These notes build upon a course I taught at the University of Maryland during the fall of 1983. My great thanks go to Martino Bardi, who took careful notes, saved them all these years and recently mailed them to me. Faye Yeager typed up his notes into a first draft of these lectures as they now appear. Scott Armstrong read over the notes and suggested many improvements: thanks, Scott. Stephen Moye of the American Math Society helped me a lot with AMSTeX versus LaTeX issues. My thanks also to Atilla Yilmaz for spotting lots of typos and errors, which I have corrected. I have radically modified much of the notation (to be consistent with my other writings), updated the references, added several new examples, and provided a proof of the Pontryagin Maximum Principle. As this is a course for undergraduates, I have dispensed in certain proofs with various measurability and continuity issues, and as compensation have added various critiques as to the lack of total rigor. This current version of the notes is not yet complete, but meets I think the usual high standards for material posted on the internet. Please email me at evans@math.berkeley.edu with any corrections or comments. An Introduction to Mathematical Optimal Control Theory Version 0.2

This post is authored by Tara Shankar Jana, Senior Technical Product Marketing Manager at Microsoft.

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Sockeye We describe Sockeye (version 1.12), an open-source sequence-to-sequence toolkit for Neural Machine Translation (NMT). Sockeye is a production-ready framework for training and applying models as well as an experimental platform for researchers. Written in Python and built on MXNet, the toolkit offers scalable training and inference for the three most prominent encoder-decoder architectures: attentional recurrent neural networks, self-attentional transformers, and fully convolutional networks. Sockeye also supports a wide range of optimizers, normalization and regularization techniques, and inference improvements from current NMT literature. Users can easily run standard training recipes, explore different model settings, and incorporate new ideas. In this paper, we highlight Sockeye’s features and benchmark it against other NMT toolkits on two language arcs from the 2017 Conference on Machine Translation (WMT): English-German and Latvian-English. We report competitive BLEU scores across all three architectures, including an overall best score for Sockeye’s transformer implementation. To facilitate further comparison, we release all system outputs and training scripts used in our experiments. The Sockeye toolkit is free software released under the Apache 2.0 license. …

 Features

This paper reviews recent developments in statistical structure learning; namely, Bayesian model reduction. Bayesian model reduction is a special but ubiquitous case of Bayesian model comparison that, in the setting of variational Bayes, furnishes an analytic solution for (a lower bound on) model evidence induced by a change in priors. This analytic solution finesses the problem of scoring large model spaces in model comparison or structure learning. This is because each new model can be cast in terms of an alternative set of priors over model parameters. Furthermore, the reduced free energy (i.e. evidence bound on the reduced model) finds an expedient application in hierarchical models, where it plays the role of a summary statistic. In other words, it contains all the necessary information contained in the posterior distributions over parameters of lower levels. In this technical note, we review Bayesian model reduction – in terms of common forms of reduced free energy – and illustrate recent applications in structure learning, hierarchical or empirical Bayes and as a metaphor for neurobiological processes like abductive reasoning and sleep. Bayesian model reduction

Amazon SageMaker and the AWS Deep Learning AMIs (DLAMI) now provide an easy way to evaluate the PyTorch 1.0 preview release. PyTorch 1.0 adds seamless research-to-production capabilities, while retaining the ease-of-use that has enabled PyTorch to rapidly gain popularity. The AWS Deep Learning AMI comes pre-built with PyTorch 1.0, Anaconda, and Python packages, with CUDA and MKL libraries to take advantage of accelerated compute instances. Amazon SageMaker is an end-to-end platform to quickly and easily build, train, tune, and deploy machine learning (ML) models at any scale. Now, Amazon SageMaker provides pre-configured environments with the PyTorch 1.0 preview that enables customers to leverage all SageMaker capabilities with PyTorch 1.0, including automatic model tuning.

Python offers a variety of data structures to hold our information — the dictionary being one of the most useful. Python dictionaries quick, easy to use, and flexible. As a beginning programmer, you can use this Python tutorial to become familiar with dictionaries and their common uses so that you can start incorporating them immediately into your own code.