Plenty of artifact removal tools and pipelines have been developed to correct the EEG recordings and discover the values below the waveforms. Without visual inspection from the experts, it is susceptible to derive improper preprocessing states, like the insufficient preprocessed EEG (IPE), and the excessive preprocessed EEG (EPE). However, little is known about the impacts of IPE or EPE on the postprocessing in the frequency, spatial and temporal domains, particularly as to the spectra and the functional connectivity (FC) analysis. Here, the clean EEG (CE) was synthesized as the ground truth based on the New-York head model and the multivariate autoregressive model. Later, the IPE and the EPE were simulated by injecting the Gaussian noise and losing the brain activities, respectively. Then, the impacts on postprocessing were quantified by the deviation caused by the IPE or EPE from the CE as to the 4 temporal statistics, the multichannel power, the cross spectra, the dispersion of source imaging, and the properties of scalp EEG network. Lastly, the association analysis was performed between the PaLOSi metric and the varying trends of postprocessing with the evolution of preprocessing states. This study shed light on how the postprocessing outcomes are affected by the preprocessing states and PaLOSi may be a potential effective quality metric.
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Differential privacy is often studied under two different models of neighboring datasets: the add-remove model and the swap model. While the swap model is used extensively in the academic literature, many practical libraries use the more conservative add-remove model. However, analysis under the add-remove model can be cumbersome, and obtaining results with tight constants requires some additional work. Here, we study the problem of one-dimensional mean estimation under the add-remove model of differential privacy. We propose a new algorithm and show that it is min-max optimal, that it has the correct constant in the leading term of the mean squared error, and that this constant is the same as the optimal algorithm in the swap model. Our results show that, for mean estimation, the add-remove and swap model give nearly identical error even though the add-remove model cannot treat the size of the dataset as public information. In addition, we demonstrate empirically that our proposed algorithm yields a factor of two improvement in mean squared error over algorithms often used in practice.
Pre-trained Language Models (PLMs) have shown to be consistently successful in a plethora of NLP tasks due to their ability to learn contextualized representations of words (Ethayarajh, 2019). BERT (Devlin et al., 2018), ELMo (Peters et al., 2018) and other PLMs encode word meaning via textual context, as opposed to static word embeddings, which encode all meanings of a word in a single vector representation. In this work, we present a study that aims to localize where exactly in a PLM word contextualization happens. In order to find the location of this word meaning transformation, we investigate representations of polysemous words in the basic BERT uncased 12 layer architecture (Devlin et al., 2018), a masked language model trained on an additional sentence adjacency objective, using qualitative and quantitative measures.
Differential expression (DE) plays a fundamental role toward illuminating the molecular mechanisms driving a difference between groups (e.g., due to treatment or disease). While any analysis is run on particular cells/samples, the intent is to generalize to future occurrences of the treatment or disease. Implicitly, this step is justified by assuming that present and future samples are independent and identically distributed from the same population. Though this assumption is always false, we hope that any deviation from the assumption is small enough that A) conclusions of the analysis still hold and B) standard tools like standard error, significance, and power still reflect generalizability. Conversely, we might worry about these deviations, and reliance on standard tools, if conclusions could be substantively changed by dropping a very small fraction of data. While checking every small fraction is computationally intractable, recent work develops an approximation to identify when such an influential subset exists. Building on this work, we develop a metric for dropping-data robustness of DE; namely, we cast the analysis in a form suitable to the approximation, extend the approximation to models with data-dependent hyperparameters, and extend the notion of a data point from a single cell to a pseudobulk observation. We then overcome the inherent non-differentiability of gene set enrichment analysis to develop an additional approximation for the robustness of top gene sets. We assess robustness of DE for published single-cell RNA-seq data and discover that 1000s of genes can have their results flipped by dropping <1% of the data, including 100s that are sensitive to dropping a single cell (0.07%). Surprisingly, this non-robustness extends to high-level takeaways; half of the top 10 gene sets can be changed by dropping 1-2% of cells, and 2/10 can be changed by dropping a single cell.
This paper is concerned with the numerical approximation of initial-boundary-value problems of a three-parameter family of Bona-Smith systems, derived as a model for the propagation of surface waves under a physical Boussinesq regime. The work proposed here is focused on the corresponding problem with Dirichlet boundary conditions and its approximation in space with spectral methods based on Jacobi polynomials, which are defined from the orthogonality with respect to some weighted $L^{2}$ inner product. Well-posedness of the problem on the corresponding weighted Sobolev spaces is first analyzed and existence and uniqueness of solution, locally in time, are proved. Then the spectral Galerkin semidiscrete scheme and some detailed comments on its implementation are introduced. The existence of numerical solution and error estimates on those weighted Sobolev spaces are established. Finally, the choice of the time integrator to complete the full discretization takes care of different stability issues that may be relevant when approximating the semidiscrete system. Some numerical experiments illustrate the results.
