Due to their conceptual simplicity, k-means algorithm variants have been extensively used for unsupervised cluster analysis. However, one main shortcoming of these algorithms is that they essentially fit a mixture of identical spherical Gaussians to data that vastly deviates from such a distribution. In comparison, general Gaussian Mixture Models (GMMs) can fit richer structures but require estimating a quadratic number of parameters per cluster to represent the covariance matrices. This poses two main issues: (i) the underlying optimization problems are challenging due to their larger number of local minima, and (ii) their solutions can overfit the data. In this work, we design search strategies that circumvent both issues. We develop efficient global optimization algorithms for general GMMs, and we combine these algorithms with regularization strategies that avoid overfitting. Through extensive computational analyses, we observe that global optimization or regularization in isolation does not substantially improve cluster recovery. However, combining these techniques permits a completely new level of performance previously unachieved by k-means algorithm variants, unraveling vastly different cluster structures. These results shed new light on the current status quo between GMM and k-means methods and suggest the more frequent use of general GMMs for data exploration. To facilitate such applications, we provide open-source code as well as Julia packages ("UnsupervisedClustering.jl" and "RegularizedCovarianceMatrices.jl") implementing the proposed techniques.

Deep learning models have demonstrated great potential in medical 3D imaging, but their development is limited by the expensive, large volume of annotated data required. Active learning (AL) addresses this by training a model on a subset of the most informative data samples without compromising performance. We compared different AL strategies and propose a framework that minimizes the amount of data needed for state-of-the-art performance. 638 multi-institutional brain tumor MRI images were used to train a 3D U-net model and compare AL strategies. We investigated uncertainty sampling, annotation redundancy restriction, and initial dataset selection techniques. Uncertainty estimation techniques including Bayesian estimation with dropout, bootstrapping, and margins sampling were compared to random query. Strategies to avoid annotation redundancy by removing similar images within the to-be-annotated subset were considered as well. We determined the minimum amount of data necessary to achieve similar performance to the model trained on the full dataset ({\alpha} = 0.1). A variance-based selection strategy using radiomics to identify the initial training dataset is also proposed. Bayesian approximation with dropout at training and testing showed similar results to that of the full data model with less than 20% of the training data (p=0.293) compared to random query achieving similar performance at 56.5% of the training data (p=0.814). Annotation redundancy restriction techniques achieved state-of-the-art performance at approximately 40%-50% of the training data. Radiomics dataset initialization had higher Dice with initial dataset sizes of 20 and 80 images, but improvements were not significant. In conclusion, we investigated various AL strategies with dropout uncertainty estimation achieving state-of-the-art performance with the least annotated data.

We propose the first Bayesian encoder for metric learning. Rather than relying on neural amortization as done in prior works, we learn a distribution over the network weights with the Laplace Approximation. We actualize this by first proving that the contrastive loss is a valid log-posterior. We then propose three methods that ensure a positive definite Hessian. Lastly, we present a novel decomposition of the Generalized Gauss-Newton approximation. Empirically, we show that our Laplacian Metric Learner (LAM) estimates well-calibrated uncertainties, reliably detects out-of-distribution examples, and yields state-of-the-art predictive performance.

Bayesian network is a frequently-used method for fault detection and diagnosis in industrial processes. The basis of Bayesian network is structure learning which learns a directed acyclic graph (DAG) from data. However, the search space will scale super-exponentially with the increase of process variables, which makes the data-driven structure learning a challenging problem. To this end, the DAGs with NOTEARs methods are being well studied not only for their conversion of the discrete optimization into continuous optimization problem but also their compatibility with deep learning framework. Nevertheless, there still remain challenges for NOTEAR-based methods: 1) the infeasible solution results from the gradient descent-based optimization paradigm; 2) the truncation operation to promise the learned graph acyclic. In this work, the reason for challenge 1) is analyzed theoretically, and a novel method named DAGs with Tears method is proposed based on mix-integer programming to alleviate challenge 2). In addition, prior knowledge is able to incorporate into the new proposed method, making structure learning more practical and useful in industrial processes. Finally, a numerical example and an industrial example are adopted as case studies to demonstrate the superiority of the developed method.

Product-related reviews are based on users' experiences that are mostly shared on videos in YouTube. It is the second most popular website globally in 2021. People prefer to watch videos on recently released products prior to purchasing, in order to gather overall feedback and make worthy decisions. These videos are created by vloggers who are enthusiastic about technical materials and feedback is usually placed by experienced users of the product or its brand. Analyzing the sentiment of the user reviews gives useful insights into the product in general. This study is focused on three smartphone reviews, namely, Apple iPhone 13, Google Pixel 6, and Samsung Galaxy S21 which were released in 2021. VADER, which is a lexicon and rule-based sentiment analysis tool was used to classify each comment to its appropriate positive or negative orientation. All three smartphones show a positive sentiment from the users' perspective and iPhone 13 has the highest number of positive reviews. The resulting models have been tested using N\"aive Bayes, Decision Tree, and Support Vector Machine. Among these three classifiers, Support Vector Machine shows higher accuracies and F1-scores.

