The above equation represents Bayes Theorem in which it describes the probability of an event occurring P(A) based on our prior knowledge of events that may be related to that event P(B). Example of using Bayes theorem: I'll be using the tennis weather dataset. What is the probability of playing tennis given it is rainy? The probability of playing tennis when it is rainy is 60%. The process is very simple once you obtain the frequencies for each category.

The goal of score following is to track a musical performance, usually in the form of audio, in a corresponding score representation. Established methods mainly rely on computer-readable scores in the form of MIDI or MusicXML and achieve robust and reliable tracking results. Recently, multimodal deep learning methods have been used to follow along musical performances in raw sheet images. Among the current limits of these systems is that they require a non trivial amount of preprocessing steps that unravel the raw sheet image into a single long system of staves. The current work is an attempt at removing this particular limitation. We propose an architecture capable of estimating matching score positions directly within entire unprocessed sheet images. We argue that this is a necessary first step towards a fully integrated score following system that does not rely on any preprocessing steps such as optical music recognition.

Reservoir computers (RCs) and recurrent neural networks (RNNs) can mimic any finite-state automaton in theory, and some workers demonstrated that this can hold in practice. We test the capability of generalized linear models, RCs, and Long Short-Term Memory (LSTM) RNN architectures to predict the stochastic processes generated by a large suite of probabilistic deterministic finite-state automata (PDFA). PDFAs provide an excellent performance benchmark in that they can be systematically enumerated, the randomness and correlation structure of their generated processes are exactly known, and their optimal memory-limited predictors are easily computed. Unsurprisingly, LSTMs outperform RCs, which outperform generalized linear models. Surprisingly, each of these methods can fall short of the maximal predictive accuracy by as much as 50% after training and, when optimized, tend to fall short of the maximal predictive accuracy by ~5%, even though previously available methods achieve maximal predictive accuracy with orders-of-magnitude less data. Thus, despite the representational universality of RCs and RNNs, using them can engender a surprising predictive gap for simple stimuli. One concludes that there is an important and underappreciated role for methods that infer "causal states" or "predictive state representations".

Classical probability distributions on sets of sequences can be modeled using quantum states. Here, we do so with a quantum state that is pure and entangled. Because it is entangled, the reduced densities that describe subsystems also carry information about the complementary subsystem. This is in contrast to the classical marginal distributions on a subsystem in which information about the complementary system has been integrated out and lost. A training algorithm based on the density matrix renormalization group (DMRG) procedure uses the extra information contained in the reduced densities and organizes it into a tensor network model. An understanding of the extra information contained in the reduced densities allow us to examine the mechanics of this DMRG algorithm and study the generalization error of the resulting model. As an illustration, we work with the even-parity dataset and produce an estimate for the generalization error as a function of the fraction of the dataset used in training.

We consider the problem of how a teacher algorithm can enable an unknown Deep Reinforcement Learning (DRL) student to become good at a skill over a wide range of diverse environments. To do so, we study how a teacher algorithm can learn to generate a learning curriculum, whereby it sequentially samples parameters controlling a stochastic procedural generation of environments. Because it does not initially know the capacities of its student, a key challenge for the teacher is to discover which environments are easy, difficult or unlearnable, and in what order to propose them to maximize the efficiency of learning over the learnable ones. To achieve this, this problem is transformed into a surrogate continuous bandit problem where the teacher samples environments in order to maximize absolute learning progress of its student. We present a new algorithm modeling absolute learning progress with Gaussian mixture models (ALP-GMM). We also adapt existing algorithms and provide a complete study in the context of DRL. Using parameterized variants of the BipedalWalker environment, we study their efficiency to personalize a learning curriculum for different learners (embodiments), their robustness to the ratio of learnable/unlearnable environments, and their scalability to non-linear and high-dimensional parameter spaces. Videos and code are available at https://github.com/flowersteam/teachDeepRL.

