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.

Non-Intrusive Load Monitoring (NILM) aims to predict the status or consumption of domestic appliances in a household only by knowing the aggregated power load. NILM can be formulated as regression problem or most often as a classification problem. Most datasets gathered by smart meters allow to define naturally a regression problem, but the corresponding classification problem is a derived one, since it requires a conversion from the power signal to the status of each device by a thresholding method. We treat three different thresholding methods to perform this task, discussing their differences on various devices from the UK-DALE dataset. We analyze the performance of deep learning state-of-the-art architectures on both the regression and classification problems, introducing criteria to select the most convenient thresholding method.

We present a computational model of mathematical reasoning according to which mathematics is a fundamentally stochastic process. That is, on our model, whether or not a given formula is deemed a theorem in some axiomatic system is not a matter of certainty, but is instead governed by a probability distribution. We then show that this framework gives a compelling account of several aspects of mathematical practice. These include: 1) the way in which mathematicians generate research programs, 2) the applicability of Bayesian models of mathematical heuristics, 3) the role of abductive reasoning in mathematics, 4) the way in which multiple proofs of a proposition can strengthen our degree of belief in that proposition, and 5) the nature of the hypothesis that there are multiple formal systems that are isomorphic to physically possible universes. Thus, by embracing a model of mathematics as not perfectly predictable, we generate a new and fruitful perspective on the epistemology and practice of mathematics.

We consider learning a sparse pairwise Markov Random Field (MRF) with continuous-valued variables from i.i.d samples. We adapt the algorithm of Vuffray et al. (2019) to this setting and provide finite-sample analysis revealing sample complexity scaling logarithmically with the number of variables, as in the discrete and Gaussian settings. Our approach is applicable to a large class of pairwise MRFs with continuous variables and also has desirable asymptotic properties, including consistency and normality under mild conditions. Further, we establish that the population version of the optimization criterion employed in Vuffray et al. (2019) can be interpreted as local maximum likelihood estimation (MLE). As part of our analysis, we introduce a robust variation of sparse linear regression a` la Lasso, which may be of interest in its own right.

Human annotations are an important source of information in the development of natural language understanding approaches. As under the pressure of productivity annotators can assign different labels to a given text, the quality of produced annotations frequently varies. This is especially the case if decisions are difficult, with high cognitive load, requires awareness of broader context, or careful consideration of background knowledge. To alleviate the problem, we propose two semi-supervised methods to guide the annotation process: a Bayesian deep learning model and a Bayesian ensemble method. Using a Bayesian deep learning method, we can discover annotations that cannot be trusted and might require reannotation. A recently proposed Bayesian ensemble method helps us to combine the annotators' labels with predictions of trained models. According to the results obtained from three hate speech detection experiments, the proposed Bayesian methods can improve the annotations and prediction performance of BERT models.

We provide the first polynomial-sample and polynomial-time algorithm for learning tree-structured Ising models. In particular, we show that $n$-variable tree-structured Ising models can be learned computationally-efficiently to within total variation distance~$\epsilon$ from an optimal $O(n \log n/\epsilon^2)$ samples, where $O(.)$ hides an absolute constant which does not depend on the model being learned -- neither its tree nor the magnitude of its edge strengths, on which we place no assumptions. Our guarantees hold, in fact, for the celebrated Chow-Liu [1968] algorithm, using the plug-in estimator for mutual information. While this (or any other) algorithm may fail to identify the structure of the underlying model correctly from a finite sample, we show that it will still learn a tree-structured model that is close to the true one in TV distance, a guarantee called "proper learning." Prior to our work there were no known sample- and time-efficient algorithms for learning (properly or non-properly) arbitrary tree-structured graphical models. In particular, our guarantees cannot be derived from known results for the Chow-Liu algorithm and the ensuing literature on learning graphical models, including a recent renaissance of algorithms on this learning challenge, which only yield asymptotic consistency results, or sample-inefficient and/or time-inefficient algorithms, unless further assumptions are placed on the graphical model, such as bounds on the "strengths" of the model's edges. While we establish guarantees for a widely known and simple algorithm, the analysis that this algorithm succeeds is quite complex, requiring a hierarchical classification of the edges into layers with different reconstruction guarantees, depending on their strength, combined with delicate uses of the subadditivity of the squared Hellinger distance over graphical models to control the error accumulation.

Multivariate Hawkes processes are commonly used to model streaming networked event data in a wide variety of applications. However, it remains a challenge to extract reliable inference from complex datasets with uncertainty quantification. Aiming towards this, we develop a statistical inference framework to learn causal relationships between nodes from networked data, where the underlying directed graph implies Granger causality. We provide uncertainty quantification for the maximum likelihood estimate of the network multivariate Hawkes process by providing a non-asymptotic confidence set. The main technique is based on the concentration inequalities of continuous-time martingales. We compare our method to the previously-derived asymptotic Hawkes process confidence interval, and demonstrate the strengths of our method in an application to neuronal connectivity reconstruction.