The interactive version of this post can be found here. Since Medium does not support Javascript and equations written in Latex, we recommend to check out our interactive post as well. When we think of Peter, his positive nature and his can-do attitude inevitably come to mind. He had an ability to inspire and carry the people around him, convincing them that almost everything is possible. Back in 2018 he came up with the idea for an interactive blog post on the subject of Energy Based Models and pitched it to us. It was almost impossible to resist his enthusiastic manner and of course we embarked on this adventure with him. Equipped with our knowledge in physics and machine learning and hardly any clue about Javascript, we started our journey. After a lot of hard work, we were finally able to complete this project. We are overjoyed with the final result and we wish he could see it.

Bayesian variable selection is a powerful tool for data analysis, as it offers a principled method for variable selection that accounts for prior information and uncertainty. However, wider adoption of Bayesian variable selection has been hampered by computational challenges, especially in difficult regimes with a large number of covariates or non-conjugate likelihoods. Generalized linear models for count data, which are prevalent in biology, ecology, economics, and beyond, represent an important special case. Here we introduce an efficient MCMC scheme for variable selection in binomial and negative binomial regression that exploits Tempered Gibbs Sampling (Zanella and Roberts, 2019) and that includes logistic regression as a special case. In experiments we demonstrate the effectiveness of our approach, including on cancer data with seventeen thousand covariates.

This work is driven by a practical question, corrections of Artificial Intelligence (AI) errors. Systematic re-training of a large AI system is hardly possible. To solve this problem, special external devices, correctors, are developed. They should provide quick and non-iterative system fix without modification of a legacy AI system. A common universal part of the AI corrector is a classifier that should separate undesired and erroneous behavior from normal operation. Training of such classifiers is a grand challenge at the heart of the one- and few-shot learning methods. Effectiveness of one- and few-short methods is based on either significant dimensionality reductions or the blessing of dimensionality effects. Stochastic separability is a blessing of dimensionality phenomenon that allows one-and few-shot error correction: in high-dimensional datasets under broad assumptions each point can be separated from the rest of the set by simple and robust linear discriminant. The hierarchical structure of data universe is introduced where each data cluster has a granular internal structure, etc. New stochastic separation theorems for the data distributions with fine-grained structure are formulated and proved. Separation theorems in infinite-dimensional limits are proven under assumptions of compact embedding of patterns into data space. New multi-correctors of AI systems are presented and illustrated with examples of predicting errors and learning new classes of objects by a deep convolutional neural network.

In this hands-on project, we will train a Naive Bayes classifier to predict sentiment from thousands of Twitter tweets. This project could be practically used by any company with social media presence to automatically predict customer's sentiment (i.e.: whether their customers are happy or not). The process could be done automatically without having humans manually review thousands of tweets and customer reviews. Note: This course works best for learners who are based in the North America region.

Free Coupon Discount - Deep Learning: Recurrent Neural Networks in Python, GRU, LSTM, more modern deep learning, machine learning, and data science for sequences Created by Lazy Programmer Inc. English [Auto], Italian [Auto], Preview this Udemy Course GET COUPON CODE Description Like the course I just released on Hidden Markov Models, Recurrent Neural Networks are all about learning sequences - but whereas Markov Models are limited by the Markov assumption, Recurrent Neural Networks are not - and as a result, they are more expressive, and more powerful than anything we've seen on tasks that we haven't made progress on in decades. So what's going to be in this course and how will it build on the previous neural network courses and Hidden Markov Models? In the first section of the course we are going to add the concept of time to our neural networks. I'll introduce you to the Simple Recurrent Unit, also known as the Elman unit. We are going to revisit the XOR problem, but we're going to extend it so that it becomes the parity problem - you'll see that regular feedforward neural networks will have trouble solving this problem but recurrent networks will work because the key is to treat the input as a sequence.

We consider Markov Decision Processes (MDPs) with deterministic transitions and study the problem of regret minimization, which is central to the analysis and design of optimal learning algorithms. We present logarithmic problem-specific regret lower bounds that explicitly depend on the system parameter (in contrast to previous minimax approaches) and thus, truly quantify the fundamental limit of performance achievable by any learning algorithm. Deterministic MDPs can be interpreted as graphs and analyzed in terms of their cycles, a fact which we leverage in order to identify a class of deterministic MDPs whose regret lower bound can be determined numerically. We further exemplify this result on a deterministic line search problem, and a deterministic MDP with state-dependent rewards, whose regret lower bounds we can state explicitly. These bounds share similarities with the known problem-specific bound of the multi-armed bandit problem and suggest that navigation on a deterministic MDP need not have an effect on the performance of a learning algorithm.

The widespread use of machine learning algorithms calls for automatic change detection algorithms to monitor their behavior over time. As a machine learning algorithm learns from a continuous, possibly evolving, stream of data, it is desirable and often critical to supplement it with a companion change detection algorithm to facilitate its monitoring and control. We present a generic score-based change detection method that can detect a change in any number of components of a machine learning model trained via empirical risk minimization. This proposed statistical hypothesis test can be readily implemented for such models designed within a differentiable programming framework. We establish the consistency of the hypothesis test and show how to calibrate it to achieve a prescribed false alarm rate. We illustrate the versatility of the approach on synthetic and real data.

Solving partially-observable Markov decision processes (POMDPs) is critical when applying deep reinforcement learning (DRL) to real-world robotics problems, where agents have an incomplete view of the world. We present graph convolutional memory (GCM) for solving POMDPs using deep reinforcement learning. Unlike recurrent neural networks (RNNs) or transformers, GCM embeds domain-specific priors into the memory recall process via a knowledge graph. By encapsulating priors in the graph, GCM adapts to specific tasks but remains applicable to any DRL task. Using graph convolutions, GCM extracts hierarchical graph features, analogous to image features in a convolutional neural network (CNN). We show GCM outperforms long short-term memory (LSTM), gated transformers for reinforcement learning (GTrXL), and differentiable neural computers (DNCs) on control, long-term non-sequential recall, and 3D navigation tasks while using significantly fewer parameters.

We propose a method to estimate the uncertainty of the outcome of an image classifier on a given input datum. Deep neural networks commonly used for image classification are deterministic maps from an input image to an output class. As such, their outcome on a given datum involves no uncertainty, so we must specify what variability we are referring to when defining, measuring and interpreting "confidence." To this end, we introduce the Wellington Posterior, which is the distribution of outcomes that would have been obtained in response to data that could have been generated by the same scene that produced the given image. Since there are infinitely many scenes that could have generated the given image, the Wellington Posterior requires induction from scenes other than the one portrayed. We explore alternate methods using data augmentation, ensembling, and model linearization. Additional alternatives include generative adversarial networks, conditional prior networks, and supervised single-view reconstruction. We test these alternatives against the empirical posterior obtained by inferring the class of temporally adjacent frames in a video. These developments are only a small step towards assessing the reliability of deep network classifiers in a manner that is compatible with safety-critical applications.

In this paper, we propose conjugate energy-based models (CEBMs), a new class of energy-based models that define a joint density over data and latent variables. The joint density of a CEBM decomposes into an intractable distribution over data and a tractable posterior over latent variables. CEBMs have similar use cases as variational autoencoders, in the sense that they learn an unsupervised mapping from data to latent variables. However, these models omit a generator network, which allows them to learn more flexible notions of similarity between data points. Our experiments demonstrate that conjugate EBMs achieve competitive results in terms of image modelling, predictive power of latent space, and out-of-domain detection on a variety of datasets.