Besides the Laplace distribution and the Gaussian distribution, there are many more probability distributions which is not well-understood in terms of privacy-preserving property of a random draw -- one of which is the Dirichlet distribution. In this work, we study the inherent privacy of releasing a single draw from a Dirichlet posterior distribution. As a complement to the previous study that provides general theories on the differential privacy of posterior sampling from exponential families, this study focuses specifically on the Dirichlet posterior sampling and its privacy guarantees. With the notion of truncated concentrated differential privacy (tCDP), we are able to derive a simple privacy guarantee of the Dirichlet posterior sampling, which effectively allows us to analyze its utility in various settings. Specifically, we prove accuracy guarantees of private Multinomial-Dirichlet sampling, which is prevalent in Bayesian tasks, and private release of a normalized histogram. In addition, with our results, it is possible to make Bayesian reinforcement learning differentially private by modifying the Dirichlet sampling for state transition probabilities.

We propose nonparametric Bayesian estimators for causal inference exploiting Regression Discontinuity/Kink (RD/RK) under sharp and fuzzy designs. Our estimators are based on Gaussian Process (GP) regression and classification. The GP methods are powerful probabilistic modeling approaches that are advantageous in terms of derivative estimation and uncertainty qualification, facilitating RK estimation and inference of RD/RK models. These estimators are extended to hierarchical GP models with an intermediate Bayesian neural network layer and can be characterized as hybrid deep learning models. Monte Carlo simulations show that our estimators perform similarly and often better than competing estimators in terms of precision, coverage and interval length. The hierarchical GP models improve upon one-layer GP models substantially. An empirical application of the proposed estimators is provided.

Presently, nearly all manual tasks are being automated. Machine learning algorithms are changing the definition of manual. It is very evident that machine learning is one of the hottest trends in the tech industry and is incredibly powerful to make predictions, and calculated suggestions based on large amounts of data. Machine learning engineers should be thorough with the routine algorithms to understand ML operations and execute advanced techniques. Here are the top 10 machine learning algorithms every engineer should know.

Today's business ecosystem has become very competitive. Customer satisfaction has become a major focus for business growth. Business organizations are spending a lot of money and human resources on various strategies to understand and fulfill their customer's needs. But, because of defective manual analysis on multifarious needs of customers, many organizations are failing to achieve customer satisfaction. As a result, they are losing customer's loyalty and spending extra money on marketing. We can solve the problems by implementing Sentiment Analysis. It is a combined technique of Natural Language Processing (NLP) and Machine Learning (ML). Sentiment Analysis is broadly used to extract insights from wider public opinion behind certain topics, products, and services. We can do it from any online available data. In this paper, we have introduced two NLP techniques (Bag-of-Words and TF-IDF) and various ML classification algorithms (Support Vector Machine, Logistic Regression, Multinomial Naive Bayes, Random Forest) to find an effective approach for Sentiment Analysis on a large, imbalanced, and multi-classed dataset. Our best approaches provide 77% accuracy using Support Vector Machine and Logistic Regression with Bag-of-Words technique.

Francis Bacon popularized the idea that science is based on a process of induction by which repeated observations are, in some unspecified way, generalized to theories based on the assumption that the future resembles the past. This idea was criticized by Hume and others as untenable leading to the famous problem of induction. It wasn't until the work of Karl Popper that this problem was solved, by demonstrating that induction is not the basis for science and that the development of scientific knowledge is instead based on the same principles as biological evolution. Today, machine learning is also taught as being rooted in induction from big data. Solomonoff induction implemented in an idealized Bayesian agent (Hutter's AIXI) is widely discussed and touted as a framework for understanding AI algorithms, even though real-world attempts to implement something like AIXI immediately encounter fatal problems. In this paper, we contrast frameworks based on induction with Donald T. Campbell's universal Darwinism. We show that most AI algorithms in use today can be understood as using an evolutionary trial and error process searching over a solution space. In this work we argue that a universal Darwinian framework provides a better foundation for understanding AI systems. Moreover, at a more meta level the process of development of all AI algorithms can be understood under the framework of universal Darwinism.

