Random binning features, introduced in the seminal paper of Rahimi and Recht (2007), are an efficient method for approximating a kernel matrix using locality sensitive hashing. Random binning features provide a very simple and efficient way of approximating the Laplace kernel but unfortunately do not apply to many important classes of kernels, notably ones that generate smooth Gaussian processes, such as the Gaussian kernel and Matern kernel. In this paper, we introduce a simple weighted version of random binning features and show that the corresponding kernel function generates Gaussian processes of any desired smoothness. We show that our weighted random binning features provide a spectral approximation to the corresponding kernel matrix, leading to efficient algorithms for kernel ridge regression. Experiments on large scale regression datasets show that our method outperforms the accuracy of random Fourier features method.

Bootstrap aggregation (Bagging) and boosting are two popular ensemble learning approaches, which combine multiple base learners to generate a composite learner. This article proposes BoostForest, which is an ensemble learning approach using BoostTree as base learners and can be used for both classification and regression. BoostTree constructs a tree by gradient boosting, which trains a linear or nonlinear model at each node. When a new sample comes in, BoostTree first sorts it down to a leaf, then computes the final prediction by summing up the outputs of all models along the path from the root node to that leaf. BoostTree achieves high randomness (diversity) by sampling its parameters randomly from a parameter pool, and selecting a subset of features randomly at node splitting. BoostForest further increases the randomness by bootstrapping the training data in constructing different BoostTrees. BoostForest is compared with four classical ensemble learning approaches on 30 classification and regression datasets, demonstrating that it can generate more accurate and more robust composite learners.

Imagine a typical Tuesday morning. The lot is full, with vehicles parked nose to nose. You wait in a long line, similar to what you would see at Disney on a typical weekend. When you finally get inside, you see rows upon rows of empty shelves. You maneuver your shopping cart around frenzied shoppers, only to find that Costco is out of face masks, nonperishable items, medications, hand sanitizers, and hand soaps. The fear and panic as the coronavirus (known as '2019-nCov' or'Covid-19) spreads globally.

As domain experts, engineers are highly valuable in shaping companies' AI projects. This is especially the case in Australia. Here, 98 per cent of businesses have fewer than 20 employees, and a team of data scientists trained on statistical machine-learning methods tends to be something enjoyed by bigger organisations. The growth in AI will continue in the new year and is expected to push rapidly into industrial scenarios. Non-data scientists have access to more and more information and training centred around AI.

Neuroscientific data analysis has traditionally relied on linear algebra and stochastic process theory. However, the tree-like shapes of neurons cannot be described easily as points in a vector space (the subtraction of two neuronal shapes is not a meaningful operation), and methods from computational topology are better suited to their analysis. Here we introduce methods from Discrete Morse (DM) Theory to extract the tree-skeletons of individual neurons from volumetric brain image data, and to summarize collections of neurons labelled by tracer injections. Since individual neurons are topologically trees, it is sensible to summarize the collection of neurons using a consensus tree-shape that provides a richer information summary than the traditional regional 'connectivity matrix' approach. The conceptually elegant DM approach lacks hand-tuned parameters and captures global properties of the data as opposed to previous approaches which are inherently local. For individual skeletonization of sparsely labelled neurons we obtain substantial performance gains over state-of-the-art non-topological methods (over 10% improvements in precision and faster proofreading). The consensus-tree summary of tracer injections incorporates the regional connectivity matrix information, but in addition captures the collective collateral branching patterns of the set of neurons connected to the injection site, and provides a bridge between single-neuron morphology and tracer-injection data.

Bayesian experimental design (BED) is a framework that uses statistical models and decision making under uncertainty to optimise the cost and performance of a scientific experiment. Sequential BED, as opposed to static BED, considers the scenario where we can sequentially update our beliefs about the model parameters through data gathered in the experiment. A class of models of particular interest for the natural and medical sciences are implicit models, where the data generating distribution is intractable, but sampling from it is possible. Even though there has been a lot of work on static BED for implicit models in the past few years, the notoriously difficult problem of sequential BED for implicit models has barely been touched upon. We address this gap in the literature by devising a novel sequential design framework for parameter estimation that uses the Mutual Information (MI) between model parameters and simulated data as a utility function to find optimal experimental designs, which has not been done before for implicit models. Our approach uses likelihood-free inference by ratio estimation to simultaneously estimate posterior distributions and the MI. During the sequential BED procedure we utilise Bayesian optimisation to help us optimise the MI utility. We find that our framework is efficient for the various implicit models tested, yielding accurate parameter estimates after only a few iterations.

We consider sketched approximate matrix multiplication and ridge regression in the novel setting of localized sketching, where at any given point, only part of the data matrix is available. This corresponds to a block diagonal structure on the sketching matrix. We show that, under mild conditions, block diagonal sketching matrices require only O(stable rank / \epsilon^2) and $O( stat. dim. \epsilon)$ total sample complexity for matrix multiplication and ridge regression, respectively. This matches the state-of-the-art bounds that are obtained using global sketching matrices. The localized nature of sketching considered allows for different parts of the data matrix to be sketched independently and hence is more amenable to computation in distributed and streaming settings and results in a smaller memory and computational footprint.

Being able to infer the goal of people we observe, interact with, or read stories about is one of the hallmarks of human intelligence. A prominent idea in current goal-recognition research is to infer the likelihood of an agent's goal from the estimations of the costs of plans to the different goals the agent might have. Different approaches implement this idea by relying only on handcrafted symbolic representations. Their application to real-world settings is, however, quite limited, mainly because extracting rules for the factors that influence goal-oriented behaviors remains a complicated task. In this paper, we introduce a novel idea of using a symbolic planner to compute plan-cost insights, which augment a deep neural network with an imagination capability, leading to improved goal recognition accuracy in real and synthetic domains compared to a symbolic recognizer or a deep-learning goal recognizer alone.

We present a system that utilizes machine learning for tactic proof search in the Coq Proof Assistant. In a similar vein as the TacticToe project for HOL4, our system predicts appropriate tactics and finds proofs in the form of tactic scripts. To do this, it learns from previous tactic scripts and how they are applied to proof states. The performance of the system is evaluated on the Coq Standard Library. Currently, our predictor can identify the correct tactic to be applied to a proof state 23.4% of the time. Our proof searcher can fully automatically prove 39.3% of the lemmas. When combined with the CoqHammer system, the two systems together prove 56.7% of the library's lemmas.

Imagine a typical Tuesday morning. The lot is full, with vehicles parked nose to nose. You wait in a long line, similar to what you would see at Disney on a typical weekend. When you finally get inside, you see rows upon rows of empty shelves. You maneuver your shopping cart around frenzied shoppers, only to find that Costco is out of face masks, nonperishable items, medications, hand sanitizers, and hand soaps. The fear and panic as the coronavirus (known as '2019-nCov' or'Covid-19) spreads globally.