AI constructivism as inspired by Jean Piaget, described and surveyed by Frank Guerin, and representatively implemented by Gary Drescher seeks to create algorithms and knowledge structures that enable agents to acquire, maintain, and apply a deep understanding of the environment through sensorimotor interactions. This paper aims to increase awareness of constructivist AI implementations to encourage greater progress toward enabling lifelong learning by machines. It builds on Guerin's 2008 "Learning Like a Baby: A Survey of AI approaches." After briefly recapitulating that survey, it summarizes subsequent progress by the Guerin referents, numerous works not covered by Guerin (or found in other surveys), and relevant efforts in related areas. The focus is on knowledge representations and learning algorithms that have been used in practice viewed through lenses of Piaget's schemas, adaptation processes, and staged development. The paper concludes with a preview of a simple framework for constructive AI being developed by the author that parses concepts from sensory input and stores them in a semantic memory network linked to episodic data.

Quantifying similarity between neural representations -- e.g. hidden layer activation vectors -- is a perennial problem in deep learning and neuroscience research. Existing methods compare deterministic responses (e.g. artificial networks that lack stochastic layers) or averaged responses (e.g., trial-averaged firing rates in biological data). However, these measures of _deterministic_ representational similarity ignore the scale and geometric structure of noise, both of which play important roles in neural computation. To rectify this, we generalize previously proposed shape metrics (Williams et al. 2021) to quantify differences in _stochastic_ representations. These new distances satisfy the triangle inequality, and thus can be used as a rigorous basis for many supervised and unsupervised analyses. Leveraging this novel framework, we find that the stochastic geometries of neurobiological representations of oriented visual gratings and naturalistic scenes respectively resemble untrained and trained deep network representations. Further, we are able to more accurately predict certain network attributes (e.g. training hyperparameters) from its position in stochastic (versus deterministic) shape space.

To act in the world, robots rely on a representation of salient task aspects: for example, to carry a cup of coffee, a robot must consider movement efficiency and cup orientation in its behaviour. However, if we want robots to act for and with people, their representations must not be just functional but also reflective of what humans care about, i.e. their representations must be aligned with humans'. In this survey, we pose that current reward and imitation learning approaches suffer from representation misalignment, where the robot's learned representation does not capture the human's representation. We suggest that because humans will be the ultimate evaluator of robot performance in the world, it is critical that we explicitly focus our efforts on aligning learned task representations with humans, in addition to learning the downstream task. We advocate that current representation learning approaches in robotics should be studied from the perspective of how well they accomplish the objective of representation alignment. To do so, we mathematically define the problem, identify its key desiderata, and situate current robot learning methods within this formalism. We conclude the survey by suggesting future directions for exploring open challenges.

In this paper, we propose REASON, a novel framework that enables the automatic discovery of both intra-level (i.e., within-network) and inter-level (i.e., across-network) causal relationships for root cause localization. REASON consists of Topological Causal Discovery and Individual Causal Discovery. The Topological Causal Discovery component aims to model the fault propagation in order to trace back to the root causes. To achieve this, we propose novel hierarchical graph neural networks to construct interdependent causal networks by modeling both intra-level and inter-level non-linear causal relations. Based on the learned interdependent causal networks, we then leverage random walks with restarts to model the network propagation of a system fault. The Individual Causal Discovery component focuses on capturing abrupt change patterns of a single system entity. This component examines the temporal patterns of each entity's metric data (i.e., time series), and estimates its likelihood of being a root cause based on the Extreme Value theory. Combining the topological and individual causal scores, the top K system entities are identified as root causes. Extensive experiments on three real-world datasets with case studies demonstrate the effectiveness and superiority of the proposed framework.

Despite the great interest in the bandit problem, designing efficient algorithms for complex models remains challenging, as there is typically no analytical way to quantify uncertainty. In this paper, we propose Multiplier Bootstrap-based Exploration (MBE), a novel exploration strategy that is applicable to any reward model amenable to weighted loss minimization. We prove both instance-dependent and instance-independent rate-optimal regret bounds for MBE in sub-Gaussian multi-armed bandits. With extensive simulation and real data experiments, we show the generality and adaptivity of MBE.