The purpose of this paper is twofold. First, we propose a novel algorithm for estimating parameters in one-dimensional Gaussian mixture models (GMMs). The algorithm takes advantage of the Hankel structure inherent in the Fourier data obtained from independent and identically distributed (i.i.d) samples of the mixture. For GMMs with a unified variance, a singular value ratio functional using the Fourier data is introduced and used to resolve the variance and component number simultaneously. The consistency of the estimator is derived. Compared to classic algorithms such as the method of moments and the maximum likelihood method, the proposed algorithm does not require prior knowledge of the number of Gaussian components or good initial guesses. Numerical experiments demonstrate its superior performance in estimation accuracy and computational cost. Second, we reveal that there exists a fundamental limit to the problem of estimating the number of Gaussian components or model order in the mixture model if the number of i.i.d samples is finite. For the case of a single variance, we show that the model order can be successfully estimated only if the minimum separation distance between the component means exceeds a certain threshold value and can fail if below. We derive a lower bound for this threshold value, referred to as the computational resolution limit, in terms of the number of i.i.d samples, the variance, and the number of Gaussian components. Numerical experiments confirm this phase transition phenomenon in estimating the model order. Moreover, we demonstrate that our algorithm achieves better scores in likelihood, AIC, and BIC when compared to the EM algorithm.
相關內容
Superlatives are used to single out elements with a maximal/minimal property. Semantically, superlatives perform a set comparison: something (or some things) has the min/max property out of a set. As such, superlatives provide an ideal phenomenon for studying implicit phenomena and discourse restrictions. While this comparison set is often not explicitly defined, its (implicit) restrictions can be inferred from the discourse context the expression appears in. In this work we provide an extensive computational study on the semantics of superlatives. We propose a unified account of superlative semantics which allows us to derive a broad-coverage annotation schema. Using this unified schema we annotated a multi-domain dataset of superlatives and their semantic interpretations. We specifically focus on interpreting implicit or ambiguous superlative expressions, by analyzing how the discourse context restricts the set of interpretations. In a set of experiments we then analyze how well models perform at variations of predicting superlative semantics, with and without context. We show that the fine-grained semantics of superlatives in context can be challenging for contemporary models, including GPT-4.
In this paper, we propose a novel data augmentation technique called GenMix, which combines generative and mixture approaches to leverage the strengths of both methods. While generative models excel at creating new data patterns, they face challenges such as mode collapse in GANs and difficulties in training diffusion models, especially with limited medical imaging data. On the other hand, mixture models enhance class boundary regions but tend to favor the major class in scenarios with class imbalance. To address these limitations, GenMix integrates both approaches to complement each other. GenMix operates in two stages: (1) training a generative model to produce synthetic images, and (2) performing mixup between synthetic and real data. This process improves the quality and diversity of synthetic data while simultaneously benefiting from the new pattern learning of generative models and the boundary enhancement of mixture models. We validate the effectiveness of our method on the task of classifying focal liver lesions (FLLs) in CT images. Our results demonstrate that GenMix enhances the performance of various generative models, including DCGAN, StyleGAN, Textual Inversion, and Diffusion Models. Notably, the proposed method with Textual Inversion outperforms other methods without fine-tuning diffusion model on the FLL dataset.
In this paper, we introduce Partial Information Decomposition of Features (PIDF), a new paradigm for simultaneous data interpretability and feature selection. Contrary to traditional methods that assign a single importance value, our approach is based on three metrics per feature: the mutual information shared with the target variable, the feature's contribution to synergistic information, and the amount of this information that is redundant. In particular, we develop a novel procedure based on these three metrics, which reveals not only how features are correlated with the target but also the additional and overlapping information provided by considering them in combination with other features. We extensively evaluate PIDF using both synthetic and real-world data, demonstrating its potential applications and effectiveness, by considering case studies from genetics and neuroscience.
This paper introduces a novel formulation of the clustering problem, namely the Minimum Sum-of-Squares Clustering of Infinitely Tall Data (MSSC-ITD), and presents HPClust, an innovative set of hybrid parallel approaches for its effective solution. By utilizing modern high-performance computing techniques, HPClust enhances key clustering metrics: effectiveness, computational efficiency, and scalability. In contrast to vanilla data parallelism, which only accelerates processing time through the MapReduce framework, our approach unlocks superior performance by leveraging the multi-strategy competitive-cooperative parallelism and intricate properties of the objective function landscape. Unlike other available algorithms that struggle to scale, our algorithm is inherently parallel in nature, improving solution quality through increased scalability and parallelism, and outperforming even advanced algorithms designed for small and medium-sized datasets. Our evaluation of HPClust, featuring four parallel strategies, demonstrates its superiority over traditional and cutting-edge methods by offering better performance in the key metrics. These results also show that parallel processing not only enhances the clustering efficiency, but the accuracy as well. Additionally, we explore the balance between computational efficiency and clustering quality, providing insights into optimal parallel strategies based on dataset specifics and resource availability. This research advances our understanding of parallelism in clustering algorithms, demonstrating that a judicious hybridization of advanced parallel approaches yields optimal results for MSSC-ITD. Experiments on synthetic data further confirm HPClust's exceptional scalability and robustness to noise.
