**GPyTorch**

Despite advances in scalable models, the inference tools used for Gaussian processes (GPs) have yet to fully capitalize on recent developments in machine learning hardware. We present an efficient and general approach to GP inference based on Blackbox Matrix-Matrix multiplication (BBMM). BBMM inference uses a modified batched version of the conjugate gradients algorithm to derive all terms required for training and inference in a single call. Adapting this algorithm to complex models simply requires a routine for efficient matrix-matrix multiplication with the kernel and its derivative. In addition, BBMM utilizes a specialized preconditioner that substantially speeds up convergence. In experiments, we show that BBMM efficiently utilizes GPU hardware, speeding up GP inference by an order of magnitude on a variety of popular GP models. Additionally, we provide GPyTorch, a new software platform for scalable Gaussian process inference via BBMM, built on PyTorch. … **Modified Q-Learner for the Vasicek Model (MQLV)**

In a reinforcement learning approach, an optimal value function is learned across a set of actions, or decisions, that leads to a set of states giving different rewards, with the objective to maximize the overall reward. A policy assigns to each state-action pairs an expected return. We call an optimal policy a policy for which the value function is optimal. QLBS, Q-Learner in the Black-Scholes(-Merton) Worlds, applies the reinforcement learning concepts, and noticeably, the popular Q-learning algorithm, to the financial stochastic model described by Black, Scholes and Merton. However, QLBS is specifically optimized for the geometric Brownian motion and the pricing of vanilla options. Consequently, it suffers from the traditional over-estimation of the Q-values reflected by an over-estimation of the vanilla option prices. Furthermore, its range of application is limited to vanilla option pricing within the financial markets. We propose MQLV, Modified Q-Learner for the Vasicek model, a new reinforcement learning approach that limits the Q-values over-estimation observed in QLBS and extends the simulation to mean reverting stochastic diffusion processes. Additionally, MQLV uses a digital function to estimate the future probability of an event, thus widening the scope of the financial application to any other domain involving time series. Our experiments underline the potential of MQLV on generated Monte Carlo simulations, particularly representative of the retail banking time series. In particular, MQLV is able to determine the optimal policy of money management based on the aggregated financial transactions of the clients, unlocking new frontiers to establish personalized credit card limits or loans. Finally, MQLV is the first methodology compatible with the Vasicek model capable of an event probability estimation targeting simulation of event probabilities in retail banking. … **ease.ml/ci**

Continuous integration is an indispensable step of modern software engineering practices to systematically manage the life cycles of system development. Developing a machine learning model is no difference – it is an engineering process with a life cycle, including design, implementation, tuning, testing, and deployment. However, most, if not all, existing continuous integration engines do not support machine learning as first-class citizens. In this paper, we present ease.ml/ci, to our best knowledge, the first continuous integration system for machine learning. The challenge of building ease.ml/ci is to provide rigorous guarantees, e.g., single accuracy point error tolerance with 0.999 reliability, with a practical amount of labeling effort, e.g., 2K labels per test. We design a domain specific language that allows users to specify integration conditions with reliability constraints, and develop simple novel optimizations that can lower the number of labels required by up to two orders of magnitude for test conditions popularly used in real production systems. … **AgrLearn**

We establish an equivalence between information bottleneck (IB) learning and an unconventional quantization problem, `IB quantization’. Under this equivalence, standard neural network models correspond to scalar IB quantizers. We prove a coding theorem for IB quantization, which implies that scalar IB quantizers are in general inferior to vector IB quantizers. This inspires us to develop a learning framework for neural networks, AgrLearn, that corresponds to vector IB quantizers. We experimentally verify that AgrLearn applied to some deep network models of current art improves upon them, while requiring less training data. With a heuristic smoothing, AgrLearn further improves its performance, resulting in new state of the art in image classification on Cifar10. …

# If you did not already know

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May 2021

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