Gradient boosting machines (GBMs) based on decision trees consistently demonstrate state-of-the-art results on regression and classification tasks with tabular data, often outperforming deep neural networks. However, these models do not provide well-calibrated predictive uncertainties, which prevents their use for decision making in high-risk applications. The Bayesian treatment is known to improve predictive uncertainty calibration, but previously proposed Bayesian GBM methods are either computationally expensive, or resort to crude approximations. Variational inference is often used to implement Bayesian neural networks, but is difficult to apply to GBMs, because the decision trees used as weak learners are non-differentiable. In this paper, we propose to implement Bayesian GBMs using variational inference with soft decision trees, a fully differentiable alternative to standard decision trees introduced by Irsoy et al. Our experiments demonstrate that variational soft trees and variational soft GBMs provide useful uncertainty estimates, while retaining good predictive performance. The proposed models show higher test likelihoods when compared to the state-of-the-art Bayesian GBMs in 7/10 tabular regression datasets and improved out-of-distribution detection in 5/10 datasets.

Rate-distortion theory-based outlier detection builds upon the rationale that a good data compression will encode outliers with unique symbols. Based on this rationale, we propose Cluster Purging, which is an extension of clustering-based outlier detection. This extension allows one to assess the representivity of clusterings, and to find data that are best represented by individual unique clusters. We propose two efficient algorithms for performing Cluster Purging, one being parameter-free, while the other algorithm has a parameter that controls representivity estimations, allowing it to be tuned in supervised setups. In an experimental evaluation, we show that Cluster Purging improves upon outliers detected from raw clusterings, and that Cluster Purging competes strongly against state-of-the-art alternatives.

Explaining algorithmic decisions and recommending actionable feedback is increasingly important for machine learning applications. Recently, significant efforts have been invested in finding a diverse set of recourses to cover the wide spectrum of users' preferences. However, existing works often neglect the requirement that the recourses should be close to the data manifold; hence, the constructed recourses might be implausible and unsatisfying to users. To address these issues, we propose a novel approach that explicitly directs the diverse set of actionable recourses towards the data manifold. We first find a diverse set of prototypes in the favorable class that balances the trade-off between diversity and proximity. We demonstrate two specific methods to find these prototypes: either by finding the maximum a posteriori estimate of a determinantal point process or by solving a quadratic binary program. To ensure the actionability constraints, we construct an actionability graph in which the nodes represent the training samples and the edges indicate the feasible action between two instances. We then find a feasible path to each prototype, and this path demonstrates the feasible actions for each recourse in the plan. The experimental results show that our method produces a set of recourses that are close to the data manifold while delivering a better cost-diversity trade-off than existing approaches.

We consider the problem of content caching at the wireless edge to serve a set of end users via unreliable wireless channels so as to minimize the average latency experienced by end users due to the constrained wireless edge cache capacity. We formulate this problem as a Markov decision process, or more specifically a restless multi-armed bandit problem, which is provably hard to solve. We begin by investigating a discounted counterpart, and prove that it admits an optimal policy of the threshold-type. We then show that this result also holds for average latency problem. Using this structural result, we establish the indexability of our problem, and employ the Whittle index policy to minimize average latency. Since system parameters such as content request rates and wireless channel conditions are often unknown and time-varying, we further develop a model-free reinforcement learning algorithm dubbed as Q^{+}-Whittle that relies on Whittle index policy. However, Q^{+}-Whittle requires to store the Q-function values for all state-action pairs, the number of which can be extremely large for wireless edge caching. To this end, we approximate the Q-function by a parameterized function class with a much smaller dimension, and further design a Q^{+}-Whittle algorithm with linear function approximation, which is called Q^{+}-Whittle-LFA. We provide a finite-time bound on the mean-square error of Q^{+}-Whittle-LFA. Simulation results using real traces demonstrate that Q^{+}-Whittle-LFA yields excellent empirical performance.

Bernstein's condition is a key assumption that guarantees fast rates in machine learning. For example, the Gibbs algorithm with prior $\pi$ has an excess risk in $O(d_{\pi}/n)$, as opposed to the standard $O(\sqrt{d_{\pi}/n})$, where $n$ denotes the number of observations and $d_{\pi}$ is a complexity parameter which depends on the prior $\pi$. In this paper, we examine the Gibbs algorithm in the context of meta-learning, i.e., when learning the prior $\pi$ from $T$ tasks (with $n$ observations each) generated by a meta distribution. Our main result is that Bernstein's condition always holds at the meta level, regardless of its validity at the observation level. This implies that the additional cost to learn the Gibbs prior $\pi$, which will reduce the term $d_\pi$ across tasks, is in $O(1/T)$, instead of the expected $O(1/\sqrt{T})$. We further illustrate how this result improves on standard rates in three different settings: discrete priors, Gaussian priors and mixture of Gaussians priors.

