Gaussian Process (GPs) models are a rich distribution over functions with inductive biases controlled by a kernel function. Learning occurs through the optimisation of kernel hyperparameters using the marginal likelihood as the objective. This classical approach known as Type-II maximum likelihood (ML-II) yields point estimates of the hyperparameters, and continues to be the default method for training GPs. However, this approach risks underestimating predictive uncertainty and is prone to overfitting especially when there are many hyperparameters. Furthermore, gradient based optimisation makes ML-II point estimates highly susceptible to the presence of local minima. This work presents an alternative learning procedure where the hyperparameters of the kernel function are marginalised using Nested Sampling (NS), a technique that is well suited to sample from complex, multi-modal distributions. We focus on regression tasks with the spectral mixture (SM) class of kernels and find that a principled approach to quantifying model uncertainty leads to substantial gains in predictive performance across a range of synthetic and benchmark data sets. In this context, nested sampling is also found to offer a speed advantage over Hamiltonian Monte Carlo (HMC), widely considered to be the gold-standard in MCMC based inference.

We apply some of the latest techniques from machine-learning to the arithmetic of hyperelliptic curves. More precisely we show that, with impressive accuracy and confidence (between 99 and 100 percent precision), and in very short time (matter of seconds on an ordinary laptop), a Bayesian classifier can distinguish between Sato-Tate groups given a small number of Euler factors for the L-function. Our observations are in keeping with the Sato-Tate conjecture for curves of low genus. For elliptic curves, this amounts to distinguishing generic curves (with Sato-Tate group SU(2)) from those with complex multiplication. In genus 2, a principal component analysis is observed to separate the generic Sato-Tate group USp(4) from the non-generic groups. Furthermore in this case, for which there are many more non-generic possibilities than in the case of elliptic curves, we demonstrate an accurate characterisation of several Sato-Tate groups with the same identity component. Throughout, our observations are verified using known results from the literature and the data available in the LMFDB. The results in this paper suggest that a machine can be trained to learn the Sato-Tate distributions and may be able to classify curves much more efficiently than the methods available in the literature.

Neural processes (NPs) constitute a family of variational approximate models for stochastic processes with promising properties in computational efficiency and uncertainty quantification. These processes use neural networks with latent variable inputs to induce predictive distributions. However, the expressiveness of vanilla NPs is limited as they only use a global latent variable, while target specific local variation may be crucial sometimes. To address this challenge, we investigate NPs systematically and present a new variant of NP model that we call Doubly Stochastic Variational Neural Process (DSVNP). This model combines the global latent variable and local latent variables for prediction. We evaluate this model in several experiments, and our results demonstrate competitive prediction performance in multi-output regression and uncertainty estimation in classification.

Brittle optimization has been observed to adversely impact model likelihoods for regression and VAEs when simultaneously fitting neural network mappings from a (random) variable onto the mean and variance of a dependent Gaussian variable. Previous works have bolstered optimization and improved likelihoods, but fail other basic posterior predictive checks (PPCs). Under the PPC framework, we propose critiques to test predictive mean and variance calibration and the predictive distribution's ability to generate sensible data. We find that our attractively simple solution, to treat heteroscedastic variance variationally, sufficiently regularizes variance to pass these PPCs. We consider a diverse gamut of existing and novel priors and find our methods preserve or outperform existing model likelihoods while significantly improving parameter calibration and sample quality for regression and VAEs.

Clinical decision making about treatments and interventions based on personal characteristics leads to effective health improvement. Machine learning (ML) has been the central concern of the diagnosis support and disease prediction based on comprehensive patient information. Because the black-box problem in ML is serious for medical applications, explainable artificial intelligence (XAI) techniques to explain the reasons for ML models predictions have been focused. A remaining important issue in clinical situations is discovery of concrete and realistic treatment processes. This paper proposes an innovative framework to plan concrete treatment processes based on an ML model. A key point of our proposed framework is to evaluate an "actionability" of the treatment process using a stochastic surrogate model constructed through hierarchical Bayesian modeling. The actionability is an essential concept for suggesting a realistic treatment process, which leads to clinical applications for personal health improvement. This paper also presents two experiments to evaluate our framework. We first demonstrate the feasibility of our framework from the viewpoint of the methodology using a synthetic dataset. Subsequently, our framework is applied to an actual health checkup dataset, which comprises 3,132 participants, considering an application to improve systolic blood pressure values at a personal level. We confirmed that the computed treatment processes are actionable and consistent with clinical knowledge for lowering blood pressure. These results demonstrate that our framework can contribute to decision making in the medical field. Our framework can be expected to provide clinicians deeper insights by proposing concrete and actionable treatment process based on the ML model.

