We study the optimal sample complexity of learning a Gaussian directed acyclic graph (DAG) from observational data. Our main result establishes the minimax optimal sample complexity for learning the structure of a linear Gaussian DAG model with equal variances to be $n\asymp q\log(d/q)$, where $q$ is the maximum number of parents and $d$ is the number of nodes. We further make comparisons with the classical problem of learning (undirected) Gaussian graphical models, showing that under the equal variance assumption, these two problems share the same optimal sample complexity. In other words, at least for Gaussian models with equal error variances, learning a directed graphical model is not more difficult than learning an undirected graphical model. Our results also extend to more general identification assumptions as well as subgaussian errors.

A range of applications for automatic machine learning need the generation process to be controllable. In this work, we propose a way to control the output via a sequence of simple actions, that are called semantic code classes. Finally, we present a semantic code classification task and discuss methods for solving this problem on the Natural Language to Machine Learning (NL2ML) dataset.

A new generation of increasingly autonomous and self-learning cyber-physical systems (CPS) is being developed for control applications in the real world. These systems are AI-based in that they leverage techniques from the field of Artificial intelligence (AI) to flexibly cope with imprecision, inconsistency, incompleteness, to have an inherent ability to learn from experience, and to adapt according to changing and even unforeseen situations. This extra flexibility of AI systems makes it harder to predict their behavior. Moreover, AI systems usually are safety-critical in that they may be causing real harm in (and to) the real world. Consequently, the central question regarding the development of such systems is how to handle or even overcome this basic dichotomy between unpredictable and safe behavior of AI systems. In other words, how can we best construct systems that exploit AI techniques, without incurring the frailties of "AI-like" behavior?

As the costs of sensors and associated IT infrastructure decreases - as exemplified by the Internet of Things - increasing volumes of observational data are becoming available for use by environmental scientists. However, as the number of available observation sites increases, so too does the opportunity for data quality issues to emerge, particularly given that many of these sensors do not have the benefit of official maintenance teams. To realise the value of crowd sourced 'Internet of Things' type observations for environmental modelling, we require approaches that can automate the detection of outliers during the data modelling process so that they do not contaminate the true distribution of the phenomena of interest. To this end, here we present a Bayesian deep learning approach for spatio-temporal modelling of environmental variables with automatic outlier detection. Our approach implements a Gaussian-uniform mixture density network whose dual purposes - modelling the phenomenon of interest, and learning to classify and ignore outliers - are achieved simultaneously, each by specifically designed branches of our neural network. For our example application, we use the Met Office's Weather Observation Website data, an archive of observations from around 1900 privately run and unofficial weather stations across the British Isles. Using data on surface air temperature, we demonstrate how our deep mixture model approach enables the modelling of a highly skilled spatio-temporal temperature distribution without contamination from spurious observations. We hope that adoption of our approach will help unlock the potential of incorporating a wider range of observation sources, including from crowd sourcing, into future environmental models.

The hierarchical and recursive expressive capability of rooted trees is applicable to represent statistical models in various areas, such as data compression, image processing, and machine learning. On the other hand, such hierarchical expressive capability causes a problem in tree selection to avoid overfitting. One unified approach to solve this is a Bayesian approach, on which the rooted tree is regarded as a random variable and a direct loss function can be assumed on the selected model or the predicted value for a new data point. However, all the previous studies on this approach are based on the probability distribution on full trees, to the best of our knowledge. In this paper, we propose a generalized probability distribution for any rooted trees in which only the maximum number of child nodes and the maximum depth are fixed. Furthermore, we derive recursive methods to evaluate the characteristics of the probability distribution without any approximations.

