Marginalising over families of Gaussian Process kernels produces flexible model classes with well-calibrated uncertainty estimates. Existing approaches require likelihood evaluations of many kernels, rendering them prohibitively expensive for larger datasets. We propose a Bayesian Quadrature scheme to make this marginalisation more efficient and thereby more practical. Through use of the maximum mean discrepancies between distributions, we define a kernel over kernels that captures invariances between Spectral Mixture (SM) Kernels. Kernel samples are selected by generalising an information-theoretic acquisition function for warped Bayesian Quadrature. We show that our framework achieves more accurate predictions with better calibrated uncertainty than state-of-the-art baselines, especially when given limited (wall-clock) time budgets.
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Anomalous diffusion is often modelled in terms of the subdiffusion equation, which can involve a weakly singular source term. For this case, many predominant time stepping methods, including the correction of high-order BDF schemes [{\sc Jin, Li, and Zhou}, SIAM J. Sci. Comput., 39 (2017), A3129--A3152], may suffer from a severe order reduction. To fill in this gap, we propose a smoothing method for time stepping schemes, where the singular term is regularized by using a $m$-fold integral-differential calculus and the equation is discretized by the $k$-step BDF convolution quadrature, called ID$m$-BDF$k$ method. We prove that the desired $k$th-order convergence can be recovered even if the source term is a weakly singular and the initial data is not compatible. Numerical experiments illustrate the theoretical results.
In this paper we discuss potentially practical ways to produce expander graphs with good spectral properties and a compact description. We focus on several classes of uniform and bipartite expander graphs defined as random Schreier graphs of the general linear group over the finite field of size two. We perform numerical experiments and show that such constructions produce spectral expanders that can be useful for practical applications. To find a theoretical explanation of the observed experimental results, we used the method of moments to prove upper bounds for the expected second largest eigenvalue of the random Schreier graphs used in our constructions. We focus on bounds for which it is difficult to study the asymptotic behaviour but it is possible to compute non-trivial conclusions for relatively small graphs with parameters from our numerical experiments (e.g., with less than 2^200 vertices and degree at least logarithmic in the number of vertices).
Conversational recommendation systems (CRS) aim to timely and proactively acquire user dynamic preferred attributes through conversations for item recommendation. In each turn of CRS, there naturally have two decision-making processes with different roles that influence each other: 1) director, which is to select the follow-up option (i.e., ask or recommend) that is more effective for reducing the action space and acquiring user preferences; and 2) actor, which is to accordingly choose primitive actions (i.e., asked attribute or recommended item) that satisfy user preferences and give feedback to estimate the effectiveness of the director's option. However, existing methods heavily rely on a unified decision-making module or heuristic rules, while neglecting to distinguish the roles of different decision procedures, as well as the mutual influences between them. To address this, we propose a novel Director-Actor Hierarchical Conversational Recommender (DAHCR), where the director selects the most effective option, followed by the actor accordingly choosing primitive actions that satisfy user preferences. Specifically, we develop a dynamic hypergraph to model user preferences and introduce an intrinsic motivation to train from weak supervision over the director. Finally, to alleviate the bad effect of model bias on the mutual influence between the director and actor, we model the director's option by sampling from a categorical distribution. Extensive experiments demonstrate that DAHCR outperforms state-of-the-art methods.
Model-based approaches to reinforcement learning (MBRL) exhibit favorable performance in practice, but their theoretical guarantees in large spaces are mostly restricted to the setting when transition model is Gaussian or Lipschitz, and demands a posterior estimate whose representational complexity grows unbounded with time. In this work, we develop a novel MBRL method (i) which relaxes the assumptions on the target transition model to belong to a generic family of mixture models; (ii) is applicable to large-scale training by incorporating a compression step such that the posterior estimate consists of a Bayesian coreset of only statistically significant past state-action pairs; and (iii) exhibits a sublinear Bayesian regret. To achieve these results, we adopt an approach based upon Stein's method, which, under a smoothness condition on the constructed posterior and target, allows distributional distance to be evaluated in closed form as the kernelized Stein discrepancy (KSD). The aforementioned compression step is then computed in terms of greedily retaining only those samples which are more than a certain KSD away from the previous model estimate. Experimentally, we observe that this approach is competitive with several state-of-the-art RL methodologies, and can achieve up-to 50 percent reduction in wall clock time in some continuous control environments.
Constructing decision trees online is a classical machine learning problem. Existing works often assume that features are readily available for each incoming data point. However, in many real world applications, both feature values and the labels are unknown a priori and can only be obtained at a cost. For example, in medical diagnosis, doctors have to choose which tests to perform (i.e., making costly feature queries) on a patient in order to make a diagnosis decision (i.e., predicting labels). We provide a fresh perspective to tackle this practical challenge. Our framework consists of an active planning oracle embedded in an online learning scheme for which we investigate several information acquisition functions. Specifically, we employ a surrogate information acquisition function based on adaptive submodularity to actively query feature values with a minimal cost, while using a posterior sampling scheme to maintain a low regret for online prediction. We demonstrate the efficiency and effectiveness of our framework via extensive experiments on various real-world datasets. Our framework also naturally adapts to the challenging setting of online learning with concept drift and is shown to be competitive with baseline models while being more flexible.