A fundamental question in neuroscience is how the brain creates an internal model of the world to guide actions using sequences of ambiguous sensory information. This is naturally formulated as a reinforcement learning problem under partial observations, where an agent must estimate relevant latent variables in the world from its evidence, anticipate possible future states, and choose actions that optimize total expected reward. This problem can be solved by control theory, which allows us to find the optimal actions for a given system dynamics and objective function. However, animals often appear to behave suboptimally. Why? We hypothesize that animals have their own flawed internal model of the world, and choose actions with the highest expected subjective reward according to that flawed model. We describe this behavior as rational but not optimal. The problem of Inverse Rational Control (IRC) aims to identify which internal model would best explain an agent's actions. Our contribution here generalizes past work on Inverse Rational Control which solved this problem for discrete control in partially observable Markov decision processes. Here we accommodate continuous nonlinear dynamics and continuous actions, and impute sensory observations corrupted by unknown noise that is private to the animal. We first build an optimal Bayesian agent that learns an optimal policy generalized over the entire model space of dynamics and subjective rewards using deep reinforcement learning. Crucially, this allows us to compute a likelihood over models for experimentally observable action trajectories acquired from a suboptimal agent. We then find the model parameters that maximize the likelihood using gradient ascent.

We propose to learn energy-based model (EBM) in the latent space of a generator model, so that the EBM serves as a prior model that stands on the top-down network of the generator model. Both the latent space EBM and the top-down network can be learned jointly by maximum likelihood, which involves short-run MCMC sampling from both the prior and posterior distributions of the latent vector. Due to the low dimensionality of the latent space and the expressiveness of the top-down network, a simple EBM in latent space can capture regularities in the data effectively, and MCMC sampling in latent space is efficient and mixes well. We show that the learned model exhibits strong performances in terms of image and text generation and anomaly detection. The one-page code can be found in supplementary materials.

We investigate partial identification of causal relative and attributable risk---the ratio of two counterfactual proportions and the difference between them---in case-control and case-population studies. The odds ratio is shown to be a sharp upper bound on causal relative risk under the monotone treatment response and monotone treatment selection assumptions, without resorting to strong ignorability, nor to the rare-disease assumption. Sharp bounds on causal attributable risk are also obtained under the same assumptions. Paying special attention to the (conditional) odds ratio, we propose a semiparametrically efficient estimator of the aggregated (log) odds ratio. Further, we develop easy-to-implement causal inference procedures for relative and attributable risk. Finally, we showcase our methodology by applying it to two unique datasets in the literature. We find that attending private school may have little effect on entering a very selective university in Pakistan and that dropping out of school could substantially increase relative and attributable risk of joining a criminal gang in Brazil.

Online Courses Udemy - Full Guide to Implementing Classic Machine Learning Algorithms in Python and with Sci-Kit Learn Created by Lazy Programmer Inc English [Auto-generated], Spanish [Auto-generated] Students also bought Bayesian Machine Learning in Python: A/B Testing The Complete Python Course Learn Python by Doing Complete Python Developer in 2020: Zero to Mastery Artificial Intelligence: Reinforcement Learning in Python Natural Language Processing with Deep Learning in Python Preview this course GET COUPON CODE Description In recent years, we've seen a resurgence in AI, or artificial intelligence, and machine learning. Machine learning has led to some amazing results, like being able to analyze medical images and predict diseases on-par with human experts. Google's AlphaGo program was able to beat a world champion in the strategy game go using deep reinforcement learning. Machine learning is even being used to program self driving cars, which is going to change the automotive industry forever. Imagine a world with drastically reduced car accidents, simply by removing the element of human error.

Probability is the cornerstone of Artificial Intelligence. The management of uncertainty is key to many applications of AI, such as machine learning, filtering, robotics, computer vision, NLP, search and so on. And no other sector is the management of uncertainty as crucial as it is in the health sector. At first glance, the false-negative seems more devastating. Of course, a false allergy test-result has the likely outcome of a GP administering a drug to you that could cause life-threatening issues.