Bayesian Optimization (BO) is a powerful method for optimizing black-box functions by combining prior knowledge with ongoing function evaluations. BO constructs a probabilistic surrogate model of the objective function given the covariates, which is in turn used to inform the selection of future evaluation points through an acquisition function. For smooth continuous search spaces, Gaussian Processes (GPs) are commonly used as the surrogate model as they offer analytical access to posterior predictive distributions, thus facilitating the computation and optimization of acquisition functions. However, in complex scenarios involving optimizations over categorical or mixed covariate spaces, GPs may not be ideal. This paper introduces Simulation Based Bayesian Optimization (SBBO) as a novel approach to optimizing acquisition functions that only requires \emph{sampling-based} access to posterior predictive distributions. SBBO allows the use of surrogate probabilistic models tailored for combinatorial spaces with discrete variables. Any Bayesian model in which posterior inference is carried out through Markov chain Monte Carlo can be selected as the surrogate model in SBBO. In applications involving combinatorial optimization, we demonstrate empirically the effectiveness of SBBO method using various choices of surrogate models.

Fair machine learning aims to prevent discrimination against individuals or sub-populations based on sensitive attributes such as gender and race. In recent years, causal inference methods have been increasingly used in fair machine learning to measure unfairness by causal effects. However, current methods assume that the true causal graph is given, which is often not true in real-world applications. To address this limitation, this paper proposes a framework for achieving causal fairness based on the notion of interventions when the true causal graph is partially known. The proposed approach involves modeling fair prediction using a Partially Directed Acyclic Graph (PDAG), specifically, a class of causal DAGs that can be learned from observational data combined with domain knowledge. The PDAG is used to measure causal fairness, and a constrained optimization problem is formulated to balance between fairness and accuracy. Results on both simulated and real-world datasets demonstrate the effectiveness of this method.

Through examples of coordinate and probability transformation between different distributions, the basic principle of normalizing flow is introduced in a simple and concise manner. From the perspective of the distribution of random variable function, the essence of probability transformation is explained, and the scaling factor Jacobian determinant of probability transformation is introduced. Treating the dataset as a sample from the population, obtaining normalizing flow is essentially through sampling surveys to statistically infer the numerical features of the population, and then the loss function is established by using the maximum likelihood estimation method. This article introduces how normalizing flow cleverly solves the two major application challenges of high-dimensional matrix determinant calculation and neural network reversible transformation. Using symmetric structured image dataset of three-span beam bridge, arch bridge, cable-stayed bridge and suspension bridge, constructing and training normalizing flow based on the Glow API in the TensorFlow Probability library. The model can smoothly transform the complex distribution of the bridge dataset into a standard normal distribution, and from the obtained latent space sampling, it can generate new bridge types that are different from the training dataset.

Causal and counterfactual reasoning are emerging directions in data science that allow us to reason about hypothetical scenarios. This is particularly useful in domains where experimental data are usually not available. In the context of environmental and ecological sciences, causality enables us, for example, to predict how an ecosystem would respond to hypothetical interventions. A structural causal model is a class of probabilistic graphical models for causality, which, due to its intuitive nature, can be easily understood by experts in multiple fields. However, certain queries, called unidentifiable, cannot be calculated in an exact and precise manner. This paper proposes applying a novel and recent technique for bounding unidentifiable queries within the domain of socioecological systems. Our findings indicate that traditional statistical analysis, including probabilistic graphical models, can identify the influence between variables. However, such methods do not offer insights into the nature of the relationship, specifically whether it involves necessity or sufficiency. This is where counterfactual reasoning becomes valuable.

Rule set learning has recently been frequently revisited because of its interpretability. Existing methods have several shortcomings though. First, most existing methods impose orders among rules, either explicitly or implicitly, which makes the models less comprehensible. Second, due to the difficulty of handling conflicts caused by overlaps (i.e., instances covered by multiple rules), existing methods often do not consider probabilistic rules. Third, learning classification rules for multi-class target is understudied, as most existing methods focus on binary classification or multi-class classification via the ``one-versus-rest" approach. To address these shortcomings, we propose TURS, for Truly Unordered Rule Sets. To resolve conflicts caused by overlapping rules, we propose a novel model that exploits the probabilistic properties of our rule sets, with the intuition of only allowing rules to overlap if they have similar probabilistic outputs. We next formalize the problem of learning a TURS model based on the MDL principle and develop a carefully designed heuristic algorithm. We benchmark against a wide range of rule-based methods and demonstrate that our method learns rule sets that have lower model complexity and highly competitive predictive performance. In addition, we empirically show that rules in our model are empirically ``independent" and hence truly unordered.

