The distribution of objective vectors in a Pareto Front Approximation (PFA) is crucial for representing the associated manifold accurately. Distribution Indicators (DIs) assess the distribution of a PFA numerically, utilizing concepts like distance calculation, Biodiversity, Entropy, Potential Energy, or Clustering. Despite the diversity of DIs, their strengths and weaknesses across assessment scenarios are not well-understood. This paper introduces a taxonomy for classifying DIs, followed by a preference analysis of nine DIs, each representing a category in the taxonomy. Experimental results, considering various PFAs under controlled scenarios (loss of coverage, loss of uniformity, pathological distributions), reveal that some DIs can be misleading and need cautious use. Additionally, DIs based on Biodiversity and Potential Energy show promise for PFA evaluation and comparison of Multi-Objective Evolutionary Algorithms.
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Matrix-vector multiplication forms the basis of many iterative solution algorithms and as such is an important algorithm also for hierarchical matrices. However, due to its low computational intensity, its performance is typically limited by the available memory bandwidth. By optimizing the storage representation of the data within such matrices, this limitation can be lifted and the performance increased. This applies not only to hierarchical matrices but for also for other low-rank approximation schemes, e.g. block low-rank matrices.
Failure mode and effects analysis (FMEA) is a systematic approach to identify and analyse potential failures and their effects in a system or process. The FMEA approach, however, requires domain experts to manually analyse the FMEA model to derive risk-reducing actions that should be applied. In this paper, we provide a formal framework to allow for automatic planning and acting in FMEA models. More specifically, we cast the FMEA model into a Markov decision process which can then be solved by existing solvers. We show that the FMEA approach can not only be used to support medical experts during the modelling process but also to automatically derive optimal therapies for the treatment of patients.
Large Language Models (LLMs) have demonstrated unparalleled effectiveness in various NLP tasks, and integrating LLMs with automatic speech recognition (ASR) is becoming a mainstream paradigm. Building upon this momentum, our research delves into an in-depth examination of this paradigm on a large open-source Chinese dataset. Specifically, our research aims to evaluate the impact of various configurations of speech encoders, LLMs, and projector modules in the context of the speech foundation encoder-LLM ASR paradigm. Furthermore, we introduce a three-stage training approach, expressly developed to enhance the model's ability to align auditory and textual information. The implementation of this approach, alongside the strategic integration of ASR components, enabled us to achieve the SOTA performance on the AISHELL-1, Test_Net, and Test_Meeting test sets. Our analysis presents an empirical foundation for future research in LLM-based ASR systems and offers insights into optimizing performance using Chinese datasets. We will publicly release all scripts used for data preparation, training, inference, and scoring, as well as pre-trained models and training logs to promote reproducible research.
For estimating the proportion of false null hypotheses in multiple testing, a family of estimators by Storey (2002) is widely used in the applied and statistical literature, with many methods suggested for selecting the parameter $\lambda$. Inspired by change-point concepts, our new approach to the latter problem first approximates the $p$-value plot with a piecewise linear function with a single change-point and then selects the $p$-value at the change-point location as $\lambda$. Simulations show that our method has among the smallest RMSE across various settings, and we extend it to address the estimation in cases of superuniform $p$-values. We provide asymptotic theory for our estimator, relying on the theory of quantile processes. Additionally, we propose an application in the change-point literature and illustrate it using high-dimensional CNV data.
The development of connected autonomous vehicles (CAVs) facilitates the enhancement of traffic efficiency in complicated scenarios. In unsignalized roundabout scenarios, difficulties remain unsolved in developing an effective and efficient coordination strategy for CAVs. In this paper, we formulate the cooperative autonomous driving problem of CAVs in the roundabout scenario as a constrained optimal control problem, and propose a computationally-efficient parallel optimization framework to generate strategies for CAVs such that the travel efficiency is improved with hard safety guarantees. All constraints involved in the roundabout scenario are addressed appropriately with convex approximation, such that the convexity property of the reformulated optimization problem is exhibited. Then, a parallel optimization algorithm is presented to solve the reformulated optimization problem, where an embodied iterative nearest neighbor search strategy to determine the optimal passing sequence in the roundabout scenario. It is noteworthy that the travel efficiency in the roundabout scenario is enhanced and the computation burden is considerably alleviated with the innovation development. We also examine the proposed method in CARLA simulator and perform thorough comparisons with a rule-based baseline and the commonly used IPOPT optimization solver to demonstrate the effectiveness and efficiency of the proposed approach.