Thompson Sampling has been widely used for contextual bandit problems due to the flexibility of its modeling power. However, a general theory for this class of methods in the frequentist setting is still lacking. In this paper, we present a theoretical analysis of Thompson Sampling, with a focus on frequentist regret bounds. In this setting, we show that the standard Thompson Sampling is not aggressive enough in exploring new actions, leading to suboptimality in some pessimistic situations. A simple modification called Feel-Good Thompson Sampling, which favors high reward models more aggressively than the standard Thompson Sampling, is proposed to remedy this problem. We show that the theoretical framework can be used to derive Bayesian regret bounds for standard Thompson Sampling, and frequentist regret bounds for Feel-Good Thompson Sampling. It is shown that in both cases, we can reduce the bandit regret problem to online least squares regression estimation. For the frequentist analysis, the online least squares regression bound can be directly obtained using online aggregation techniques which have been well studied. The resulting bandit regret bound matches the minimax lower bound in the finite action case. Moreover, the analysis can be generalized to handle a class of linearly embeddable contextual bandit problems (which generalizes the popular linear contextual bandit model). The obtained result again matches the minimax lower bound. Finally we illustrate that the analysis can be extended to handle some MDP problems.

Following the growing success of generative neural networks in LHC simulations, the crucial question is how to control the networks and assign uncertainties to their event output. We show how Bayesian normalizing flows or invertible networks capture uncertainties from the training and turn them into an uncertainty on the event weight. Fundamentally, the interplay between density and uncertainty estimates indicates that these networks learn functions in analogy to parameter fits rather than binned event counts.

Background: Single-cell RNA sequencing (scRNA-seq) yields valuable insights about gene expression and gives critical information about complex tissue cellular composition. In the analysis of single-cell RNA sequencing, the annotations of cell subtypes are often done manually, which is time-consuming and irreproducible. Garnett is a cell-type annotation software based the on elastic net method. Besides cell-type annotation, supervised machine learning methods can also be applied to predict other cell phenotypes from genomic data. Despite the popularity of such applications, there is no existing study to systematically investigate the performance of those supervised algorithms in various sizes of scRNA-seq data sets. Methods and Results: This study evaluates 13 popular supervised machine learning algorithms to classify cell phenotypes, using published real and simulated data sets with diverse cell sizes. The benchmark contained two parts. In the first part, we used real data sets to assess the popular supervised algorithms' computing speed and cell phenotype classification performance. The classification performances were evaluated using AUC statistics, F1-score, precision, recall, and false-positive rate. In the second part, we evaluated gene selection performance using published simulated data sets with a known list of real genes. Conclusion: The study outcomes showed that ElasticNet with interactions performed best in small and medium data sets. NB was another appropriate method for medium data sets. In large data sets, XGB works excellent. Ensemble algorithms were not significantly superior to individual machine learning methods. Adding interactions to ElasticNet can help, and the improvement was significant in small data sets.

Entropy regularization is a popular method in reinforcement learning (RL). Although it has many advantages, it alters the RL objective and makes the converged policy deviate from the optimal policy of the original Markov Decision Process. Though divergence regularization has been proposed to settle this problem, it cannot be trivially applied to cooperative multi-agent reinforcement learning (MARL). In this paper, we investigate divergence regularization in cooperative MARL and propose a novel off-policy cooperative MARL framework, divergence-regularized multi-agent actor-critic (DMAC). Mathematically, we derive the update rule of DMAC which is naturally off-policy, guarantees a monotonic policy improvement and is not biased by the regularization. DMAC is a flexible framework and can be combined with many existing MARL algorithms. We evaluate DMAC in a didactic stochastic game and StarCraft Multi-Agent Challenge and empirically show that DMAC substantially improves the performance of existing MARL algorithms.

Supervised Causal Learning (SCL) aims to learn causal relations from observational data by accessing previously seen datasets associated with ground truth causal relations. This paper presents a first attempt at addressing a fundamental question: What are the benefits from supervision and how does it benefit? Starting from seeing that SCL is not better than random guessing if the learning target is non-identifiable a priori, we propose a two-phase paradigm for SCL by explicitly considering structure identifiability. Following this paradigm, we tackle the problem of SCL on discrete data and propose ML4C. The core of ML4C is a binary classifier with a novel learning target: it classifies whether an Unshielded Triple (UT) is a v-structure or not. Starting from an input dataset with the corresponding skeleton provided, ML4C orients each UT once it is classified as a v-structure. These v-structures are together used to construct the final output. To address the fundamental question of SCL, we propose a principled method for ML4C featurization: we exploit the vicinity of a given UT (i.e., the neighbors of UT in skeleton), and derive features by considering the conditional dependencies and structural entanglement within the vicinity. We further prove that ML4C is asymptotically perfect. Last but foremost, thorough experiments conducted on benchmark datasets demonstrate that ML4C remarkably outperforms other state-of-the-art algorithms in terms of accuracy, robustness, tolerance and transferability. In summary, ML4C shows promising results on validating the effectiveness of supervision for causal learning.