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Most traditional classifiers implicitly assume that data samples belong to at least one class among predefined several classes. However, all data patterns may not be known at the time of data collection or a new pattern can be emerging over time. In this paper, a new method is presented for monitoring the change in class distribution and detecting an emerging class. First a statistical significance test is designed which can signal for a change in class distribution. When an alarm for new class generation is set on, retrieval of new class members is performed using density estimation and entropy-based thresholding. Our experimental results demonstrate competent performances of the proposed method.

Because of the large-scale variation, counting in scenes of different densities is an extremely difficult task. In this paper, based on the attention mechanism, we propose a new self-weighted multi-scale fusion network structure named SMFNet to solve the problem of multi-scale changes and can significantly improve the effect of crowd counting in monitoring scene. The proposed SMFNet uses VGG as the backbone network to extract multi-scale features, uses a SMFNet as the neck to fuse multiple-scale features, and uses the atrous spatial pyramid pooling (ASPP) network and ordinary convolution as the head to generate both the attention map and the density map. The attention map highlighting crowd regions in the image contributes to a high-quality density map, and the density map records the crowd distribution. The number of crowd in the image can be obtained by summing the pixel values of the density map. We conduct experiments on three crowd counting datasets and one vehicle counting dataset to show that our proposed SMFNet can improve the state-of-the-art counting methods.

Monte Carlo estimators of sensitivity indices and the marginal density of the price dynamics are derived for the Hobson-Rogers stochastic volatility model. Our approach is based mainly upon the Kolmogorov backward equation by making full use of the Markovian property of the dynamics given the past information. Some numerical examples are presented with a GARCH-like volatility function and its extension to illustrate the effectiveness of our formulae together with a clear exhibition of the skewness and the heavy tails of the price dynamics.

Using compactly supported wavelets, Giné and Nickl [Uniform limit theorems for wavelet density estimators, Ann. Probab.37(4) (2009) 1605–1646] obtain the optimal strong $L^{\infty }(ℝ)$ convergence rates of wavelet estimators for a fixed noise-free density function. They also study the same problem by spline wavelets [Adaptive estimation of a distribution function and its density in sup-norm loss by wavelet and spline projections, Bernoulli16(4) (2010) 1137–1163]. This paper considers the strong $L^p(ℝ)(1\le p\le \infty )$ convergence of wavelet deconvolution density estimators. We first show the strong $L^p$ consistency of our wavelet estimator, when the Fourier transform of the noise density has no zeros. Then strong $L^p$ convergence rates are provided, when the noises are severely and moderately ill-posed. In particular, for moderately ill-posed noises and $p=\infty$, our convergence rate is close to Giné and Nickl’s.

This paper discusses the uniformly strong convergence of multivariate density estimation with moderately ill-posed noise over a bounded set. We provide a convergence rate over Besov spaces by using a compactly supported wavelet. When the model degenerates to one-dimensional noise-free case, the convergence rate coincides with that of Giné and Nickl’s (Ann. Probab., 2009 or Bernoulli, 2010). Our result can also be considered as an extension of Masry’s theorem (Stoch. Process. Appl., 1997) to some extent.

By using biorthogonal wavelets, Reynaud-Bouret, Rivoirard and Tuleau-Malot provide the adaptive and optimal $L^2$-risk estimation for density functions (not necessarily having compact support) in a Besov space $B_{r,q}^s(ℝ)$ [P. Reynaud-Bouret, V. Rivoirard and C. Tuleau-Malot, Adaptive density estimation: A curse of support?, J. Stat. Plan. Inference141(1) (2011) 115–139]. The authors pose an open problem: Can $L^p$-risk ($1\le p<\infty$) estimation be given in their setting? In this paper, we try to solve that problem for $p\in [2,+\infty )$ by using wavelet estimators.

Cuckoo Search (CS) is a recent addition to the field of swarm-based metaheuristics. It has been shown to be an efficient approach for global optimization. Moreover, its application for solving Multi-objective Optimization (MOO) shows very promising results as well. In multi-objective context, a bounded archive is required to store the set of nondominated solutions. But, what is the best archiving strategy to use in order to maintain a bounded set with good characteristics is a critical issue that may lead to a questionable choice. In this work, the behavior of the developed multi-objective CS is studied under several archiving strategies. An extensive experimental study has been conducted using several test problems and two performance metrics related to convergence and diversity. A nonparametric test for statistical analysis is performed. In addition, we used a Multi-Objective Particle Swarm Optimization (MOPSO) for further analysis and comparison. The results revealed that archiving strategies play an important role as they can impact differently on the quality of obtained fronts depending on the problem’s characteristics. Also, this study confirms that the proposed MOCS algorithm is a very promising approach for MOPs compared to the widely used MOPSO.

