Considering the case where the response variable is a categorical variable and the predictor is a random function, two novel functional sufficient dimensional reduction (FSDR) methods are proposed based on mutual information and square loss mutual information. Compared to the classical FSDR methods, such as functional sliced inverse regression and functional sliced average variance estimation, the proposed methods are appealing because they are capable of estimating multiple effective dimension reduction directions in the case of a relatively small number of categories, especially for the binary response. Moreover, the proposed methods do not require the restrictive linear conditional mean assumption and the constant covariance assumption. They avoid the inverse problem of the covariance operator which is often encountered in the functional sufficient dimension reduction. The functional principal component analysis with truncation be used as a regularization mechanism. Under some mild conditions, the statistical consistency of the proposed methods is established. It is demonstrated that the two methods are competitive compared with some existing FSDR methods by simulations and real data analyses.
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We are interested in creating statistical methods to provide informative summaries of random fields through the geometry of their excursion sets. To this end, we introduce an estimator for the length of the perimeter of excursion sets of random fields on $\mathbb{R}^2$ observed over regular square tilings. The proposed estimator acts on the empirically accessible binary digital images of the excursion regions and computes the length of a piecewise linear approximation of the excursion boundary. The estimator is shown to be consistent as the pixel size decreases, without the need of any normalization constant, and with neither assumption of Gaussianity nor isotropy imposed on the underlying random field. In this general framework, even when the domain grows to cover $\mathbb{R}^2$, the estimation error is shown to be of smaller order than the side length of the domain. For affine, strongly mixing random fields, this translates to a multivariate Central Limit Theorem for our estimator when multiple levels are considered simultaneously. Finally, we conduct several numerical studies to investigate statistical properties of the proposed estimator in the finite-sample data setting.
This study proposes a self-learning algorithm for closed-loop cylinder wake control targeting lower drag and lower lift fluctuations with the additional challenge of sparse sensor information, taking deep reinforcement learning as the starting point. DRL performance is significantly improved by lifting the sensor signals to dynamic features (DF), which predict future flow states. The resulting dynamic feature-based DRL (DF-DRL) automatically learns a feedback control in the plant without a dynamic model. Results show that the drag coefficient of the DF-DRL model is 25% less than the vanilla model based on direct sensor feedback. More importantly, using only one surface pressure sensor, DF-DRL can reduce the drag coefficient to a state-of-the-art performance of about 8% at Re = 100 and significantly mitigate lift coefficient fluctuations. Hence, DF-DRL allows the deployment of sparse sensing of the flow without degrading the control performance. This method also shows good robustness in controlling flow under higher Reynolds numbers, which reduces the drag coefficient by 32.2% and 46.55% at Re = 500 and 1000, respectively, indicating the broad applicability of the method. Since surface pressure information is more straightforward to measure in realistic scenarios than flow velocity information, this study provides a valuable reference for experimentally designing the active flow control of a circular cylinder based on wall pressure signals, which is an essential step toward further developing intelligent control in realistic multi-input multi-output (MIMO) system.
This paper studies the efficient estimation of a large class of treatment effect parameters that arise in the analysis of experiments. Here, efficiency is understood to be with respect to a broad class of treatment assignment schemes for which the marginal probability that any unit is assigned to treatment equals a pre-specified value, e.g., one half. Importantly, we do not require that treatment status is assigned in an i.i.d. fashion, thereby accommodating complicated treatment assignment schemes that are used in practice, such as stratified block randomization and matched pairs. The class of parameters considered are those that can be expressed as the solution to a restriction on the expectation of a known function of the observed data, including possibly the pre-specified value for the marginal probability of treatment assignment. We show that this class of parameters includes, among other things, average treatment effects, quantile treatment effects, local average treatment effects as well as the counterparts to these quantities in experiments in which the unit is itself a cluster. In this setting, we establish two results. First, we derive a lower bound on the asymptotic variance of estimators of the parameter of interest in the form of a convolution theorem. Second, we show that the n\"aive method of moments estimator achieves this bound on the asymptotic variance quite generally if treatment is assigned using a "finely stratified" design. By a "finely stratified" design, we mean experiments in which units are divided into groups of a fixed size and a proportion within each group is assigned to treatment uniformly at random so that it respects the restriction on the marginal probability of treatment assignment. In this sense, "finely stratified" experiments lead to efficient estimators of treatment effect parameters "by design" rather than through ex post covariate adjustment.
