Monte Carlo (MC) integration is the de facto method for approximating the predictive distribution of Bayesian neural networks (BNNs). But, even with many MC samples, Gaussian-based BNNs could still yield bad predictive performance due to the posterior approximation's error. Meanwhile, alternatives to MC integration tend to be more expensive or biased. In this work, we experimentally show that the key to good MC-approximated predictive distributions is the quality of the approximate posterior itself. However, previous methods for obtaining accurate posterior approximations are expensive and non-trivial to implement. We, therefore, propose to refine Gaussian approximate posteriors with normalizing flows. When applied to last-layer BNNs, it yields a simple \emph{post hoc} method for improving pre-existing parametric approximations. We show that the resulting posterior approximation is competitive with even the gold-standard full-batch Hamiltonian Monte Carlo.

Human brains are commonly modeled as networks of Regions of Interest (ROIs) and their connections for the understanding of brain functions and mental disorders. Recently, Transformer-based models have been studied over different types of data, including graphs, shown to bring performance gains widely. In this work, we study Transformer-based models for brain network analysis. Driven by the unique properties of data, we model brain networks as graphs with nodes of fixed size and order, which allows us to (1) use connection profiles as node features to provide natural and low-cost positional information and (2) learn pair-wise connection strengths among ROIs with efficient attention weights across individuals that are predictive towards downstream analysis tasks. Moreover, we propose an Orthonormal Clustering Readout operation based on self-supervised soft clustering and orthonormal projection. This design accounts for the underlying functional modules that determine similar behaviors among groups of ROIs, leading to distinguishable cluster-aware node embeddings and informative graph embeddings. Finally, we re-standardize the evaluation pipeline on the only one publicly available large-scale brain network dataset of ABIDE, to enable meaningful comparison of different models. Experiment results show clear improvements of our proposed Brain Network Transformer on both the public ABIDE and our restricted ABCD datasets. The implementation is available at https://github.com/Wayfear/BrainNetworkTransformer.

The development of accurate constitutive models for materials that undergo path-dependent processes continues to be a complex challenge in computational solid mechanics. Challenges arise both in considering the appropriate model assumptions and from the viewpoint of data availability, verification, and validation. Recently, data-driven modeling approaches have been proposed that aim to establish stress-evolution laws that avoid user-chosen functional forms by relying on machine learning representations and algorithms. However, these approaches not only require a significant amount of data but also need data that probes the full stress space with a variety of complex loading paths. Furthermore, they rarely enforce all necessary thermodynamic principles as hard constraints. Hence, they are in particular not suitable for low-data or limited-data regimes, where the first arises from the cost of obtaining the data and the latter from the experimental limitations of obtaining labeled data, which is commonly the case in engineering applications. In this work, we discuss a hybrid framework that can work on a variable amount of data by relying on the modularity of the elastoplasticity formulation where each component of the model can be chosen to be either a classical phenomenological or a data-driven model depending on the amount of available information and the complexity of the response. The method is tested on synthetic uniaxial data coming from simulations as well as cyclic experimental data for structural materials. The discovered material models are found to not only interpolate well but also allow for accurate extrapolation in a thermodynamically consistent manner far outside the domain of the training data. Training aspects and details of the implementation of these models into Finite Element simulations are discussed and analyzed.

This research aims to develop machine learning models for students academic performance and study strategies prediction which could be generalized to all courses in higher education. Key learning attributes (intrinsic, extrinsic, autonomy, relatedness, competence, and self-esteem) essential for students learning process were used in building the models. Determining the broad effect of these attributes on students' academic performance and study strategy is the center of our interest. To investigate this, we used Scikit-learn in python to build five machine learning models (Decision Tree, K-Nearest Neighbour, Random Forest, Linear/Logistic Regression, and Support Vector Machine) for both regression and classification tasks to perform our analysis. The models were trained, evaluated, and tested for accuracy using 924 university dentistry students' data collected by Chilean authors through quantitative research design. A comparative analysis of the models revealed that the tree-based models such as the random forest (with prediction accuracy of 94.9%) and decision tree show the best results compared to the linear, support vector, and k-nearest neighbours. The models built in this research can be used in predicting student performance and study strategy so that appropriate interventions could be implemented to improve student learning progress. Thus, incorporating strategies that could improve diverse student learning attributes in the design of online educational systems may increase the likelihood of students continuing with their learning tasks as required. Moreover, the results show that the attributes could be modelled together and used to adapt/personalize the learning process.