We consider the task of learning causal structures from data stored on multiple machines, and propose a novel structure learning method called distributed annealing on regularized likelihood score (DARLS) to solve this problem. We model causal structures by a directed acyclic graph that is parameterized with generalized linear models, so that our method is applicable to various types of data. To obtain a high-scoring causal graph, DARLS simulates an annealing process to search over the space of topological sorts, where the optimal graphical structure compatible with a sort is found by a distributed optimization method. This distributed optimization relies on multiple rounds of communication between local and central machines to estimate the optimal structure. We establish its convergence to a global optimizer of the overall score that is computed on all data across local machines. To the best of our knowledge, DARLS is the first distributed method for learning causal graphs with such theoretical guarantees. Through extensive simulation studies, DARLS has shown competing performance against existing methods on distributed data, and achieved comparable structure learning accuracy and test-data likelihood with competing methods applied to pooled data across all local machines. In a real-world application for modeling protein-DNA binding networks with distributed ChIP-Sequencing data, DARLS also exhibits higher predictive power than other methods, demonstrating a great advantage in estimating causal networks from distributed data.

While dropout is known to be a successful regularization technique, insights into the mechanisms that lead to this success are still lacking. We introduce the concept of weight expansion, an increase in the signed volume of a parallelotope spanned by the column or row vectors of the weight covariance matrix, and show that weight expansion is an effective means of increasing the generalization in a PAC-Bayesian setting. We provide a theoretical argument that dropout leads to weight expansion and extensive empirical support for the correlation between dropout and weight expansion. To support our hypothesis that weight expansion can be regarded as an indicator of the enhanced generalization capability endowed by dropout, and not just as a mere by-product, we have studied other methods that achieve weight expansion (resp. This suggests that dropout is an attractive regularizer, because it is a computationally cheap method for obtaining weight expansion. This insight justifies the role of dropout as a regularizer, while paving the way for identifying regularizers that promise improved generalization through weight expansion. Research on why dropout is so effective in improving the generalization ability of neural networks has been intensive. Many intriguing phenomena induced by dropout have also been studied in this research (Gao et al., 2019; Lengerich et al., 2020; Wei et al., 2020).

Causal discovery for purely observational, categorical data is a long-standing challenging problem. Unlike continuous data, the vast majority of existing methods for categorical data focus on inferring the Markov equivalence class only, which leaves the direction of some causal relationships undetermined. This paper proposes an identifiable ordinal causal discovery method that exploits the ordinal information contained in many real-world applications to uniquely identify the causal structure. The proposed method is applicable beyond ordinal data via data discretization. Through real-world and synthetic experiments, we demonstrate that the proposed ordinal causal discovery method combined with simple score-and-search algorithms has favorable and robust performance compared to state-of-the-art alternative methods in both ordinal categorical and non-categorical data. An accompanied R package OCD is freely available at https://web.stat.tamu.edu/

MIT press provides another excellent book in creative commons. I plan to buy it and I recommend you do. This book provides a broad introduction to algorithms for decision making under uncertainty. An agent is an entity that acts based on observations of its environment. The interaction between the agent and the environment follows an observe-act cycle or loop.

Bone Marrow Transplant, a gradational rescue for a wide range of disorders emanating from the bone marrow, is an efficacious surgical treatment. Several risk factors, such as post-transplant illnesses, new malignancies, and even organ damage, can impair long-term survival. Therefore, technologies like Machine Learning are deployed for investigating the survival prediction of BMT receivers along with the influences that limit their resilience. In this study, an efficient survival classification model is presented in a comprehensive manner, incorporating the Chi-squared feature selection method to address the dimensionality problem and Hyper Parameter Optimization (HPO) to increase accuracy. A synthetic dataset is generated by imputing the missing values, transforming the data using dummy variable encoding, and compressing the dataset from 59 features to the 11 most correlated features using Chi-squared feature selection. The dataset was split into train and test sets at a ratio of 80:20, and the hyperparameters were optimized using Grid Search Cross-Validation. Several supervised ML methods were trained in this regard, like Decision Tree, Random Forest, Logistic Regression, K-Nearest Neighbors, Gradient Boosting Classifier, Ada Boost, and XG Boost. The simulations have been performed for both the default and optimized hyperparameters by using the original and reduced synthetic dataset. After ranking the features using the Chi-squared test, it was observed that the top 11 features with HPO, resulted in the same accuracy of prediction (94.73%) as the entire dataset with default parameters. Moreover, this approach requires less time and resources for predicting the survivability of children undergoing BMT. Hence, the proposed approach may aid in the development of a computer-aided diagnostic system with satisfactory accuracy and minimal computation time by utilizing medical data records.