The expressivity of Graph Neural Networks (GNNs) can be entirely characterized by appropriate fragments of the first-order logic. Namely, any query of the two variable fragment of graded modal logic (GC2) interpreted over labeled graphs can be expressed using a GNN whose size depends only on the depth of the query. As pointed out by [Barcelo & Al., 2020, Grohe, 2021], this description holds for a family of activation functions, leaving the possibility for a hierarchy of logics expressible by GNNs depending on the chosen activation function. In this article, we show that such hierarchy indeed exists by proving that GC2 queries cannot be expressed by GNNs with polynomial activation functions. This implies a separation between polynomial and popular non-polynomial activations (such as Rectified Linear Units) and answers an open question formulated by [Grohe, 2021].
The success of Bayesian persuasion relies on the key assumption that the sender will commit to a predetermined information disclosure policy (signaling scheme). However, in practice, it is usually difficult for the receiver to monitor whether the sender sticks to the disclosure policy, which makes the credibility of the sender's disclosure policy questionable. The sender's credibility is particularly tenuous when there are obvious deviations that benefit the sender. In this work, we identify such a deviation: the sender may be unwilling to send a signal that will lead to a less desirable outcome compared to no information disclosure. We thus propose the notion of ex-post individually rational (ex-post IR) Bayesian persuasion: after observing the state, the sender is never required to send a signal that will make the outcome worse off (compared to no information disclosure). An ex-post IR Bayesian persuasion policy is more likely to be truthfully followed by the sender, and thus more credible for the receiver. Our contribution is threefold. Firstly, we demonstrate that the optimal ex-post IR Bayesian persuasion policy can be efficiently computed through a linear program, while also offering geometric characterizations of this optimal policy. Second, we show that surprisingly, for non-trivial classes of games, the imposition of ex-post IR constraints does not affect the sender's expected utility. Finally, we compare ex-post IR Bayesian persuasion to other information disclosure models that ensure different notions of credibility.
We introduce the new setting of open-vocabulary object 6D pose estimation, in which a textual prompt is used to specify the object of interest. In contrast to existing approaches, in our setting (i) the object of interest is specified solely through the textual prompt, (ii) no object model (e.g. CAD or video sequence) is required at inference, (iii) the object is imaged from two different viewpoints of two different scenes, and (iv) the object was not observed during the training phase. To operate in this setting, we introduce a novel approach that leverages a Vision-Language Model to segment the object of interest from two distinct scenes and to estimate its relative 6D pose. The key of our approach is a carefully devised strategy to fuse object-level information provided by the prompt with local image features, resulting in a feature space that can generalize to novel concepts. We validate our approach on a new benchmark based on two popular datasets, REAL275 and Toyota-Light, which collectively encompass 39 object instances appearing in four thousand image pairs. The results demonstrate that our approach outperforms both a well-established hand-crafted method and a recent deep learning-based baseline in estimating the relative 6D pose of objects in different scenes. Project page: //jcorsetti.github.io/oryon/.
Current approaches to generic segmentation start by creating a hierarchy of nested image partitions and then specifying a segmentation from it. Our first contribution is to describe several ways, most of them new, for specifying segmentations using the hierarchy elements. Then, we consider the best hierarchy-induced segmentation specified by a limited number of hierarchy elements. We focus on a common quality measure for binary segmentations, the Jaccard index (also known as IoU). Optimizing the Jaccard index is highly non-trivial, and yet we propose an efficient approach for doing exactly that. This way we get algorithm-independent upper bounds on the quality of any segmentation created from the hierarchy. We found that the obtainable segmentation quality varies significantly depending on the way that the segments are specified by the hierarchy elements, and that representing a segmentation with only a few hierarchy elements is often possible. (Code is available).
This paper develops a general methodology to conduct statistical inference for observations indexed by multiple sets of entities. We propose a novel multiway empirical likelihood statistic that converges to a chi-square distribution under the non-degenerate case, where corresponding Hoeffding type decomposition is dominated by linear terms. Our methodology is related to the notion of jackknife empirical likelihood but the leave-out pseudo values are constructed by leaving columns or rows. We further develop a modified version of our multiway empirical likelihood statistic, which converges to a chi-square distribution regardless of the degeneracy, and discover its desirable higher-order property compared to the t-ratio by the conventional Eicker-White type variance estimator. The proposed methodology is illustrated by several important statistical problems, such as bipartite network, generalized estimating equations, and three-way observations.
Compared with cheap addition operation, multiplication operation is of much higher computation complexity. The widely-used convolutions in deep neural networks are exactly cross-correlation to measure the similarity between input feature and convolution filters, which involves massive multiplications between float values. In this paper, we present adder networks (AdderNets) to trade these massive multiplications in deep neural networks, especially convolutional neural networks (CNNs), for much cheaper additions to reduce computation costs. In AdderNets, we take the $\ell_1$-norm distance between filters and input feature as the output response. The influence of this new similarity measure on the optimization of neural network have been thoroughly analyzed. To achieve a better performance, we develop a special back-propagation approach for AdderNets by investigating the full-precision gradient. We then propose an adaptive learning rate strategy to enhance the training procedure of AdderNets according to the magnitude of each neuron's gradient. As a result, the proposed AdderNets can achieve 74.9% Top-1 accuracy 91.7% Top-5 accuracy using ResNet-50 on the ImageNet dataset without any multiplication in convolution layer.
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