Detecting which nodes in graphs are outliers is a relatively new machine learning task with numerous applications. Despite the proliferation of algorithms developed in recent years for this task, there has been no standard comprehensive setting for performance evaluation. Consequently, it has been difficult to understand which methods work well and when under a broad range of settings. To bridge this gap, we present--to the best of our knowledge--the first comprehensive benchmark for unsupervised outlier node detection on static attributed graphs called BOND, with the following highlights. (1) We benchmark the outlier detection performance of 14 methods ranging from classical matrix factorization to the latest graph neural networks. (2) Using nine real datasets, our benchmark assesses how the different detection methods respond to two major types of synthetic outliers and separately to "organic" (real non-synthetic) outliers. (3) Using an existing random graph generation technique, we produce a family of synthetically generated datasets of different graph sizes that enable us to compare the running time and memory usage of the different outlier detection algorithms. Based on our experimental results, we discuss the pros and cons of existing graph outlier detection algorithms, and we highlight opportunities for future research. Importantly, our code is freely available and meant to be easily extendable: https://github.com/pygod-team/pygod/tree/main/benchmark

Conformal prediction aims to determine precise levels of confidence in predictions for new objects using past experience. However, the commonly used exchangeable assumptions between the training data and testing data limit its usage in dealing with contaminated testing sets. In this paper, we develop a novel flow-based conformal inference (FCI) method to build predictive sets and infer outliers for complex and high-dimensional data. We leverage ideas from adversarial flow to transfer the input data to a random vector with known distributions. Our roundtrip transformation can map the input data to a low-dimensional space, meanwhile reserving the conditional distribution of input data given each class label, which enables us to construct a non-conformity score for uncertainty quantification. Our approach is applicable and robust when the testing data is contaminated. We evaluate our method, robust flow-based conformal inference, on benchmark datasets. We find that it produces effective predictive sets and accurate outlier detection and is more powerful relative to competing approaches.

In this paper, we propose an improved linear discriminant analysis, called spectrally-corrected and regularized linear discriminant analysis (SCRLDA). This method integrates the design ideas of the sample spectrally-corrected covariance matrix and the regularized discriminant analysis. The SCRLDA method is specially designed for classification problems under the assumption that the covariance matrix follows a spiked model. Through the real and simulated data analysis, it is shown that our proposed classifier outperforms the classical R-LDA and can be as competitive as the KNN, SVM classifiers while requiring lower computational complexity.

Recently, research has increasingly focused on developing efficient neural network architectures. In this work, we explore logic gate networks for machine learning tasks by learning combinations of logic gates. These networks comprise logic gates such as "AND" and "XOR", which allow for very fast execution. The difficulty in learning logic gate networks is that they are conventionally non-differentiable and therefore do not allow training with gradient descent. Thus, to allow for effective training, we propose differentiable logic gate networks, an architecture that combines real-valued logics and a continuously parameterized relaxation of the network. The resulting discretized logic gate networks achieve fast inference speeds, e.g., beyond a million images of MNIST per second on a single CPU core.

Recent years have witnessed a great success of supervised deep learning, where predictive models were trained from a large amount of fully labeled data. However, in practice, labeling such big data can be very costly and may not even be possible for privacy reasons. Therefore, in this paper, we aim to learn an accurate classifier without any class labels. More specifically, we consider the case where multiple sets of unlabeled data and only their class priors, i.e., the proportions of each class, are available. Under this problem setup, we first derive an unbiased estimator of the classification risk that can be estimated from the given unlabeled sets and theoretically analyze the generalization error of the learned classifier. We then find that the classifier obtained as such tends to cause overfitting as its empirical risks go negative during training. To prevent overfitting, we further propose a partial risk regularization that maintains the partial risks with respect to unlabeled datasets and classes to certain levels. Experiments demonstrate that our method effectively mitigates overfitting and outperforms state-of-the-art methods for learning from multiple unlabeled sets.

Knowledge Graph Embedding models have become an important area of machine learning.Those models provide a latent representation of entities and relations in a knowledge graph which can then be used in downstream machine learning tasks such as link prediction. The learning process of such models can be performed by contrasting positive and negative triples. While all triples of a KG are considered positive, negative triples are usually not readily available. Therefore, the choice of the sampling method to obtain the negative triples play a crucial role in the performance and effectiveness of Knowledge Graph Embedding models. Most of the current methods fetch negative samples from a random distribution of entities in the underlying Knowledge Graph which also often includes meaningless triples. Other known methods use adversarial techniques or generative neural networks which consequently reduce the efficiency of the process. In this paper, we propose an approach for generating informative negative samples considering available complementary knowledge about entities. Particularly, Pre-trained Language Models are used to form neighborhood clusters by utilizing the distances between entities to obtain representations of symbolic entities via their textual information. Our comprehensive evaluations demonstrate the effectiveness of the proposed approach on benchmark Knowledge Graphs with textual information for the link prediction task.