Model selection in the context of bandit optimization is a challenging problem, as it requires balancing exploration and exploitation not only for action selection, but also for model selection. One natural approach is to rely on online learning algorithms that treat different models as experts. Existing methods, however, scale poorly ($\text{poly}M$) with the number of models $M$ in terms of their regret. Our key insight is that, for model selection in linear bandits, we can emulate full-information feedback to the online learner with a favorable bias-variance trade-off. This allows us to develop ALEXP, which has an exponentially improved ($\log M$) dependence on $M$ for its regret. ALEXP has anytime guarantees on its regret, and neither requires knowledge of the horizon $n$, nor relies on an initial purely exploratory stage. Our approach utilizes a novel time-uniform analysis of the Lasso, establishing a new connection between online learning and high-dimensional statistics.
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Nonnegative tensor factorization (NTF) has become an important tool for feature extraction and part-based representation with preserved intrinsic structure information from nonnegative high-order data. However, the original NTF methods utilize Euclidean or Kullback-Leibler divergence as the loss function which treats each feature equally leading to the neglect of the side-information of features. To utilize correlation information of features and manifold information of samples, we introduce Wasserstein manifold nonnegative tensor factorization (WMNTF), which minimizes the Wasserstein distance between the distribution of input tensorial data and the distribution of reconstruction. Although some researches about Wasserstein distance have been proposed in nonnegative matrix factorization (NMF), they ignore the spatial structure information of higher-order data. We use Wasserstein distance (a.k.a Earth Mover's distance or Optimal Transport distance) as a metric and add a graph regularizer to a latent factor. Experimental results demonstrate the effectiveness of the proposed method compared with other NMF and NTF methods.
Quantum computing is finding promising applications in optimization, machine learning and physics, leading to the development of various models for representing quantum information. Because these representations are often studied in different contexts (many-body physics, machine learning, formal verification, simulation), little is known about fundamental trade-offs between their succinctness and the runtime of operations to update them. We therefore analytically investigate three widely-used quantum state representations: matrix product states (MPS), decision diagrams (DDs), and restricted Boltzmann machines (RBMs). We map the relative succinctness of these data structures and provide the complexity for relevant query and manipulation operations. Further, to chart the balance between succinctness and operation efficiency, we extend the concept of rapidity with support for the non-canonical data structures studied in this work, showing in particular that MPS is at least as rapid as some DDs. By providing a knowledge compilation map for quantum state representations, this paper contributes to the understanding of the inherent time and space efficiency trade-offs in this area.
Comparative opinion mining is a specialized field of sentiment analysis that aims to identify and extract sentiments expressed comparatively. To address this task, we propose an approach that consists of solving three sequential sub-tasks: (i) identifying comparative sentence, i.e., if a sentence has a comparative meaning, (ii) extracting comparative elements, i.e., what are comparison subjects, objects, aspects, predicates, and (iii) classifying comparison types which contribute to a deeper comprehension of user sentiments in Vietnamese product reviews. Our method is ranked fifth at the Vietnamese Language and Speech Processing (VLSP) 2023 challenge on Comparative Opinion Mining (ComOM) from Vietnamese Product Reviews.
Structured data in the form of tabular datasets contain features that are distinct and discrete, with varying individual and relative importances to the target. Combinations of one or more features may be more predictive and meaningful than simple individual feature contributions. R's mixed effect linear models library allows users to provide such interactive feature combinations in the model design. However, given many features and possible interactions to select from, model selection becomes an exponentially difficult task. We aim to automate the model selection process for predictions on tabular datasets incorporating feature interactions while keeping computational costs small. The framework includes two distinct approaches for feature selection: a Priority-based Random Grid Search and a Greedy Search method. The Priority-based approach efficiently explores feature combinations using prior probabilities to guide the search. The Greedy method builds the solution iteratively by adding or removing features based on their impact. Experiments on synthetic demonstrate the ability to effectively capture predictive feature combinations.
Text analysis is an interesting research area in data science and has various applications, such as in artificial intelligence, biomedical research, and engineering. We review popular methods for text analysis, ranging from topic modeling to the recent neural language models. In particular, we review Topic-SCORE, a statistical approach to topic modeling, and discuss how to use it to analyze MADStat - a dataset on statistical publications that we collected and cleaned. The application of Topic-SCORE and other methods on MADStat leads to interesting findings. For example, $11$ representative topics in statistics are identified. For each journal, the evolution of topic weights over time can be visualized, and these results are used to analyze the trends in statistical research. In particular, we propose a new statistical model for ranking the citation impacts of $11$ topics, and we also build a cross-topic citation graph to illustrate how research results on different topics spread to one another. The results on MADStat provide a data-driven picture of the statistical research in $1975$--$2015$, from a text analysis perspective.
