An unsupervised learning algorithm to cluster hyperspectral image (HSI) data is proposed that exploits spatially-regularized random walks. Markov diffusions are defined on the space of HSI spectra with transitions constrained to near spatial neighbors. The explicit incorporation of spatial regularity into the diffusion construction leads to smoother random processes that are more adapted for unsupervised machine learning than those based on spectra alone. The regularized diffusion process is subsequently used to embed the high-dimensional HSI into a lower dimensional space through diffusion distances. Cluster modes are computed using density estimation and diffusion distances, and all other points are labeled according to these modes. The proposed method has low computational complexity and performs competitively against state-of-the-art HSI clustering algorithms on real data. In particular, the proposed spatial regularization confers an empirical advantage over non-regularized methods.

This paper focuses on single-channel semi-supervised speech enhancement. We learn a speaker-independent deep generative speech model using the framework of variational autoencoders. The noise model remains unsupervised because we do not assume prior knowledge of the noisy recording environment. In this context, our contribution is to propose a noise model based on alpha-stable distributions, instead of the more conventional Gaussian non-negative matrix factorization approach found in previous studies. We develop a Monte Carlo expectation-maximization algorithm for estimating the model parameters at test time. Experimental results show the superiority of the proposed approach both in terms of perceptual quality and intelligibility of the enhanced speech signal.

We propose to learn curvature information for better generalization and fast model adaptation, called meta-curvature. Based on the model-agnostic meta-learner (MAML), we learn to transform the gradients in the inner optimization such that the transformed gradients achieve better generalization performance to a new task. For training large scale neural networks, we decompose the curvature matrix into smaller matrices and capture the dependencies of the model's parameters with a series of tensor products. We demonstrate the effects of our proposed method on both few-shot image classification and few-shot reinforcement learning tasks. Experimental results show consistent improvements on classification tasks and promising results on reinforcement learning tasks. Furthermore, we observe faster convergence rates of the meta-training process. Finally, we present an analysis that explains better generalization performance with the meta-trained curvature.

Representations learnt through deep neural networks tend to be highly informative, but opaque in terms of what information they learn to encode. We introduce an approach to probabilistic modelling that learns to represent data with two separate deep representations: an invariant representation that encodes the information of the class from which the data belongs, and an equivariant representation that encodes the symmetry transformation defining the particular data point within the class manifold (equivariant in the sense that the representation varies naturally with symmetry transformations). This approach is based primarily on the strategic routing of data through the two latent variables, and thus is conceptually transparent, easy to implement, and in-principle generally applicable to any data comprised of discrete classes of continuous distributions (e.g. objects in images, topics in language, individuals in behavioural data). We demonstrate qualitatively compelling representation learning and competitive quantitative performance, in both supervised and semi-supervised settings, versus comparable modelling approaches in the literature with little fine tuning.

Bayesian optimization is known to be difficult to scale to high dimensions, because the acquisition step requires solving a non-convex optimization problem in the same search space. In order to scale the method and keep its benefits, we propose an algorithm (LineBO) that restricts the problem to a sequence of iteratively chosen one-dimensional sub-problems. We show that our algorithm converges globally and obtains a fast local rate when the function is strongly convex. Further, if the objective has an invariant subspace, our method automatically adapts to the effective dimension without changing the algorithm. Our method scales well to high dimensions and makes use of a global Gaussian process model. When combined with the SafeOpt algorithm to solve the sub-problems, we obtain the first safe Bayesian optimization algorithm with theoretical guarantees applicable in high-dimensional settings. We evaluate our method on multiple synthetic benchmarks, where we obtain competitive performance. Further, we deploy our algorithm to optimize the beam intensity of the Swiss Free Electron Laser with up to 40 parameters while satisfying safe operation constraints.