Multi-scale design has been considered in recent image super-resolution (SR) works to explore the hierarchical feature information. Existing multi-scale networks aim to build elaborate blocks or progressive architecture for restoration. In general, larger scale features concentrate more on structural and high-level information, while smaller scale features contain plentiful details and textured information. In this point of view, information from larger scale features can be derived from smaller ones. Based on the observation, in this paper, we build a sequential hierarchical learning super-resolution network (SHSR) for effective image SR. Specially, we consider the inter-scale correlations of features, and devise a sequential multi-scale block (SMB) to progressively explore the hierarchical information. SMB is designed in a recursive way based on the linearity of convolution with restricted parameters. Besides the sequential hierarchical learning, we also investigate the correlations among the feature maps and devise a distribution transformation block (DTB). Different from attention-based methods, DTB regards the transformation in a normalization manner, and jointly considers the spatial and channel-wise correlations with scaling and bias factors. Experiment results show SHSR achieves superior quantitative performance and visual quality to state-of-the-art methods with near 34\% parameters and 50\% MACs off when scaling factor is $\times4$. To boost the performance without further training, the extension model SHSR$^+$ with self-ensemble achieves competitive performance than larger networks with near 92\% parameters and 42\% MACs off with scaling factor $\times4$.
Bayesian optimization (BO) is a popular approach for sample-efficient optimization of black-box objective functions. While BO has been successfully applied to a wide range of scientific applications, traditional approaches to single-objective BO only seek to find a single best solution. This can be a significant limitation in situations where solutions may later turn out to be intractable. For example, a designed molecule may turn out to violate constraints that can only be reasonably evaluated after the optimization process has concluded. To address this issue, we propose Rank-Ordered Bayesian Optimization with Trust-regions (ROBOT) which aims to find a portfolio of high-performing solutions that are diverse according to a user-specified diversity metric. We evaluate ROBOT on several real-world applications and show that it can discover large sets of high-performing diverse solutions while requiring few additional function evaluations compared to finding a single best solution.
We present a study using new computational methods, based on a novel combination of machine learning for inferring admixture hidden Markov models and probabilistic model checking, to uncover interaction styles in a mobile app. These styles are then used to inform a redesign, which is implemented, deployed, and then analysed using the same methods. The data sets are logged user traces, collected over two six-month deployments of each version, involving thousands of users and segmented into different time intervals. The methods do not assume tasks or absolute metrics such as measures of engagement, but uncover the styles through unsupervised inference of clusters and analysis with probabilistic temporal logic. For both versions there was a clear distinction between the styles adopted by users during the first day/week/month of usage, and during the second and third months, a result we had not anticipated.
The Bayesian paradigm has the potential to solve core issues of deep neural networks such as poor calibration and data inefficiency. Alas, scaling Bayesian inference to large weight spaces often requires restrictive approximations. In this work, we show that it suffices to perform inference over a small subset of model weights in order to obtain accurate predictive posteriors. The other weights are kept as point estimates. This subnetwork inference framework enables us to use expressive, otherwise intractable, posterior approximations over such subsets. In particular, we implement subnetwork linearized Laplace: We first obtain a MAP estimate of all weights and then infer a full-covariance Gaussian posterior over a subnetwork. We propose a subnetwork selection strategy that aims to maximally preserve the model's predictive uncertainty. Empirically, our approach is effective compared to ensembles and less expressive posterior approximations over full networks.
Convolutional neural networks (CNNs) have shown dramatic improvements in single image super-resolution (SISR) by using large-scale external samples. Despite their remarkable performance based on the external dataset, they cannot exploit internal information within a specific image. Another problem is that they are applicable only to the specific condition of data that they are supervised. For instance, the low-resolution (LR) image should be a "bicubic" downsampled noise-free image from a high-resolution (HR) one. To address both issues, zero-shot super-resolution (ZSSR) has been proposed for flexible internal learning. However, they require thousands of gradient updates, i.e., long inference time. In this paper, we present Meta-Transfer Learning for Zero-Shot Super-Resolution (MZSR), which leverages ZSSR. Precisely, it is based on finding a generic initial parameter that is suitable for internal learning. Thus, we can exploit both external and internal information, where one single gradient update can yield quite considerable results. (See Figure 1). With our method, the network can quickly adapt to a given image condition. In this respect, our method can be applied to a large spectrum of image conditions within a fast adaptation process.
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