Binomial N-mixture models have proven very useful in ecology, conservation, and monitoring: they allow estimation and modeling of abundance separately from detection probability using simple counts. ...Recently, doubts about parameter identifiability have been voiced. I conducted a large-scale screening test with 137 bird data sets from 2,037 sites. I found virtually no identifiability problems for Poisson and zero-inflated Poisson (ZIP) binomial N-mixture models, but negative-binomial (NB) models had problems in 25% of all data sets. The corresponding multinomial N-mixture models had no problems. Parameter estimates under Poisson and ZIP binomial and multinomial N-mixture models were extremely similar. Identifiability problems became a little more frequent with smaller sample sizes (267 and 50 sites), but were unaffected by whether the models did or did not include covariates. Hence, binomial N-mixture model parameters with Poisson and ZIP mixtures typically appeared identifiable. In contrast, NB mixtures were often unidentifiable, which is worrying since these were often selected by Akaike’s information criterion. Identifiability of binomial N-mixture models should always be checked. If problems are found, simpler models, integrated models that combine different observation models or the use of external information via informative priors or penalized likelihoods, may help.
Recent work has shown that finite mixture models with <inline-formula> <tex-math notation="LaTeX">m </tex-math></inline-formula> components are identifiable, while making no assumptions on the ...mixture components, so long as one has access to groups of samples of size <inline-formula> <tex-math notation="LaTeX">2m-1 </tex-math></inline-formula> which are known to come from the same mixture component. In this work we generalize that result and show that, if every subset of <inline-formula> <tex-math notation="LaTeX">k </tex-math></inline-formula> mixture components of a mixture model are linearly independent, then that mixture model is identifiable with only <inline-formula> <tex-math notation="LaTeX">(2m-1)/(k-1) </tex-math></inline-formula> samples per group. We further show that this value cannot be improved. We prove an analogous result for a stronger form of identifiability known as "determinedness" along with a corresponding lower bound. This independence assumption almost surely holds if mixture components are chosen randomly from a <inline-formula> <tex-math notation="LaTeX">k </tex-math></inline-formula>-dimensional space. We describe some implications of our results for multinomial mixture models and topic modeling.
Due to the lack of transparent and friendly human-robot interaction (HRI) interface, as well as various uncertainties, it is usually a challenge to remotely manipulate a robot to accomplish a ...complicated task. To improve the teleoperation performance, we propose a new perception mechanism by integrating a novel learning method to operate the robots in the distance. In order to enhance the perception of the teleoperation system, we utilize a surface electromyogram signal to extract the human operator's muscle activation. As a response to the changes in the external environment, as sensed through haptic and visual feedback, a human operator naturally reacts with various muscle activations. By imitating the human behaviors in task execution, not only motion trajectory but also arm stiffness adjusted by muscle activation, it is expected that the robot would be able to carry out the repetitive tasks autonomously or uncertain tasks with improved intelligence. To this end, we develop a robot learning algorithm based on probability statistics under an integrated framework of the hidden semi-Markov model (HSMM) and the Gaussian mixture method. This method is employed to obtain a generative task model based on the robot's trajectory. Then, Gaussian mixture regression based on HSMM is applied to correct the robot trajectory with the reproduced results from the learned task model. The execution procedures consist of a learning phase and a reproduction phase. To guarantee the stability, immersion, and maneuverability of the teleoperation system, a variable gain control method that involves electromyography (EMG) is introduced. Experimental results have demonstrated the effectiveness of the proposed method.
We investigate the landscape of the negative log-likelihood function of Gaussian Mixture Models (GMMs) with a general number of components in the population limit. As the objective function is ...non-convex, there can exist multiple spurious local minima that are not globally optimal, even for well-separated mixture models. Our study reveals that all local minima share a common structure that partially identifies the cluster centers (i.e., means of the Gaussian components) of the true location mixture. Specifically, each local minimum can be represented as a non-overlapping combination of two types of sub-configurations: 1) fitting a single mean estimate to multiple Gaussian components; or 2) fitting multiple estimates to a single true component. These results apply to settings where the true mixture components satisfy a certain separation condition, and are valid even when the number of components is over- or under-specified. We also present a more fine-grained analysis for the setting of one-dimensional GMMs with three components, which provide sharper approximation error bounds with improved dependence on the separation parameter.