Increasingly complex datasets pose a number of challenges for Bayesian inference. Conventional posterior sampling based on Markov chain Monte Carlo can be too computationally intensive, is serial in nature and mixes poorly between posterior modes. Further, all models are misspecified, which brings into question the validity of the conventional Bayesian update. We present a scalable Bayesian nonparametric learning routine that enables posterior sampling through the optimization of suitably randomized objective functions. A Dirichlet process prior on the unknown data distribution accounts for model misspecification, and admits an embarrassingly parallel posterior bootstrap algorithm that generates independent and exact samples from the nonparametric posterior distribution. Our method is particularly adept at sampling from multimodal posterior distributions via a random restart mechanism. We demonstrate our method on Gaussian mixture model and sparse logistic regression examples.

This paper introduces Bounded Fuzzy Possibilistic Method (BFPM) by addressing several issues that previous clustering/classification methods have not considered. In fuzzy clustering, object's membership values should sum to 1. Hence, any object may obtain full membership in at most one cluster. Possibilistic clustering methods remove this restriction. However, BFPM differs from previous fuzzy and possibilistic clustering approaches by allowing the membership function to take larger values with respect to all clusters. Furthermore, in BFPM, a data object can have full membership in multiple clusters or even in all clusters. BFPM relaxes the boundary conditions (restrictions) in membership assignment. The proposed methodology satisfies the necessity of obtaining full memberships and overcomes the issues with conventional methods on dealing with overlapping. Analysing the objects' movements from their own cluster to another (mutation) is also proposed in this paper. BFPM has been applied in different domains in geometry, set theory, anomaly detection, risk management, diagnosis diseases, and other disciplines. Validity and comparison indexes have been also used to evaluate the accuracy of BFPM. BFPM has been evaluated in terms of accuracy, fuzzification constant (different norms), objects' movement analysis, and covering diversity. The promising results prove the importance of considering the proposed methodology in learning methods to track the behaviour of data objects, in addition to obtain accurate results.

Neural planners for RDDL MDPs produce deep reactive policies in an offline fashion. These scale well with large domains, but are sample inefficient and time-consuming to train from scratch for each new problem. To mitigate this, recent work has studied neural transfer learning, so that a generic planner trained on other problems of the same domain can rapidly transfer to a new problem. However, this approach only transfers across problems of the same size. We present the first method for neural transfer of RDDL MDPs that can transfer across problems of different sizes. Our architecture has two key innovations to achieve size independence: (1) a state encoder, which outputs a fixed length state embedding by max pooling over varying number of object embeddings, (2) a single parameter-tied action decoder that projects object embeddings into action probabilities for the final policy. On the two challenging RDDL domains of SysAdmin and Game Of Life, our approach powerfully transfers across problem sizes and has superior learning curves over training from scratch.

It is well-known that exploiting label correlations is crucially important to multi-label learning. Most of the existing approaches take label correlations as prior knowledge, which may not correctly characterize the real relationships among labels. Besides, label correlations are normally used to regularize the hypothesis space, while the final predictions are not explicitly correlated. In this paper, we suggest that for each individual label, the final prediction involves the collaboration between its own prediction and the predictions of other labels. Based on this assumption, we first propose a novel method to learn the label correlations via sparse reconstruction in the label space. Then, by seamlessly integrating the learned label correlations into model training, we propose a novel multi-label learning approach that aims to explicitly account for the correlated predictions of labels while training the desired model simultaneously. Extensive experimental results show that our approach outperforms the state-of-the-art counterparts.

Partial label learning deals with the problem where each training instance is assigned a set of candidate labels, only one of which is correct. This paper provides the first attempt to leverage the idea of self-training for dealing with partially labeled examples. Specifically, we propose a unified formulation with proper constraints to train the desired model and perform pseudo-labeling jointly. For pseudo-labeling, unlike traditional self-training that manually differentiates the ground-truth label with enough high confidence, we introduce the maximum infinity norm regularization on the modeling outputs to automatically achieve this consideratum, which results in a convex-concave optimization problem. We show that optimizing this convex-concave problem is equivalent to solving a set of quadratic programming (QP) problems. By proposing an upper-bound surrogate objective function, we turn to solving only one QP problem for improving the optimization efficiency. Extensive experiments on synthesized and real-world datasets demonstrate that the proposed approach significantly outperforms the state-of-the-art partial label learning approaches.