Complex evidence theory, as a generalized D-S evidence theory, has attracted academic attention because it can well express uncertainty by means of complex basic belief assignment (CBBA), and realize uncertainty reasoning by complex combination rule. However, the uncertainty measurement in complex evidence theory is still an open issue. In order to make better decisions, a complex pignistic belief transformation (CPBT) method has been proposed to assign CBBAs of multi-element focal elements to subsets. The essence of CPBT is the redistribution of complex mass function by means of the concept of fractal. In this paper, based on fractal theory, experimental simulation and analysis have been carried out on the generation process of CPBT in time dimension. Then, a new fractal-based complex belief (FCB) entropy is proposed to measure the uncertainty of CBBA. Finally, the properties of FCB entropy are analyzed, and several examples are used to verify its effectiveness.
Biometric systems based on brain activity have been proposed as an alternative to passwords or to complement current authentication techniques. By leveraging the unique brainwave patterns of individuals, these systems offer the possibility of creating authentication solutions that are resistant to theft, hands-free, accessible, and potentially even revocable. However, despite the growing stream of research in this area, faster advance is hindered by reproducibility problems. Issues such as the lack of standard reporting schemes for performance results and system configuration, or the absence of common evaluation benchmarks, make comparability and proper assessment of different biometric solutions challenging. Further, barriers are erected to future work when, as so often, source code is not published open access. To bridge this gap, we introduce NeuroBench, a flexible open source tool to benchmark brainwave-based authentication models. It incorporates nine diverse datasets, implements a comprehensive set of pre-processing parameters and machine learning algorithms, enables testing under two common adversary models (known vs unknown attacker), and allows researchers to generate full performance reports and visualizations. We use NeuroBench to investigate the shallow classifiers and deep learning-based approaches proposed in the literature, and to test robustness across multiple sessions. We observe a 37.6\% reduction in Equal Error Rate (EER) for unknown attacker scenarios (typically not tested in the literature), and we highlight the importance of session variability to brainwave authentication. All in all, our results demonstrate the viability and relevance of NeuroBench in streamlining fair comparisons of algorithms, thereby furthering the advancement of brainwave-based authentication through robust methodological practices.
Modern policy optimization methods in reinforcement learning, such as TRPO and PPO, owe their success to the use of parameterized policies. However, while theoretical guarantees have been established for this class of algorithms, especially in the tabular setting, the use of general parameterization schemes remains mostly unjustified. In this work, we introduce a novel framework for policy optimization based on mirror descent that naturally accommodates general parameterizations. The policy class induced by our scheme recovers known classes, e.g., softmax, and generates new ones depending on the choice of mirror map. Using our framework, we obtain the first result that guarantees linear convergence for a policy-gradient-based method involving general parameterization. To demonstrate the ability of our framework to accommodate general parameterization schemes, we provide its sample complexity when using shallow neural networks, show that it represents an improvement upon the previous best results, and empirically validate the effectiveness of our theoretical claims on classic control tasks.
Identifying causal structure is central to many fields ranging from strategic decision-making to biology and economics. In this work, we propose CD-UCT, a model-based reinforcement learning method for causal discovery based on tree search that builds directed acyclic graphs incrementally. We also formalize and prove the correctness of an efficient algorithm for excluding edges that would introduce cycles, which enables deeper discrete search and sampling in DAG space. The proposed method can be applied broadly to causal Bayesian networks with both discrete and continuous random variables. We conduct a comprehensive evaluation on synthetic and real-world datasets, showing that CD-UCT substantially outperforms the state-of-the-art model-free reinforcement learning technique and greedy search, constituting a promising advancement for combinatorial methods.
Table understanding capability of Large Language Models (LLMs) has been extensively studied through the task of question-answering (QA) over tables. Typically, only a small part of the whole table is relevant to derive the answer for a given question. The irrelevant parts act as noise and are distracting information, resulting in sub-optimal performance due to the vulnerability of LLMs to noise. To mitigate this, we propose CABINET (Content RelevAnce-Based NoIse ReductioN for TablE QuesTion-Answering) - a framework to enable LLMs to focus on relevant tabular data by suppressing extraneous information. CABINET comprises an Unsupervised Relevance Scorer (URS), trained differentially with the QA LLM, that weighs the table content based on its relevance to the input question before feeding it to the question-answering LLM (QA LLM). To further aid the relevance scorer, CABINET employs a weakly supervised module that generates a parsing statement describing the criteria of rows and columns relevant to the question and highlights the content of corresponding table cells. CABINET significantly outperforms various tabular LLM baselines, as well as GPT3-based in-context learning methods, is more robust to noise, maintains outperformance on tables of varying sizes, and establishes new SoTA performance on WikiTQ, FeTaQA, and WikiSQL datasets. We release our code and datasets at //github.com/Sohanpatnaik106/CABINET_QA.