Efficiently capturing consistent and complementary semantic features in a multimodal conversation context is crucial for Multimodal Emotion Recognition in Conversation (MERC). Existing methods mainly use graph structures to model dialogue context semantic dependencies and employ Graph Neural Networks (GNN) to capture multimodal semantic features for emotion recognition. However, these methods are limited by some inherent characteristics of GNN, such as over-smoothing and low-pass filtering, resulting in the inability to learn long-distance consistency information and complementary information efficiently. Since consistency and complementarity information correspond to low-frequency and high-frequency information, respectively, this paper revisits the problem of multimodal emotion recognition in conversation from the perspective of the graph spectrum. Specifically, we propose a Graph-Spectrum-based Multimodal Consistency and Complementary collaborative learning framework GS-MCC. First, GS-MCC uses a sliding window to construct a multimodal interaction graph to model conversational relationships and uses efficient Fourier graph operators to extract long-distance high-frequency and low-frequency information, respectively. Then, GS-MCC uses contrastive learning to construct self-supervised signals that reflect complementarity and consistent semantic collaboration with high and low-frequency signals, thereby improving the ability of high and low-frequency information to reflect real emotions. Finally, GS-MCC inputs the collaborative high and low-frequency information into the MLP network and softmax function for emotion prediction. Extensive experiments have proven the superiority of the GS-MCC architecture proposed in this paper on two benchmark data sets.
The stability of the Ghurye-Olkin (GO) characterization of Gaussian vectors is analyzed using a partition of the vectors into equivalence classes defined by their matrix factors. The sum of the vectors in each class is near-Gaussian in the characteristic function (c.f.) domain if the GO independence condition is approximately met in the c.f. domain. All vectors have the property that any vector projection is near-Gaussian in the distribution function (d.f.) domain. The proofs of these c.f. and d.f. stabilities use tools that establish the stabilities of theorems by Kac-Bernstein and Cram\'er, respectively. The results are used to prove stability theorems for differential entropies of Gaussian vectors and blind source separation of non-Gaussian sources.
Out-of-distribution (OOD) detection is essential in autonomous driving, to determine when learning-based components encounter unexpected inputs. Traditional detectors typically use encoder models with fixed settings, thus lacking effective human interaction capabilities. With the rise of large foundation models, multimodal inputs offer the possibility of taking human language as a latent representation, thus enabling language-defined OOD detection. In this paper, we use the cosine similarity of image and text representations encoded by the multimodal model CLIP as a new representation to improve the transparency and controllability of latent encodings used for visual anomaly detection. We compare our approach with existing pre-trained encoders that can only produce latent representations that are meaningless from the user's standpoint. Our experiments on realistic driving data show that the language-based latent representation performs better than the traditional representation of the vision encoder and helps improve the detection performance when combined with standard representations.
Quantum parameter estimation theory is an important component of quantum information theory and provides the statistical foundation that underpins important topics such as quantum system identification and quantum waveform estimation. When there is more than one parameter the ultimate precision in the mean square error given by the quantum Cram\'er-Rao bound is not necessarily achievable. For non-full rank quantum states, it was not known when this bound can be saturated (achieved) when only a single copy of the quantum state encoding the unknown parameters is available. This single-copy scenario is important because of its experimental/practical tractability. Recently, necessary and sufficient conditions for saturability of the quantum Cram\'er-Rao bound in the multiparameter single-copy scenario have been established in terms of i) the commutativity of a set of projected symmetric logarithmic derivatives and ii) the existence of a unitary solution to a system of coupled nonlinear partial differential equations. New sufficient conditions were also obtained that only depend on properties of the symmetric logarithmic derivatives. In this paper, key structural properties of optimal measurements that saturate the quantum Cram\'er-Rao bound are illuminated. These properties are exploited to i) show that the sufficient conditions are in fact necessary and sufficient for an optimal measurement to be projective, ii) give an alternative proof of previously established necessary conditions, and iii) describe general POVMs, not necessarily projective, that saturate the multiparameter QCRB. Examples are given where a unitary solution to the system of nonlinear partial differential equations can be explicitly calculated when the required conditions are fulfilled.
We present a flexible, deterministic numerical method for computing left-tail rare events of sums of non-negative, independent random variables. The method is based on iterative numerical integration of linear convolutions by means of Newtons-Cotes rules. The periodicity properties of convoluted densities combined with the Trapezoidal rule are exploited to produce a robust and efficient method, and the method is flexible in the sense that it can be applied to all kinds of non-negative continuous RVs. We present an error analysis and study the benefits of utilizing Newton-Cotes rules versus the fast Fourier transform (FFT) for numerical integration, showing that although there can be efficiency-benefits to using FFT, Newton-Cotes rules tend to preserve the relative error better, and indeed do so at an acceptable computational cost. Numerical studies on problems with both known and unknown rare-event probabilities showcase the method's performance and support our theoretical findings.
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