We introduce GAUCHE, a library for GAUssian processes in CHEmistry. Gaussian processes have long been a cornerstone of probabilistic machine learning, affording particular advantages for uncertainty quantification and Bayesian optimisation. Extending Gaussian processes to chemical representations, however, is nontrivial, necessitating kernels defined over structured inputs such as graphs, strings and bit vectors. By defining such kernels in GAUCHE, we seek to open the door to powerful tools for uncertainty quantification and Bayesian optimisation in chemistry. Motivated by scenarios frequently encountered in experimental chemistry, we showcase applications for GAUCHE in molecular discovery and chemical reaction optimisation. The codebase is made available at https://github.com/leojklarner/gauche

With the growth of neural network size, model compression has attracted increasing interest in recent research. As one of the most common techniques, pruning has been studied for a long time. By exploiting the structured sparsity of the neural network, existing methods can prune neurons instead of individual weights. However, in most existing pruning methods, surviving neurons are randomly connected in the neural network without any structure, and the non-zero weights within each neuron are also randomly distributed. Such irregular sparse structure can cause very high control overhead and irregular memory access for the hardware and even increase the neural network computational complexity. In this paper, we propose a three-layer hierarchical prior to promote a more regular sparse structure during pruning. The proposed three-layer hierarchical prior can achieve per-neuron weight-level structured sparsity and neuron-level structured sparsity. We derive an efficient Turbo-variational Bayesian inferencing (Turbo-VBI) algorithm to solve the resulting model compression problem with the proposed prior. The proposed Turbo-VBI algorithm has low complexity and can support more general priors than existing model compression algorithms. Simulation results show that our proposed algorithm can promote a more regular structure in the pruned neural networks while achieving even better performance in terms of compression rate and inferencing accuracy compared with the baselines.

While the Bayesian decision-theoretic framework offers an elegant solution to the problem of decision making under uncertainty, one question is how to appropriately select the prior distribution. One idea is to employ a worst-case prior. However, this is not as easy to specify in sequential decision making as in simple statistical estimation problems. This paper studies (sometimes approximate) minimax-Bayes solutions for various reinforcement learning problems to gain insights into the properties of the corresponding priors and policies. We find that while the worst-case prior depends on the setting, the corresponding minimax policies are more robust than those that assume a standard (i.e. uniform) prior.

In this big data era, it is hard for the current generation to find the right data from the huge amount of data contained within online platforms. In such a situation, there is a need for an information filtering system that might help them find the information they are looking for. In recent years, a research field has emerged known as recommender systems. Recommenders have become important as they have many real-life applications. This paper reviews the different techniques and developments of recommender systems in e-commerce, e-tourism, e-resources, e-government, e-learning, and e-library. By analyzing recent work on this topic, we will be able to provide a detailed overview of current developments and identify existing difficulties in recommendation systems. The final results give practitioners and researchers the necessary guidance and insights into the recommendation system and its application.

In this article, we propose a novel pessimism-based Bayesian learning method for optimal dynamic treatment regimes in the offline setting. When the coverage condition does not hold, which is common for offline data, the existing solutions would produce sub-optimal policies. The pessimism principle addresses this issue by discouraging recommendation of actions that are less explored conditioning on the state. However, nearly all pessimism-based methods rely on a key hyper-parameter that quantifies the degree of pessimism, and the performance of the methods can be highly sensitive to the choice of this parameter. We propose to integrate the pessimism principle with Thompson sampling and Bayesian machine learning for optimizing the degree of pessimism. We derive a credible set whose boundary uniformly lower bounds the optimal Q-function, and thus we do not require additional tuning of the degree of pessimism. We develop a general Bayesian learning method that works with a range of models, from Bayesian linear basis model to Bayesian neural network model. We develop the computational algorithm based on variational inference, which is highly efficient and scalable. We establish the theoretical guarantees of the proposed method, and show empirically that it outperforms the existing state-of-the-art solutions through both simulations and a real data example.