Counterfactual examples have emerged as an effective approach to produce simple and understandable post-hoc explanations. In the context of graph classification, previous work has focused on generating counterfactual explanations by manipulating the most elementary units of a graph, i.e., removing an existing edge, or adding a non-existing one. In this paper, we claim that such language of explanation might be too fine-grained, and turn our attention to some of the main characterizing features of real-world complex networks, such as the tendency to close triangles, the existence of recurring motifs, and the organization into dense modules. We thus define a general density-based counterfactual search framework to generate instance-level counterfactual explanations for graph classifiers, which can be instantiated with different notions of dense substructures. In particular, we show two specific instantiations of this general framework: a method that searches for counterfactual graphs by opening or closing triangles, and a method driven by maximal cliques. We also discuss how the general method can be instantiated to exploit any other notion of dense substructures, including, for instance, a given taxonomy of nodes. We evaluate the effectiveness of our approaches in 7 brain network datasets and compare the counterfactual statements generated according to several widely-used metrics. Results confirm that adopting a semantic-relevant unit of change like density is essential to define versatile and interpretable counterfactual explanation methods.
An Electroencephalogram (EEG) is a non-invasive exam that records the electrical activity of the brain. This exam is used to help diagnose conditions such as different brain problems. EEG signals are taken for the purpose of epilepsy detection and with Discrete Wavelet Transform (DWT) and machine learning classifier, they perform epilepsy detection. In Epilepsy seizure detection, mainly machine learning classifiers and statistical features are used. The hidden information in the EEG signal is useful for detecting diseases affecting the brain. Sometimes it is very difficult to identify the minimum changes in the EEG in the time and frequency domains purpose. The DWT can give a good decomposition of the signals in different frequency bands and feature extraction. We use the tri-dimensionality reduction algorithm.; Principal Component Analysis (PCA), Independent Component Analysis (ICA), and Linear Discriminant Analysis (LDA). Finally, features are selected by using a fusion rule and at the last step three different classifiers Support Vector Machine (SVM), Naive Bayes (NB) and K-Nearest-Neighbor(KNN) have been used individually for the classification. The proposed framework is tested on the Bonn dataset and the simulation results provide the accuracy for the combination of LDA and SVM 89.17%, LDA and KNN 80.42%, PCA and NB 89.92%, PCA and SVM 85.58%, PCA and KNN 80.42%, ICA and NB 82.33%, ICA and SVM 90.42%, and ICA and KNN 90%, LDA and NB 100%, accuracy. It shows the sensitivity, specificity, accuracy, Precision, and Recall of 100%, 100%, 100%, 100%, and 100%. This combination of LDA with NB method provides the accuracy of 100% outperforming all existing methods. The results prove the effectiveness of this model.
This work proposes a wavelet shrinkage rule under asymmetric LINEX loss function and a mixture of a point mass function at zero and the logistic distribution as prior distribution to the wavelet coefficients in a nonparametric regression model with gaussian error. Underestimation of a significant wavelet coefficient can lead to a bad detection of features of the unknown function such as peaks, discontinuities and oscillations. It can also occur under asymmetrically distributed wavelet coefficients. Thus the proposed rule is suitable when overestimation and underestimation have asymmetric losses. Statistical properties of the rule such as squared bias, variance, frequentist and bayesian risks are obtained. Simulation studies are conducted to evaluate the performance of the rule against standard methods and an application in a real dataset involving infrared spectra is provided.