When teams of robots collaborate to complete a task, communication is often necessary. Like humans, robot teammates should implicitly communicate through their actions: but interpreting our partner's actions is typically difficult, since a given action may have many different underlying reasons. Here we propose an alternate approach: instead of not being able to infer whether an action is due to exploration, exploitation, or communication, we define separate roles for each agent. Because each role defines a distinct reason for acting (e.g., only exploit, only communicate), teammates now correctly interpret the meaning behind their partner's actions. Our results suggest that leveraging and alternating roles leads to performance comparable to teams that explicitly exchange messages.

Who has not heard that Bayesian statistics are difficult, computationally slow, cannot scale-up to big data, the results are subjective; and we don't need it at all? Do we really need to learn a lot of math and a lot of classical statistics first before approaching Bayesian techniques. Why do the most popular books about Bayesian statistics have over 500 pages? Bayesian nightmare is real or myth? Someone once compared Bayesian approach to the kitchen of a Michelin star chef with high-quality chef knife, a stockpot and an expensive sautee pan; while Frequentism is like your ordinary kitchen, with banana slicers and pasta pots. People talk about Bayesianism and Frequentism as if they were two different religions. Does Bayes really put more burden on the data scientist to use her brain at the outset because Bayesianism is a religion for the brightest of the brightest?

We can easily use the widely available libraries available in Python and R to build models!" I have lost count of the number of times I've heard this from amateur data scientists. This fallacy is all too common and has created a false expectation among aspiring data science professionals. Let's get this out of the way right now – you need to understand the mathematics behind machine learning algorithms to become a data scientist. There is no way around it. It is an intrinsic part of a data scientist's role and every recruiter and experienced machine learning professional will vouch for this.

A plethora of problems in AI, engineering and the sciences are naturally formalized as inference in discrete probabilistic models. Exact inference is often prohibitively expensive, as it may require evaluating the (unnormalized) target density on its entire domain. Here we consider the setting where only a limited budget of calls to the unnormalized density oracle is available, raising the challenge of where in the domain to allocate these function calls in order to construct a good approximate solution. We formulate this problem as an instance of sequential decision-making under uncertainty and leverage methods from reinforcement learning for probabilistic inference with budget constraints. In particular, we propose the TreeSample algorithm, an adaptation of Monte Carlo Tree Search to approximate inference. This algorithm caches all previous queries to the density oracle in an explicit search tree, and dynamically allocates new queries based on a "best-first" heuristic for exploration, using existing upper confidence bound methods. Our non-parametric inference method can be effectively combined with neural networks that compile approximate conditionals of the target, which are then used to guide the inference search and enable generalization across multiple target distributions. We show empirically that TreeSample outperforms standard approximate inference methods on synthetic factor graphs.

--GitHub has become an important platform for code sharing and scientific exchange. With the massive number of repositories available, there is a pressing need for topic-based search. Even though the topic label functionality has been introduced, the majority of GitHub repositories do not have any labels, impeding the utility of search and topic-based analysis. This work targets the automatic repository classification problem as keyword-driven hierarchical classification . Specifically, users only need to provide a label hierarchy with keywords to supply as supervision. This setting is flexible, adaptive to the users' needs, accounts for the different granularity of topic labels and requires minimal human effort. We identify three key challenges of this problem, namely (1) the presence of multi-modal signals; (2) supervision scarcity and bias; (3) supervision format mismatch. In recognition of these challenges, we propose the H IG ITC LASS framework, comprising of three modules: heterogeneous information network embedding; keyword enrichment; topic modeling and pseudo document generation. Experimental results on two GitHub repository collections confirm that H IG ITC LASS is superior to existing weakly-supervised and dataless hierarchical classification methods, especially in its ability to integrate both structured and unstructured data for repository classification. I NTRODUCTION For the computer science field, code repositories are an indispensable part of the knowledge dissemination process, containing valuable details for reproduction. For software engineers, sharing code also promotes the adoption of best practices and accelerates code development. The needs of the scientific community and that of software developers have facilitated the growth of online code collaboration platforms, the most popular of which is GitHub, with over 96 million repositories and 31 million users as of 2018. With the overwhelming number of repositories hosted on GitHub, there is a natural need to enable search functionality so that users can quickly target repositories of interest. To accommodate this need, GitHub introduced topic labels 1 which allowed users to declare topics for their own repositories.