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.

Structural matrix-variate observations routinely arise in diverse fields such as multi-layer network analysis and brain image clustering. While data of this type have been extensively investigated with fruitful outcomes being delivered, the fundamental questions like its statistical optimality and computational limit are largely under-explored. In this paper, we propose a low-rank Gaussian mixture model (LrMM) assuming each matrix-valued observation has a planted low-rank structure. Minimax lower bounds for estimating the underlying low-rank matrix are established allowing a whole range of sample sizes and signal strength. Under a minimal condition on signal strength, referred to as the information-theoretical limit or statistical limit, we prove the minimax optimality of a maximum likelihood estimator which, in general, is computationally infeasible. If the signal is stronger than a certain threshold, called the computational limit, we design a computationally fast estimator based on spectral aggregation and demonstrate its minimax optimality. Moreover, when the signal strength is smaller than the computational limit, we provide evidences based on the low-degree likelihood ratio framework to claim that no polynomial-time algorithm can consistently recover the underlying low-rank matrix. Our results reveal multiple phase transitions in the minimax error rates and the statistical-to-computational gap. Numerical experiments confirm our theoretical findings. We further showcase the merit of our spectral aggregation method on the worldwide food trading dataset.

In metric learning, the goal is to learn an embedding so that data points with the same class are close to each other and data points with different classes are far apart. We propose a distance-ratio-based (DR) formulation for metric learning. Like softmax-based formulation for metric learning, it models $p(y=c|x')$, which is a probability that a query point $x'$ belongs to a class $c$. The DR formulation has two useful properties. First, the corresponding loss is not affected by scale changes of an embedding. Second, it outputs the optimal (maximum or minimum) classification confidence scores on representing points for classes. To demonstrate the effectiveness of our formulation, we conduct few-shot classification experiments using softmax-based and DR formulations on CUB and mini-ImageNet datasets. The results show that DR formulation generally enables faster and more stable metric learning than the softmax-based formulation. As a result, using DR formulation achieves improved or comparable generalization performances.

Recent advances in reinforcement learning (RL) have increased complexity which, especially for deep RL, has brought forth challenges related to explainability [1]. The opacity of state-of-the-art RL algorithms has led to model developers having a limited understanding of their agents' policies and no influence over learned strategies [2]. While concerns surrounding explainability have been noted for AI in general, it is only more recently that attempts have been made to explain RL systems [3, 1, 4, 5]. These attempts have resulted in a wide suite of methods requiring various degrees of expert knowledge, either about the state-action domain or about the specific RL algorithm. Further, they typically rely on post-hoc analysis of learned policies which give only observational assurances of agents' behaviour. We instead propose an intrinsic method of regularizing agents' actions based on a given prior. While current methods for RL regularization aim to improve training performance - e.g., by maximizing the entropy of the action distribution [6], or by minimising the distance to a prior sub-optimal state-action distribution [7] - our aim is the characterization of our agents' behaviours. We also extend the current regularization techniques to accommodate multi-agent systems which allows intrinsic characterization of individual agents. We provide a formal argument for the rationale of our method and demonstrate its efficacy in a toy problem where agents learn to navigate to a destination on a grid by performing, e.g., only right turns (under the premise that right turns are

We consider the problem: is the optimal expected total reward to reach a goal state in a partially observable Markov decision process (POMDP) below a given threshold? We tackle this -- generally undecidable -- problem by computing under-approximations on these total expected rewards. This is done by abstracting finite unfoldings of the infinite belief MDP of the POMDP. The key issue is to find a suitable under-approximation of the value function. We provide two techniques: a simple (cut-off) technique that uses a good policy on the POMDP, and a more advanced technique (belief clipping) that uses minimal shifts of probabilities between beliefs. We use mixed-integer linear programming (MILP) to find such minimal probability shifts and experimentally show that our techniques scale quite well while providing tight lower bounds on the expected total reward.

Across research disciplines, cluster randomized trials (CRTs) are commonly implemented to evaluate interventions delivered to groups of participants, such as communities and clinics. Despite advances in the design and analysis of CRTs, several challenges remain. First, there are many possible ways to specify the intervention effect (e.g., at the individual-level or at the cluster-level). Second, the theoretical and practical performance of common methods for CRT analysis remain poorly understood. Here, we use causal models to formally define an array of causal effects as summary measures of counterfactual outcomes. Next, we provide a comprehensive overview of well-known CRT estimators, including the t-test and generalized estimating equations (GEE), as well as less known methods, including augmented-GEE and targeted maximum likelihood estimation (TMLE). In finite sample simulations, we illustrate the performance of these estimators and the importance of effect specification, especially when cluster size varies. Finally, our application to data from the Preterm Birth Initiative (PTBi) study demonstrates the real-world importance of selecting an analytic approach corresponding to the research question. Given its flexibility to estimate a variety of effects and ability to adaptively adjust for covariates for precision gains while maintaining Type-I error control, we conclude TMLE is a promising tool for CRT analysis.

Many datasets represent a combination of several viewpoints - different ways of looking at the same data that lead to different generalizations. For example, a corpus with examples generated by different people may be mixtures of many perspectives and can be viewed with different perspectives by others. It isn't always possible to represent the viewpoints by a clean separation, in advance, of examples representing each viewpoint and train a separate model for each viewpoint. We introduce lensing, a mixed-initiative technique to (1) extract'lenses' or mappings between machine-learned representations and perspectives of human experts, and to (2) generate'lensed' models that afford multiple perspectives of the same dataset. We apply lensing for two classes of latent variable models (a) a mixed-membership model and (b) a matrix factorization model in the context of two mental health applications, and we capture and imbue the perspectives of clinical psychologists into these models. Our work shows the benefits of the machine learning practitioner formally incorporating the perspective of a knowledgeable domain expert into their models rather than estimating unlensed models themselves in isolation.