In this paper, we propose a novel approach to Bayesian experimental design for non-exchangeable data that formulates it as risk-sensitive policy optimization. We develop the Inside-Out SMC$^2$ algorithm, a nested sequential Monte Carlo technique to infer optimal designs, and embed it into a particle Markov chain Monte Carlo framework to perform gradient-based policy amortization. Our approach is distinct from other amortized experimental design techniques, as it does not rely on contrastive estimators. Numerical validation on a set of dynamical systems showcases the efficacy of our method in comparison to other state-of-the-art strategies.
In this paper, we propose a continuous-time lidar-inertial odometry (CT-LIO) system named SLICT2, which promotes two main insights. One, contrary to conventional wisdom, CT-LIO algorithm can be optimized by linear solvers in only a few iterations, which is more efficient than commonly used nonlinear solvers. Two, CT-LIO benefits more from the correct association than the number of iterations. Based on these ideas, we implement our method with a customized solver where the feature association process is performed immediately after each incremental step, and the solution can converge within a few iterations. Our implementation can achieve real-time performance with a high density of control points while yielding competitive performance in highly dynamical motion scenarios. We demonstrate the advantages of our method by comparing with other existing state-of-the-art CT-LIO methods. The source code will be released for the benefit of the community.
In this paper, we introduce a novel discriminative loss function with large margin in the context of Deep Learning. This loss boosts the discriminative power of neural nets, represented by intra-class compactness and inter-class separability. On the one hand, the class compactness is ensured by close distance of samples of the same class to each other. On the other hand, the inter-class separability is boosted by a margin loss that ensures the minimum distance of each class to its closest boundary. All the terms in our loss have an explicit meaning, giving a direct view of the feature space obtained. We analyze mathematically the relation between compactness and margin term, giving a guideline about the impact of the hyper-parameters on the learned features. Moreover, we also analyze properties of the gradient of the loss with respect to the parameters of the neural net. Based on this, we design a strategy called partial momentum updating that enjoys simultaneously stability and consistency in training. Furthermore, we also investigate generalization errors to have better theoretical insights. Our loss function systematically boosts the test accuracy of models compared to the standard softmax loss in our experiments.
In this paper, we propose a novel Feature Decomposition and Reconstruction Learning (FDRL) method for effective facial expression recognition. We view the expression information as the combination of the shared information (expression similarities) across different expressions and the unique information (expression-specific variations) for each expression. More specifically, FDRL mainly consists of two crucial networks: a Feature Decomposition Network (FDN) and a Feature Reconstruction Network (FRN). In particular, FDN first decomposes the basic features extracted from a backbone network into a set of facial action-aware latent features to model expression similarities. Then, FRN captures the intra-feature and inter-feature relationships for latent features to characterize expression-specific variations, and reconstructs the expression feature. To this end, two modules including an intra-feature relation modeling module and an inter-feature relation modeling module are developed in FRN. Experimental results on both the in-the-lab databases (including CK+, MMI, and Oulu-CASIA) and the in-the-wild databases (including RAF-DB and SFEW) show that the proposed FDRL method consistently achieves higher recognition accuracy than several state-of-the-art methods. This clearly highlights the benefit of feature decomposition and reconstruction for classifying expressions.
In this paper, we proposed to apply meta learning approach for low-resource automatic speech recognition (ASR). We formulated ASR for different languages as different tasks, and meta-learned the initialization parameters from many pretraining languages to achieve fast adaptation on unseen target language, via recently proposed model-agnostic meta learning algorithm (MAML). We evaluated the proposed approach using six languages as pretraining tasks and four languages as target tasks. Preliminary results showed that the proposed method, MetaASR, significantly outperforms the state-of-the-art multitask pretraining approach on all target languages with different combinations of pretraining languages. In addition, since MAML's model-agnostic property, this paper also opens new research direction of applying meta learning to more speech-related applications.
In this paper, we propose a conceptually simple and geometrically interpretable objective function, i.e. additive margin Softmax (AM-Softmax), for deep face verification. In general, the face verification task can be viewed as a metric learning problem, so learning large-margin face features whose intra-class variation is small and inter-class difference is large is of great importance in order to achieve good performance. Recently, Large-margin Softmax and Angular Softmax have been proposed to incorporate the angular margin in a multiplicative manner. In this work, we introduce a novel additive angular margin for the Softmax loss, which is intuitively appealing and more interpretable than the existing works. We also emphasize and discuss the importance of feature normalization in the paper. Most importantly, our experiments on LFW BLUFR and MegaFace show that our additive margin softmax loss consistently performs better than the current state-of-the-art methods using the same network architecture and training dataset. Our code has also been made available at //github.com/happynear/AMSoftmax
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