Continual Learning (CL) algorithms have recently received a lot of attention as they attempt to overcome the need to train with an i.i.d. sample from some unknown target data distribution. Building on prior work, we study principled ways to tackle the CL problem by adopting a Bayesian perspective and focus on continually learning a task-specific posterior distribution via a shared meta-model, a task-conditioned hypernetwork. This approach, which we term Posterior-replay CL, is in sharp contrast to most Bayesian CL approaches that focus on the recursive update of a single posterior distribution. The benefits of our approach are (1) an increased flexibility to model solutions in weight space and therewith less susceptibility to task dissimilarity, (2) access to principled task-specific predictive uncertainty estimates, that can be used to infer task identity during test time and to detect task boundaries during training, and (3) the ability to revisit and update task-specific posteriors in a principled manner without requiring access to past data. The proposed framework is versatile, which we demonstrate using simple posterior approximations (such as Gaussians) as well as powerful, implicit distributions modelled via a neural network. We illustrate the conceptual advance of our framework on low-dimensional problems and show performance gains on computer vision benchmarks.

The digitization of historical handwritten document images is important for the preservation of cultural heritage. Moreover, the transcription of text images obtained from digitization is necessary to provide efficient information access to the content of these documents. Handwritten Text Recognition (HTR) has become an important research topic in the areas of image and computational language ... [Show full abstract] processing that allows us to obtain transcriptions from text images. State-of-the-art HTR systems are, however, far from perfect. One difficulty is that they have to cope with image noise and handwriting variability.

We propose and analyse a novel nonparametric goodness of fit testing procedure for exchangeable exponential random graph models (ERGMs) when a single network realisation is observed. The test determines how likely it is that the observation is generated from a target unnormalised ERGM density. Our test statistics are derived from a kernel Stein discrepancy, a divergence constructed via Steins method using functions in a reproducing kernel Hilbert space, combined with a discrete Stein operator for ERGMs. The test is a Monte Carlo test based on simulated networks from the target ERGM. We show theoretical properties for the testing procedure for a class of ERGMs. Simulation studies and real network applications are presented.

Active learning is an area of modern machine learning that studies how data points can be sequentially selected for labeling to train a model with as few labeled examples as possible (Settles, 2009). Minimizing the number of labeled examples is critical in any learning scenario where labels are expensive to obtain, such as in healthcare applications where a medical expert must hand-label each training example (Liu, 2004), or where only a limited number of examples can be evaluated, such as in drug discovery (Warmuth et al., 2003). The active selection of data points shares many technical parallels with channel coding with feedback, where a message is encoded into a sequence of symbols transmitted across a noisy channel and each symbol is selected based on the message and past channel outputs. In active learning, the optimal classifier parameters play the role of the "message" while the sequence of examples with noisy labels plays the role of "channel outputs" available through feedback to select the next example for labeling. Both feedback channel coding and active learning seek to minimize the number of encoder actions, leverage a history of noisy observations to select the next most informative action, must account for observation noise, and should operate in a computationally efficient manner. Although there exists a large literature studying the intersection of information theory with machine learning (Xu and Raginsky, 2017) and specifically active learning (Naghshvar et al., 2015), there remain open questions about the best ways to directly leverage techniques in channel coding for active example selection. The main contribution of this work is a formulation of general active learning problems in terms of a feedback coding system, and a demonstration of this approach through the application and analysis of active learning in logistic regression. To motivate this approach, we first examine active learning through the lens of feedback channel coding by identifying communications system components, including a deterministic encoder, noisy channel, channel input constraints, and capacity-achieving distribution. With these components identified, we show how typical structural constraints in active learning problems prevent the direct application of existing feedback coding approaches such as posterior matching (Ma and Coleman, 2011).

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In a recent post, famous futurist Ray Kurzweil mentions that -- in his opinion -- brain structures in the neocortex are technically similar to hierarchical hidden Markov models (HHMM). An idea he also explained in more detail in his 2012 book "How to Create a Mind" [1]. Unfortunately though, neither the article nor the book has enough information to understand this machine learning model in detail, let alone implement it. So, let's use this article to try and understand hierarchical hidden Markov models. We'll have a brief, high-level look at most of the concepts it builds on and prepare the stage for an actual implementation (which will follow in another article due to content length).

Bayesian optimization (BO) is a powerful paradigm for efficient optimization of black-box objective functions. High-dimensional BO presents a particular challenge, in part because the curse of dimensionality makes it difficult to define as well as do inference over a suitable class of surrogate models. We argue that Gaussian process surrogate models defined on sparse axis-aligned subspaces offer an attractive compromise between flexibility and parsimony. We demonstrate that our approach, which relies on Hamiltonian Monte Carlo for inference, can rapidly identify sparse subspaces relevant to modeling the unknown objective function, enabling sample-efficient high-dimensional BO. In an extensive suite of experiments comparing to existing methods for high-dimensional BO we demonstrate that our algorithm, Sparse Axis-Aligned Subspace BO (SAASBO), achieves excellent performance on several synthetic and real-world problems without the need to set problem-specific hyperparameters.

We consider the problem of learning the optimal policy for infinite-horizon Markov decision processes (MDPs). For this purpose, some variant of Stochastic Mirror Descent is proposed for convex programming problems with Lipschitz-continuous functionals. An important detail is the ability to use inexact values of functional constraints. We analyze this algorithm in a general case and obtain an estimate of the convergence rate that does not accumulate errors during the operation of the method. Using this algorithm, we get the first parallel algorithm for average-reward MDPs with a generative model. One of the main features of the presented method is low communication costs in a distributed centralized setting.

We develop variational Laplace for Bayesian neural networks (BNNs) which exploits a local approximation of the curvature of the likelihood to estimate the ELBO without the need for stochastic sampling of the neural-network weights. Variational Laplace performs better on image classification tasks than MAP inference and far better than standard variational inference with stochastic sampling despite using the same mean-field Gaussian approximate posterior. The Variational Laplace objective is simple to evaluate, as it is (in essence) the log-likelihood, plus weight-decay, plus a squared-gradient regularizer. Finally, we emphasise care needed in benchmarking standard VI as there is a risk of stopping before the variance parameters have converged. We show that early-stopping can be avoided by increasing the learning rate for the variance parameters.

Local causal structure learning aims to discover and distinguish direct causes (parents) and direct effects (children) of a variable of interest from data. While emerging successes have been made, existing methods need to search a large space to distinguish direct causes from direct effects of a target variable T. To tackle this issue, we propose a novel Efficient Local Causal Structure learning algorithm, named ELCS. Specifically, we first propose the concept of N-structures, then design an efficient Markov Blanket (MB) discovery subroutine to integrate MB learning with N-structures to learn the MB of T and simultaneously distinguish direct causes from direct effects of T. With the proposed MB subroutine, ELCS starts from the target variable, sequentially finds MBs of variables connected to the target variable and simultaneously constructs local causal structures over MBs until the direct causes and direct effects of the target variable have been distinguished. Using eight Bayesian networks the extensive experiments have validated that ELCS achieves better accuracy and efficiency than the state-of-the-art algorithms.