Learning from Label Proportions (LLP) is a learning problem where only aggregate level labels are available for groups of instances, called bags, during training, and the aim is to get the best performance at the instance-level on the test data. This setting arises in domains like advertising and medicine due to privacy considerations. We propose a novel algorithmic framework for this problem that iteratively performs two main steps. For the first step (Pseudo Labeling) in every iteration, we define a Gibbs distribution over binary instance labels that incorporates a) covariate information through the constraint that instances with similar covariates should have similar labels and b) the bag level aggregated label. We then use Belief Propagation (BP) to marginalize the Gibbs distribution to obtain pseudo labels. In the second step (Embedding Refinement), we use the pseudo labels to provide supervision for a learner that yields a better embedding. In the final iteration, a classifier is trained using the pseudo labels. Our algorithm displays strong gains against several SOTA baselines (up to 15%) for the LLP Binary Classification problem on various dataset types - tabular and Image. We achieve these improvements with minimal computational overhead above standard supervised learning due to Belief Propagation, for large bag sizes, even for a million samples. Learning from Label Proportions (henceforth LLP) has seen renewed interest in recent times due to the rising concerns of privacy and leakage of sensitive information (Ardehaly & Culotta, 2017; Busa-Fekete et al., 2023; Zhang et al., 2022; Kobayashi et al., 2022; Yu et al., 2014). In the LLP binary classification setting, all the training instances are aggregated into bags and only the aggregated label count for a bag is available, i.e. proportion of 1's in a bag. Features of all instances are available. This can be seen as a form of weak supervision compared to providing instance-level labels.

In the era of information proliferation, discerning the credibility of news content poses an ever-growing challenge. This paper introduces RELIANCE, a pioneering ensemble learning system designed for robust information and fake news credibility evaluation. Comprising five diverse base models, including Support Vector Machine (SVM), naive Bayes, logistic regression, random forest, and Bidirectional Long Short Term Memory Networks (BiLSTMs), RELIANCE employs an innovative approach to integrate their strengths, harnessing the collective intelligence of the ensemble for enhanced accuracy. Experiments demonstrate the superiority of RELIANCE over individual models, indicating its efficacy in distinguishing between credible and non-credible information sources. RELIANCE, also surpasses baseline models in information and news credibility assessment, establishing itself as an effective solution for evaluating the reliability of information sources.

Categorical variables often appear in datasets for classification and regression tasks, and they need to be encoded into numerical values before training. Since many encoders have been developed and can significantly impact performance, choosing the appropriate encoder for a task becomes a time-consuming yet important practical issue. This study broadly classifies machine learning models into three categories: 1) ATI models that implicitly perform affine transformations on inputs, such as multi-layer perceptron neural network; 2) Tree-based models that are based on decision trees, such as random forest; and 3) the rest, such as kNN. Theoretically, we prove that the one-hot encoder is the best choice for ATI models in the sense that it can mimic any other encoders by learning suitable weights from the data. We also explain why the target encoder and its variants are the most suitable encoders for tree-based models. This study conducted comprehensive computational experiments to evaluate 14 encoders, including one-hot and target encoders, along with eight common machine-learning models on 28 datasets. The computational results agree with our theoretical analysis. The findings in this study shed light on how to select the suitable encoder for data scientists in fields such as fraud detection, disease diagnosis, etc.

In causal discovery, non-Gaussianity has been used to characterize the complete configuration of a Linear Non-Gaussian Acyclic Model (LiNGAM), encompassing both the causal ordering of variables and their respective connection strengths. However, LiNGAM can only deal with the finite-dimensional case. To expand this concept, we extend the notion of variables to encompass vectors and even functions, leading to the Functional Linear Non-Gaussian Acyclic Model (Func-LiNGAM). Our motivation stems from the desire to identify causal relationships in brain-effective connectivity tasks involving, for example, fMRI and EEG datasets. We demonstrate why the original LiNGAM fails to handle these inherently infinite-dimensional datasets and explain the availability of functional data analysis from both empirical and theoretical perspectives. We establish theoretical guarantees of the identifiability of the causal relationship among non-Gaussian random vectors and even random functions in infinite-dimensional Hilbert spaces. To address the issue of sparsity in discrete time points within intrinsic infinite-dimensional functional data, we propose optimizing the coordinates of the vectors using functional principal component analysis. Experimental results on synthetic data verify the ability of the proposed framework to identify causal relationships among multivariate functions using the observed samples. For real data, we focus on analyzing the brain connectivity patterns derived from fMRI data.

Hyper-parameter optimization is the black art of tuning a learner's control parameters. In software analytics, a repeated result is that such tuning can result in dramatic performance improvements. Despite this, hyper-parameter optimization is often applied rarely or poorly in software analytics--perhaps due to the CPU cost of exploring all those parameter options can be prohibitive. We theorize that learners generalize better when the loss landscape is ``smooth''. This theory is useful since the influence on ``smoothness'' of different hyper-parameter choices can be tested very quickly (e.g. for a deep learner, after just one epoch). To test this theory, this paper implements and tests SMOOTHIE, a novel hyper-parameter optimizer that guides its optimizations via considerations of ``smothness''. The experiments of this paper test SMOOTHIE on numerous SE tasks including (a) GitHub issue lifetime prediction; (b) detecting false alarms in static code warnings; (c) defect prediction, and (d) a set of standard ML datasets. In all these experiments, SMOOTHIE out-performed state-of-the-art optimizers. Better yet, SMOOTHIE ran 300% faster than the prior state-of-the art. We hence conclude that this theory (that hyper-parameter optimization is best viewed as a ``smoothing'' function for the decision landscape), is both theoretically interesting and practically very useful. To support open science and other researchers working in this area, all our scripts and datasets are available on-line at https://github.com/yrahul3910/smoothness-hpo/.