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 Learning Graphical Models


Classification-Based Machine Learning for Finance

@machinelearnbot

Finally, a comprehensive hands-on machine learning course with specific focus on classification based models for the investment community and passionate investors. In the past few years, there has been a massive adoption and growth in the use of data science, artificial intelligence and machine learning to find alpha. However, information on and application of machine learning to investment are scarce. This course has been designed to address that. It is meant to spark your creative juices and get you started in this space.


Non-Technical Person's Guide To Entering The Machine Learning Industry

#artificialintelligence

As the buzz around data science grows every day, there is a slew of self-taught professionals who have kick-started the machine learning journey with Andrew Ng's online courses. Many enthusiasts are gravitating towards the computer science field. But if one wants to pursue a career in Machine Learning, they need to be familiar with statistics and linear algebra. With computer science and ML applications becoming more pervasive in everyday life, people from a non-technical background are also interested in joining the field. In this article, we have discussed in-depth roles a person from non-tech background can explore in the data science/AI field.


Face Recognition for Beginners – Towards Data Science

#artificialintelligence

Face Recognition is a recognition technique used to detect faces of individuals whose images saved in the data set. Despite the point that other methods of identification can be more accurate, face recognition has always remained a significant focus of research because of its non-meddling nature and because it is people's facile method of personal identification. Face recognition algorithms classified as geometry based or template based algorithms. The template-based methods can be constructed using statistical tools like SVM [Support Vector Machines], PCA [Principal Component Analysis], LDA [Linear Discriminant Analysis], Kernel methods or Trace Transforms. The geometric feature based methods analyse local facial features and their geometric relationship.


Revisiting Reweighted Wake-Sleep

arXiv.org Machine Learning

Discrete latent-variable models, while applicable in a variety of settings, can often be difficult to learn. Sampling discrete latent variables can result in high-variance gradient estimators for two primary reasons: 1. branching on the samples within the model, and 2. the lack of a pathwise derivative for the samples. While current state-of-the-art methods employ control-variate schemes for the former and continuous-relaxation methods for the latter, their utility is limited by the complexities of implementing and training effective control-variate schemes and the necessity of evaluating (potentially exponentially) many branch paths in the model. Here, we revisit the reweighted wake-sleep (RWS) (Bornschein and Bengio, 2015) algorithm, and through extensive evaluations, show that it circumvents both these issues, outperforming current state-of-the-art methods in learning discrete latent-variable models. Moreover, we observe that, unlike the importance weighted autoencoder, RWS learns better models and inference networks with increasing numbers of particles, and that its benefits extend to continuous latent-variable models as well. Our results suggest that RWS is a competitive, often preferable, alternative for learning deep generative models.


Finite Sample Analysis of LSTD with Random Projections and Eligibility Traces

arXiv.org Artificial Intelligence

Policy evaluation, commonly referred to as value function approximation, is an important and central part in many reinforcement learning (RL) algorithms [27], whose task is to estimate value functions for a fixed policy in a discounted Markov Decision Process (MDP) environment. The value function of each state specifies the accumulated reward an agent would receive in the future by following the fixed policy from that state. Value functions have been widely investigated in RL applications, and it can provide insightful and important information for the agent to obtain an optimal policy, such as important board configurations in Go [24], failure probabilities of large telecommunication networks [9], taxi-out times at large airports [2] and so on. Despite the value functions can be approximated by different ways, the simplest form, linear approximations, are still widely adopted and studied due to their good generalization abilities, relatively efficient computation and solid theoretical guarantees[27, 7, 13, 16]. Temporal Difference (TD) learning is a common approach to this policy evaluation with linear function approximation problem[27]. These typical TD algorithms can be divided into two categories: gradient based methods (e.g., GTD(λ) [28]) and least-square (LS) based methods (e.g., LSTD(λ)[4]). A good survey on these algorithms can be found in [17, 6, 12, 7, 13]. 1 As the development of information technologies, high-dimensional data is widely seen in RL applications [26, 30, 23], which brings serious challenges to design scalable and computationally efficient algorithms for the linear value function approximation problem. To address this practical issue, several approaches have been developed for efficient and effective value function approximation.