We consider a density estimation problem with a change-point. The contribution of the paper is theoretical: we develop an adaptive estimator based on wavelet block thresholding and we evaluate these performances via the minimax approach under the 𝕃^p risk with p ≥ 1 over a wide range of function classes: the Besov classes, (with no particular restriction on the parameters π and r). Under this general framework, we prove that it attains near optimal rates of convergence.

This paper focuses on enhancing the mission duration by deploying secondary agents to coordinate with the primary agents to accomplish the mission with a minimal interruption. The interruption considered here is due to limited fuel carrying capability of primary agents. In this study, primary and secondary agents refer to unmanned aerial vehicles (UAVs) and unmanned ground vehicles (UGVs), respectively. Conventionally, UAVs are refueled with the fixed main charging stations which lead to interruption during the ongoing mission. In this work, we propose two-stage density estimation approach for efficiently distributing the swarm of UGVs to act as mobile refueling stations for UAVs. In the first stage, the optimal number of UGVs and their initial placement are computed. In the final stage, the UGVs minimize the average distance for the nearest UAVs to refuel. The performance of the proposed method is compared with the state of the art. The numerical simulation shows a better performance with the distributed UGVs than the state of the art.

This paper focuses on enhancing the mission duration by deploying secondary agents to coordinate with the primary agents to accomplish the mission with a minimal interruption. The interruption considered here is due to limited fuel carrying capability of primary agents. In this study, primary and secondary agents refer to unmanned aerial vehicles (UAVs) and unmanned ground vehicles (UGVs), respectively. Conventionally, UAVs are refueled with the fixed main charging stations which lead to interruption during the ongoing mission. In this work, we propose two-stage density estimation approach for efficiently distributing the swarm of UGVs to act as mobile refueling stations for UAVs. In the first stage, the optimal number of UGVs and their initial placement are computed. In the final stage, the UGVs minimize the average distance for the nearest UAVs to refuel. The performance of the proposed method is compared with the state of the art. The numerical simulation shows a better performance with the distributed UGVs than the state of the art.

L₁ penalties have proven to be an attractive regularization device for nonparametric regression, image reconstruction, and model selection. For function estimation, L₁ penalties, interpreted as roughness of the candidate function measured by their total variation, are known to be capable of capturing sharp changes in the target function while still maintaining a general smoothing objective. We explore the use of penalties based on total variation of the estimated density, its square root, and its logarithm – and their derivatives – in the context of univariate and bivariate density estimation, and compare the results to some other density estimation methods including L₂ penalized likelihood methods. Our objective is to develop a unified approach to total variation penalized density estimation offering methods that are: capable of identifying qualitative features like sharp peaks, extendible to higher dimensions, and computationally tractable. Modern interior point methods for solving convex optimization problems play a critical role in achieving the final objective, as do piecewise linear finite element methods that facilitate the use of sparse linear algebra.

The classification task for a real world application shall include a confidence estimation to handle unseen patterns i.e., patterns which were not considered during the learning stage of a classifier. This is important especially for safety critical applications where the goal is to assign these situations as "unknown" before they can lead to a false classification. Several methods were proposed in the past which were based on choosing a threshold on the estimated class membership probability. In this paper we extend the use of Gaussian mixture model (GMM) to estimate the uncertainty of the estimated class membership probability in terms of confidence interval around the estimated class membership probability. This uncertainty measure takes into account the number of training patterns available in the local neighborhood of a test pattern. Accordingly, the lower bound of the confidence interval or the number of training samples around a test pattern, can be used to detect the unseen patterns. Experimental results on a real-world application are discussed.

This paper introduces a class of density estimators having both of parametric part and nonparametric factor. A plug-in parametric estimator is seen as an initial guess of the true density, and the proposed estimator is built up by adding a nonparametric adjustment factor and the initial estimator. Asymptotic theory is developed, and comparisons with the traditional kernel estimator and a multiplicative estimator are also reported.

We consider the recovery of a curve or surface from noisy data by a nonpara-metric Bayesian method. This entails modelling the surface as a realization of a "prior" stochastic process, and viewing the data as arising by measuring this realization with error. The conditional distribution of the process given the data, given by Bayes' rule and called "posterior", next serves as the basis of all further inference. As a particular example of priors we consider Gaussian processes. A nonparametric Bayesian method can be called successful if the posterior distribution concentrates most of its mass near the surface that produced the data. Unlike in classical "parametric" Bayesian inference the quality of the Bayesian reconstruction turns out to depend on the choice of the prior. For instance, it depends on the fine properties of the sample paths of a Gaussian process prior, with good results obtained only if these match the properties of the true surface. The Bayesian solution to overcome the problem that these fine properties are typically unknown is to put additional priors on hyperparameters. For instance, sample paths of a Gaussian process prior are rescaled by a random amount. This leads to mixture priors, to which Bayes' rule can be applied as before. We show that this leads to minimax precision in several examples: adapting to unknown smoothness or sparsity. We also present abstract results on hierarchical priors.