In recent years, clustering methods based on deep generative models have received great attention in various unsupervised applications, due to their capabilities for learning promising latent ...embeddings from original data. This article proposes a novel clustering method based on variational autoencoder (VAE) with spherical latent embeddings. The merits of our clustering method can be summarized as follows. First, instead of considering the Gaussian mixture model (GMM) as the prior over latent space as in a variety of existing VAE-based deep clustering methods, the von Mises-Fisher mixture model prior is deployed in our method, leading to spherical latent embeddings that can explicitly control the balance between the capacity of decoder and the utilization of latent embedding in a principled way. Second, a dual VAE structure is leveraged to impose the reconstruction constraint for the latent embedding and its corresponding noise counterpart, which embeds the input data into a hyperspherical latent space for clustering. Third, an augmented loss function is proposed to enhance the robustness of our model, which results in a self-supervised manner through the mutual guidance between the original data and the augmented ones. The effectiveness of the proposed deep generative clustering method is validated through comparisons with state-of-the-art deep clustering methods on benchmark datasets. The source code of the proposed model is available at https://github.com/fwt-team/DSVAE .
We introduce an optimal mass transport framework on the space of Gaussian mixture models. These models are widely used in statistical inference. Specifically, we treat the Gaussian mixture models as ...a submanifold of probability densities equipped with the Wasserstein metric. The topology induced by optimal transport is highly desirable and natural because, in contrast to total variation and other metrics, the Wasserstein metric is weakly continuous (i.e., convergence is equivalent to the convergence of moments). Thus, our approach provides natural ways to compare, interpolate, and average Gaussian mixture models. Moreover, the approach has low computational complexity. Different aspects of the framework are discussed, and examples are presented for illustration purposes.
In previous work on point registration, the input point sets are often represented using Gaussian mixture models and the registration is then addressed through a probabilistic approach, which aims to ...exploit global relationships on the point sets. For non-rigid shapes, however, the local structures among neighboring points are also strong and stable and thus helpful in recovering the point correspondence. In this paper, we formulate point registration as the estimation of a mixture of densities, where local features, such as shape context, are used to assign the membership probabilities of the mixture model. This enables us to preserve both global and local structures during matching. The transformation between the two point sets is specified in a reproducing kernel Hilbert space and a sparse approximation is adopted to achieve a fast implementation. Extensive experiments on both synthesized and real data show the robustness of our approach under various types of distortions, such as deformation, noise, outliers, rotation, and occlusion. It greatly outperforms the state-of-the-art methods, especially when the data is badly degraded.
Clustering is a fundamental problem that frequently arises in many fields, such as pattern recognition, data mining, and machine learning. Although various clustering algorithms have been developed ...in the past, traditional clustering algorithms with shallow structures cannot excavate the interdependence of complex data features in latent space. Recently, deep generative models, such as autoencoder (AE), variational AE (VAE), and generative adversarial network (GAN), have achieved remarkable success in many unsupervised applications thanks to their capabilities for learning promising latent representations from original data. In this work, first we propose a novel clustering approach based on both Wasserstein GAN with gradient penalty (WGAN-GP) and VAE with a Gaussian mixture prior. By combining the WGAN-GP with VAE, the generator of WGAN-GP is formulated by drawing samples from the probabilistic decoder of VAE. Moreover, to provide more robust clustering and generation performance when outliers are encountered in data, a variant of the proposed deep generative model is developed based on a Student's-t mixture prior. The effectiveness of our deep generative models is validated though experiments on both clustering analysis and samples generation. Through the comparison with other state-of-art clustering approaches based on deep generative models, the proposed approach can provide more stable training of the model, improve the accuracy of clustering, and generate realistic samples.
Noise modeling is a fundamental unexplored problem in many event camera applications. The noise modeling methods of conventional cameras are inadequate for capturing the intricate noise patterns ...unique to event cameras. To address this gap, we propose a novel event camera-driven noise modeling approach specifically designed to account for the unique characteristics of event camera data. Given the challenges in generating ground truth data, the proposed method is designed using unsupervised statistical techniques. The proposed noise model is camera-aware, i.e. it allows adaptability to the unique noise patterns of each sensor. It also facilitates asynchronous event processing as applied to downstream computer vision tasks. To validate the proposed noise modeling approach, we conducted extensive experiments in the context of denoising tasks. The results indicate that our noise model accurately represents the noise, leading to state-of-the-art performance across various datasets.
•Noise modeling algorithm in the event camera domain.•Applications include noise simulation, denoising, enhancement etc..•Asynchronous and sparse statistical processing.•Camera aware noise modeling.•Adapts unsupervised techniques.
The evaluation of pilot brain activity is very important for flight safety. This study proposes a Hidden semi-Markov Model with Hierarchical prior to detect brain activity under different flight ...tasks. A dynamic student mixture model is proposed to detect the outlier of emission probability of HSMM. Instantaneous spectrum features are also extracted from EEG signals. Compared with other latent variable models, the proposed model shows excellent performance for the automatic inference of brain cognitive activity of pilots. The results indicate that the consideration of hierarchical model and the emission probability with <inline-formula> <tex-math notation="LaTeX">{t} </tex-math></inline-formula> mixture model improves the recognition performance for Pilots' fatigue cognitive level.
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