Recent advances in event camera research emphasize processing data in its original sparse form, which allows the use of its unique features such as high temporal resolution, high dynamic range, low latency, and resistance to image blur. One promising approach for analyzing event data is through graph convolutional networks (GCNs). However, current research in this domain primarily focuses on optimizing computational costs, neglecting the associated memory costs. In this paper, we consider both factors together in order to achieve satisfying results and relatively low model complexity. For this purpose, we performed a comparative analysis of different graph convolution operations, considering factors such as execution time, the number of trainable model parameters, data format requirements, and training outcomes. Our results show a 450-fold reduction in the number of parameters for the feature extraction module and a 4.5-fold reduction in the size of the data representation while maintaining a classification accuracy of 52.3%, which is 6.3% higher compared to the operation used in state-of-the-art approaches. To further evaluate performance, we implemented the object detection architecture and evaluated its performance on the N-Caltech101 dataset. The results showed an accuracy of 53.7 % [email protected] and reached an execution rate of 82 graphs per second.
Classic machine learning methods are built on the $i.i.d.$ assumption that training and testing data are independent and identically distributed. However, in real scenarios, the $i.i.d.$ assumption can hardly be satisfied, rendering the sharp drop of classic machine learning algorithms' performances under distributional shifts, which indicates the significance of investigating the Out-of-Distribution generalization problem. Out-of-Distribution (OOD) generalization problem addresses the challenging setting where the testing distribution is unknown and different from the training. This paper serves as the first effort to systematically and comprehensively discuss the OOD generalization problem, from the definition, methodology, evaluation to the implications and future directions. Firstly, we provide the formal definition of the OOD generalization problem. Secondly, existing methods are categorized into three parts based on their positions in the whole learning pipeline, namely unsupervised representation learning, supervised model learning and optimization, and typical methods for each category are discussed in detail. We then demonstrate the theoretical connections of different categories, and introduce the commonly used datasets and evaluation metrics. Finally, we summarize the whole literature and raise some future directions for OOD generalization problem. The summary of OOD generalization methods reviewed in this survey can be found at //out-of-distribution-generalization.com.
Recent contrastive representation learning methods rely on estimating mutual information (MI) between multiple views of an underlying context. E.g., we can derive multiple views of a given image by applying data augmentation, or we can split a sequence into views comprising the past and future of some step in the sequence. Contrastive lower bounds on MI are easy to optimize, but have a strong underestimation bias when estimating large amounts of MI. We propose decomposing the full MI estimation problem into a sum of smaller estimation problems by splitting one of the views into progressively more informed subviews and by applying the chain rule on MI between the decomposed views. This expression contains a sum of unconditional and conditional MI terms, each measuring modest chunks of the total MI, which facilitates approximation via contrastive bounds. To maximize the sum, we formulate a contrastive lower bound on the conditional MI which can be approximated efficiently. We refer to our general approach as Decomposed Estimation of Mutual Information (DEMI). We show that DEMI can capture a larger amount of MI than standard non-decomposed contrastive bounds in a synthetic setting, and learns better representations in a vision domain and for dialogue generation.
Graph classification aims to perform accurate information extraction and classification over graphstructured data. In the past few years, Graph Neural Networks (GNNs) have achieved satisfactory performance on graph classification tasks. However, most GNNs based methods focus on designing graph convolutional operations and graph pooling operations, overlooking that collecting or labeling graph-structured data is more difficult than grid-based data. We utilize meta-learning for fewshot graph classification to alleviate the scarce of labeled graph samples when training new tasks.More specifically, to boost the learning of graph classification tasks, we leverage GNNs as graph embedding backbone and meta-learning as training paradigm to capture task-specific knowledge rapidly in graph classification tasks and transfer them to new tasks. To enhance the robustness of meta-learner, we designed a novel step controller driven by Reinforcement Learning. The experiments demonstrate that our framework works well compared to baselines.
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