The Poisson model is frequently employed to describe count data, but in a Bayesian context it leads to an analytically intractable posterior probability distribution. In this work, we analyze a variational Gaussian approximation to the posterior distribution arising from the Poisson model with a Gaussian prior. This is achieved by seeking an optimal Gaussian distribution minimizing the Kullback-Leibler divergence from the posterior distribution to the approximation, or equivalently maximizing the lower bound for the model evidence. We derive an explicit expression for the lower bound, and show the existence and uniqueness of the optimal Gaussian approximation. The lower bound functional can be viewed as a variant of classical Tikhonov regularization that penalizes also the covariance. Then we develop an efficient alternating direction maximization algorithm for solving the optimization problem, and analyze its convergence. We discuss strategies for reducing the computational complexity via low rank structure of the forward operator and the sparsity of the covariance. Further, as an application of the lower bound, we discuss hierarchical Bayesian modeling for selecting the hyperparameter in the prior distribution, and propose a monotonically convergent algorithm for determining the hyperparameter. We present extensive numerical experiments to illustrate the Gaussian approximation and the algorithms.

In recent years, research in Artificial Intelligence has been primarily dominated by impressive advances in Machine Learning, with a strong emphasis on the so-called Deep Learning framework. It has allowed considerable achievements such as human-level performance in visual classification [1] and description [2], in Atari video games [3] and even in the highly complex game of Go [4]. The Deep Learning approach is characterized by supposing very minimal prior on the task to be solved, compensating this lack of prior knowledge by feeding the learning algorithm with an extremely high amount of training data, while hiding the intermediary representations. However, it is important noting that the most important contributions of Deep Learning for Artificial Intelligence often owe their success in part to their integration with other types of learning algorithms. For example, the AlphaGo program which defeated the world champions in the famously complex game of Go [4], is based on the integration of Deep Reinforcement Learning with a Monte-Carlo tree search algorithm. Without the tree search addition, AlphaGo still outperforms previous machine performances but is unable to beat high-level human players. Another example can be found in the original Deep Q-Learning algorithm (DQN, Mnih et al., 2015), achieving very poor performance in some Atari games where the reward is considerably sparse and delayed (e.g.

Identifying context-specific entity networks from aggregated data is an important task, arising often in bioinformatics and neuroimaging. Computationally, this task can be formulated as jointly estimating multiple different, but related, sparse Undirected Graphical Models (UGM) from aggregated samples across several contexts. Previous joint-UGM studies have mostly focused on sparse Gaussian Graphical Models (sGGMs) and can't identify context-specific edge patterns directly. We, therefore, propose a novel approach, SIMULE (detecting Shared and Individual parts of MULtiple graphs Explicitly) to learn multi-UGM via a constrained L1 minimization. SIMULE automatically infers both specific edge patterns that are unique to each context and shared interactions preserved among all the contexts. Through the L1 constrained formulation, this problem is cast as multiple independent subtasks of linear programming that can be solved efficiently in parallel. In addition to Gaussian data, SIMULE can also handle multivariate Nonparanormal data that greatly relaxes the normality assumption that many real-world applications do not follow. We provide a novel theoretical proof showing that SIMULE achieves a consistent result at the rate O(log(Kp)/n_{tot}). On multiple synthetic datasets and two biomedical datasets, SIMULE shows significant improvement over state-of-the-art multi-sGGM and single-UGM baselines.

Did you know using XGBoost algorithm is one of the popular winning recipe of data science competitions? So, what makes it more powerful than a traditional Random Forest or Neural Network? In the last few years, predictive modeling has become much faster and accurate. I remember spending long hours on feature engineering for improving model by few decimals. A lot of that difficult work, can now be done by using better algorithms.

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The outcome is the result of two powerful forces in the evolution of information retrieval: artificial intelligence--especially natural language processing--and crowdsourcing. Computer algorithms interpret the relationship between the words we type and the vast number of possible web pages based on the frequency of linguistic connections in the billions of texts on which the system has been trained. But that is not the only source of information. The semantic relationships get strengthened by professional annotators who hand-tune results--and the algorithms that generate them--for topics of importance, and by web searchers (us) who, in our clicks, tell the algorithms which connections are the best ones. Despite the incredible, world-changing success of this model, it has its flaws.

Here is a list of the best courses in Data Science and Machine Learning from Udemy. With the back-to-school sale, you can get these and other Udemy courses for $12, 90-95% off original price. Udemy.com is an online marketplace for learning, their data science content is updated regularly by the instructors who created good courses (filled with actionable tools) and bite-size lessons that help you cover defined topics at your own pace. Ready to be thrown into the deep end and learn the real problems a data scientist faces on a daily basis? Data Science management consultant Kirill Eremenko teaches this intense, best-selling course to over 23K students and counting.

What's happening now: Myanmar's government launched its latest surge of violence against the Rohingya last October after alleged attacks by Rohingya insurgents against government posts. A report from the United Nation's Office of the High Commissioner on Human Rights calls the crackdown "systematic" and "very likely" including crimes against humanity, branding the government's work as "ethnic cleansing." The political controversy: Aung San Suu Kyi, who was imprisoned for nearly two decades after calling for democracy and human rights under the country's oppressive military junta, has refused to speak out against the violence as Myanmar's de-facto leader. Five other women who have won the Nobel Peace Prize called on Suu Kyi to acknowledge the violence in an open letter -- though the Nobel Committee remains exceedingly unlikely to revoke her prize, per the NYT.

In my last post, where I shared the code that I used to produce an example analysis to go along with my webinar on building meaningful models for disease prediction, I mentioned that it is advised to consider over- or under-sampling when you have unbalanced data sets. Because my focus in this webinar was on evaluating model performance, I did not want to add an additional layer of complexity and therefore did not further discuss how to specifically deal with unbalanced data. But because I had gotten a few questions regarding this, I thought it would be worthwhile to explain over- and under-sampling techniques in more detail and show how you can very easily implement them with caret. In this context, unbalanced data refers to classification problems where we have unequal instances for different classes. Having unbalanced data is actually very common in general, but it is especially prevalent when working with disease data where we usually have more healthy control samples than disease cases.

Adversarial examples are inputs to machine learning models that an attacker has intentionally designed to cause the model to make a mistake; they're like optical illusions for machines. In this post we'll show how adversarial examples work across different mediums, and will discuss why securing systems against them can be difficult. At OpenAI, we think adversarial examples are a good aspect of security to work on because they represent a concrete problem in AI safety that can be addressed in the short term, and because fixing them is difficult enough that it requires a serious research effort. To get an idea of what adversarial examples look like, consider this demonstration from Explaining and Harnessing Adversarial Examples: starting with an image of a panda, the attacker adds a small perturbation that has been calculated to make the image be recognized as a gibbon with high confidence. An adversarial input, overlaid on a typical image, can cause a classifier to miscategorize a panda as a gibbon.