infers the probability of making a correct response to the item for a student with various abilities. Moreover, this paper also proposes a novel PFML learning mechanism for optimizing the parameters between items and students. Finally, we adopt a K-fold cross validation mechanism to evaluate the performance of the proposed agent. Experimental results show that the novel PFML learning mechanism for the parameter estimation and learning optimization performs favorably. We believe the proposed PFML will be a reference for education research and pedagogy and an important co-learning mechanism for future human-machine educational applications.

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.

Ordered weighted averaging (OWA) operators have been widely used in decision making these past few years. An important issue facing the OWA operators' users is the determination of the OWA weights. This paper introduces an OWA determination method based on truncated distributions that enables intuitive generation of OWA weights according to a certain level of risk and trade-off. These two dimensions are represented by the two first moments of the truncated distribution. We illustrate our approach with the well-know normal distribution and the definition of a continuous parabolic decision-strategy space. We finally study the impact of the number of criteria on the results.

Determinantal point processes (DPPs) enable the modelling of repulsion: they provide diverse sets of points. This repulsion is encoded in a kernel K that we can see as a matrix storing the similarity between points. The usual algorithm to sample DPPs is exact but it uses the spectral decomposition of K, a computation that becomes costly when dealing with a high number of points. Here, we present an alternative exact algorithm that avoids the eigenvalues and the eigenvectors computation and that is, for some applications, faster than the original algorithm.

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.

Policy gradient methods have achieved remarkable successes in solving challenging reinforcement learning problems. However, it still often suffers from the large variance issue on policy gradient estimation, which leads to poor sample efficiency during training. In this work, we propose a control variate method to effectively reduce variance for policy gradient methods. Motivated by the Stein's identity, our method extends the previous control variate methods used in REINFORCE and advantage actor-critic by introducing more general action-dependent baseline functions. Empirical studies show that our method significantly improves the sample efficiency of the state-of-the-art policy gradient approaches.