This study evaluates the ability of Large Language Model (LLM)-based Subpopulation Representative Models (SRMs) to generalize from empirical data, utilizing in-context learning with data from the 2016 and 2020 American National Election Studies. We explore generalization across response variables and demographic subgroups. While conditioning with empirical data improves performance on the whole, the benefit of in-context learning varies considerably across demographics, sometimes hurting performance for one demographic while helping performance for others. The inequitable benefits of in-context learning for SRM present a challenge for practitioners implementing SRMs, and for decision-makers who might come to rely on them. Our work highlights a need for fine-grained benchmarks captured from diverse subpopulations that test not only fidelity but generalization.
In data analysis, there continues to be a need for interpretable dimensionality reduction methods whereby instrinic meaning associated with the data is retained in the reduced space. Standard approaches such as Principal Component Analysis (PCA) and the Singular Value Decomposition (SVD) fail at this task. A popular alternative is the CUR decomposition. In an SVD-like manner, the CUR decomposition approximates a matrix $A \in \mathbb{R}^{m \times n}$ as $A \approx CUR$, where $C$ and $R$ are matrices whose columns and rows are selected from the original matrix \cite{goreinov1997theory}, \cite{mahoney2009cur}. The difficulty in constructing a CUR decomposition is in determining which columns and rows to select when forming $C$ and $R$. Current column/row selection algorithms, particularly those that rely on an SVD, become infeasible as the size of the data becomes large \cite{dong2021simpler}. We address this problem by reducing the column/row selection problem to a collection of smaller sub-problems. The basic idea is to first partition the rows/columns of a matrix, and then apply an existing selection algorithm on each piece; for illustration purposes we use the Discrete Empirical Interpolation Method (\textsf{DEIM}) \cite{sorensen2016deim}. For the first task, we consider two existing algorithms that construct a Voronoi Tessellation (VT) of the rows and columns of a given matrix. We then extend these methods to automatically adapt to the data. The result is four data-driven row/column selection methods that are well-suited for parallelization, and compatible with nearly any existing column/row selection strategy. Theory and numerical examples show the design to be competitive with the original \textsf{DEIM} routine.
Originally introduced as a neural network for ensemble learning, mixture of experts (MoE) has recently become a fundamental building block of highly successful modern deep neural networks for heterogeneous data analysis in several applications of machine learning and statistics. Despite its popularity in practice, a satisfactory level of theoretical understanding of the MoE model is far from complete. To shed new light on this problem, we provide a convergence analysis for maximum likelihood estimation (MLE) in the Gaussian-gated MoE model. The main challenge of that analysis comes from the inclusion of covariates in the Gaussian gating functions and expert networks, which leads to their intrinsic interaction via some partial differential equations with respect to their parameters. We tackle these issues by designing novel Voronoi loss functions among parameters to accurately capture the heterogeneity of parameter estimation rates. Our findings reveal that the MLE has distinct behaviors under two complement settings of location parameters of the Gaussian gating functions, namely when all these parameters are non-zero versus when at least one among them vanishes. Notably, these behaviors can be characterized by the solvability of two different systems of polynomial equations. Finally, we conduct a simulation study to empirically verify our theoretical results.
A decision tree is one of the most popular approaches in machine learning fields. However, it suffers from the problem of overfitting caused by overly deepened trees. Then, a meta-tree is recently proposed. It solves the problem of overfitting caused by overly deepened trees. Moreover, the meta-tree guarantees statistical optimality based on Bayes decision theory. Therefore, the meta-tree is expected to perform better than the decision tree. In contrast to a single decision tree, it is known that ensembles of decision trees, which are typically constructed boosting algorithms, are more effective in improving predictive performance. Thus, it is expected that ensembles of meta-trees are more effective in improving predictive performance than a single meta-tree, and there are no previous studies that construct multiple meta-trees in boosting. Therefore, in this study, we propose a method to construct multiple meta-trees using a boosting approach. Through experiments with synthetic and benchmark datasets, we conduct a performance comparison between the proposed methods and the conventional methods using ensembles of decision trees. Furthermore, while ensembles of decision trees can cause overfitting as well as a single decision tree, experiments confirmed that ensembles of meta-trees can prevent overfitting due to the tree depth.
This article presents the affordances that Generative Artificial Intelligence can have in disinformation context, one of the major threats to our digitalized society. We present a research framework to generate customized agent-based social networks for disinformation simulations that would enable understanding and evaluation of the phenomena whilst discussing open challenges.
Recently, ensemble has been applied to deep metric learning to yield state-of-the-art results. Deep metric learning aims to learn deep neural networks for feature embeddings, distances of which satisfy given constraint. In deep metric learning, ensemble takes average of distances learned by multiple learners. As one important aspect of ensemble, the learners should be diverse in their feature embeddings. To this end, we propose an attention-based ensemble, which uses multiple attention masks, so that each learner can attend to different parts of the object. We also propose a divergence loss, which encourages diversity among the learners. The proposed method is applied to the standard benchmarks of deep metric learning and experimental results show that it outperforms the state-of-the-art methods by a significant margin on image retrieval tasks.