Variational Measure Preserving Flows

arXiv.org Machine Learning

Probabilistic modelling is a general and elegant framework to capture the uncertainty, ambiguity and diversity of hidden structures in data. Probabilistic inference is the key operation on probabilistic models to obtain the distribution over the latent representations given data. Unfortunately, the computation of inference on complex models is extremely challenging. In spite of the success of existing inference methods, like Markov chain Monte Carlo(MCMC) and variational inference(VI), many powerful models are not available for large scale problems because inference is simply computationally intractable. The recent advances in using neural networks for probabilistic inference have shown promising results on this challenge. In this work, we propose a novel general inference framework that has the strength from both MCMC and VI. The proposed method is not only computationally scalable and efficient, but also has its root from the ergodicity theorem, that provides the guarantee of better performance with more computational power. Our experiment results suggest that our method can outperform state-of-the-art methods on generative models and Bayesian neural networks on some popular benchmark problems.


Learning Restricted Boltzmann Machines via Influence Maximization

arXiv.org Machine Learning

Graphical models are a rich language for describing high-dimensional distributions in terms of their dependence structure. While there are provable algorithms for learning graphical models in a variety of settings, there has been much less progress when there are latent variables. Here we study Restricted Boltzmann Machines (or RBMs), which are a popular model with wide-ranging applications in dimensionality reduction, collaborative filtering, topic modeling, feature extraction and deep learning. We give a simple greedy algorithm based on influence maximization to learn ferromagnetic RBMs with bounded degree. More precisely, we learn a description of the distribution on the observed variables as a Markov Random Field (or MRF), even though it exhibits complex higher- order interactions. Our analysis is based on tools from mathematical physics that were developed to show the concavity of magnetization. Moreover our results extend in a straightforward manner to ferromagnetic Ising models with latent variables. Conversely, we show that the distribution on the observed nodes of a general RBM can simulate any MRF which allows us to show new hardness results for improperly learning RBMs even with only a constant number of latent variables.


Maximizing acquisition functions for Bayesian optimization

arXiv.org Machine Learning

Bayesian optimization is a sample-efficient approach to global optimization that relies on theoretically motivated value heuristics (acquisition functions) to guide the search process. Fully maximizing acquisition functions produces the Bayes' decision rule, but this ideal is difficult to achieve since these functions are frequently non-trivial to optimize. This statement is especially true when evaluating queries in parallel, where acquisition functions are routinely non-convex, high-dimensional, and intractable. We present two modern approaches for maximizing acquisition functions that exploit key properties thereof, namely the differentiability of Monte Carlo integration and the submodularity of parallel querying.


A Sliding-Window Algorithm for Markov Decision Processes with Arbitrarily Changing Rewards and Transitions

arXiv.org Machine Learning

We consider reinforcement learning in changing Markov Decision Processes where both the state-transition probabilities and the reward functions may vary over time. For this problem setting, we propose an algorithm using a sliding window approach and provide performance guarantees for the regret evaluated against the optimal non-stationary policy. We also characterize the optimal window size suitable for our algorithm. These results are complemented by a sample complexity bound on the number of sub-optimal steps taken by the algorithm. Finally, we present some experimental results to support our theoretical analysis.


Bayesian estimation for large scale multivariate Ornstein-Uhlenbeck model of brain connectivity

arXiv.org Machine Learning

Estimation of reliable whole-brain connectivity is a crucial step towards the use of connectivity information in quantitative approaches to the study of neuropsychiatric disorders. When estimating brain connectivity a challenge is imposed by the paucity of time samples and the large dimensionality of the measurements. Bayesian estimation methods for network models offer a number of advantages in this context but are not commonly employed. Here we compare three different estimation methods for the multivariate Ornstein-Uhlenbeck model, that has recently gained some popularity for characterizing whole-brain connectivity. We first show that a Bayesian estimation of model parameters assuming uniform priors is equivalent to an application of the method of moments. Then, using synthetic data, we show that the Bayesian estimate scales poorly with number of nodes in the network as compared to an iterative Lyapunov optimization. In particular when the network size is in the order of that used for whole-brain studies (about 100 nodes) the Bayesian method needs about eight times more time samples than Lyapunov method in order to achieve similar estimation accuracy. We also show that the higher estimation accuracy of Lyapunov method is reflected in a much better classification of individuals based on the estimated connectivity from a real dataset of BOLD fMRI. Finally we show that the poor accuracy of Bayesian method is due to numerical errors, when the imaginary part of the connectivity estimate gets large compared to its real part.