Given a conditional sentence "P=>Q" (if P then Q) and respective facts, four different types of inferences are observed in human reasoning. Affirming the antecedent (AA) (or modus ponens) reasons Q from P; affirming the consequent (AC) reasons P from Q; denying the antecedent (DA) reasons -Q from -P; and denying the consequent (DC) (or modus tollens) reasons -P from -Q. Among them, AA and DC are logically valid, while AC and DA are logically invalid and often called logical fallacies. Nevertheless, humans often perform AC or DA as pragmatic inference in daily life. In this paper, we realize AC, DA and DC inferences in answer set programming. Eight different types of completion are introduced and their semantics are given by answer sets. We investigate formal properties and characterize human reasoning tasks in cognitive psychology. Those completions are also applied to commonsense reasoning in AI.
The adaptive processing of structured data is a long-standing research topic in machine learning that investigates how to automatically learn a mapping from a structured input to outputs of various nature. Recently, there has been an increasing interest in the adaptive processing of graphs, which led to the development of different neural network-based methodologies. In this thesis, we take a different route and develop a Bayesian Deep Learning framework for graph learning. The dissertation begins with a review of the principles over which most of the methods in the field are built, followed by a study on graph classification reproducibility issues. We then proceed to bridge the basic ideas of deep learning for graphs with the Bayesian world, by building our deep architectures in an incremental fashion. This framework allows us to consider graphs with discrete and continuous edge features, producing unsupervised embeddings rich enough to reach the state of the art on several classification tasks. Our approach is also amenable to a Bayesian nonparametric extension that automatizes the choice of almost all model's hyper-parameters. Two real-world applications demonstrate the efficacy of deep learning for graphs. The first concerns the prediction of information-theoretic quantities for molecular simulations with supervised neural models. After that, we exploit our Bayesian models to solve a malware-classification task while being robust to intra-procedural code obfuscation techniques. We conclude the dissertation with an attempt to blend the best of the neural and Bayesian worlds together. The resulting hybrid model is able to predict multimodal distributions conditioned on input graphs, with the consequent ability to model stochasticity and uncertainty better than most works. Overall, we aim to provide a Bayesian perspective into the articulated research field of deep learning for graphs.
Analyzing observational data from multiple sources can be useful for increasing statistical power to detect a treatment effect; however, practical constraints such as privacy considerations may restrict individual-level information sharing across data sets. This paper develops federated methods that only utilize summary-level information from heterogeneous data sets. Our federated methods provide doubly-robust point estimates of treatment effects as well as variance estimates. We derive the asymptotic distributions of our federated estimators, which are shown to be asymptotically equivalent to the corresponding estimators from the combined, individual-level data. We show that to achieve these properties, federated methods should be adjusted based on conditions such as whether models are correctly specified and stable across heterogeneous data sets.
Humans perceive the world by concurrently processing and fusing high-dimensional inputs from multiple modalities such as vision and audio. Machine perception models, in stark contrast, are typically modality-specific and optimised for unimodal benchmarks, and hence late-stage fusion of final representations or predictions from each modality (`late-fusion') is still a dominant paradigm for multimodal video classification. Instead, we introduce a novel transformer based architecture that uses `fusion bottlenecks' for modality fusion at multiple layers. Compared to traditional pairwise self-attention, our model forces information between different modalities to pass through a small number of bottleneck latents, requiring the model to collate and condense the most relevant information in each modality and only share what is necessary. We find that such a strategy improves fusion performance, at the same time reducing computational cost. We conduct thorough ablation studies, and achieve state-of-the-art results on multiple audio-visual classification benchmarks including Audioset, Epic-Kitchens and VGGSound. All code and models will be released.
Multi-relation Question Answering is a challenging task, due to the requirement of elaborated analysis on questions and reasoning over multiple fact triples in knowledge base. In this paper, we present a novel model called Interpretable Reasoning Network that employs an interpretable, hop-by-hop reasoning process for question answering. The model dynamically decides which part of an input question should be analyzed at each hop; predicts a relation that corresponds to the current parsed results; utilizes the predicted relation to update the question representation and the state of the reasoning process; and then drives the next-hop reasoning. Experiments show that our model yields state-of-the-art results on two datasets. More interestingly, the model can offer traceable and observable intermediate predictions for reasoning analysis and failure diagnosis, thereby allowing manual manipulation in predicting the final answer.
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