Measures of association between cortical regions based on activity signals provide useful information for studying brain functional connectivity. Difficulties occur with signals of electric neuronal activity, where an observed signal is a mixture, i.e. an instantaneous weighted average of the true, unobserved signals from all regions, due to volume conduction and low spatial resolution. This is why measures of lagged association are of interest, since at least theoretically, "lagged association" is of physiological origin. In contrast, the actual physiological instantaneous zero-lag association is masked and confounded by the mixing artifact. A minimum requirement for a measure of lagged association is that it must not tend to zero with an increase of strength of true instantaneous physiological association. Such biased measures cannot tell apart if a change in its value is due to a change in lagged or a change in instantaneous association. An explicit testable definition for frequency domain lagged connectivity between two multivariate time series is proposed. It is endowed with two important properties: it is invariant to non-singular linear transformations of each vector time series separately, and it is invariant to instantaneous association. As a first sanity check: in the case of two univariate time series, the new definition leads back to the bivariate lagged coherence of 2007 (eqs 25 and 26 in //doi.org/10.48550/arXiv.0706.1776). As a second stronger sanity check: in the case of a univariate and multivariate vector time series, the new measure presented here leads back to the original multivariate lagged coherence in equation 31 of the same 2007 publication (which trivially includes the bivariate case).
相關內容
Based on interactions between individuals and others and references to social norms, this study reveals the impact of heterogeneity in time preference on wealth distribution and inequality. We present a novel approach that connects the interactions between microeconomic agents that generate heterogeneity to the dynamic equations for capital and consumption in macroeconomic models. Using this approach, we estimate the impact of changes in the discount rate due to microeconomic interactions on capital, consumption and utility and the degree of inequality. The results show that intercomparisons with others regarding consumption significantly affect capital, i.e. wealth inequality. Furthermore, the impact on utility is never small and social norms can reduce this impact. Our supporting evidence shows that the quantitative results of inequality calculations correspond to survey data from cohort and cross-cultural studies. This study's micro-macro connection approach can be deployed to connect microeconomic interactions, such as exchange, interest and debt, redistribution, mutual aid and time preference, to dynamic macroeconomic models.
Inner products of neural network feature maps arises in a wide variety of machine learning frameworks as a method of modeling relations between inputs. This work studies the approximation properties of inner products of neural networks. It is shown that the inner product of a multi-layer perceptron with itself is a universal approximator for symmetric positive-definite relation functions. In the case of asymmetric relation functions, it is shown that the inner product of two different multi-layer perceptrons is a universal approximator. In both cases, a bound is obtained on the number of neurons required to achieve a given accuracy of approximation. In the symmetric case, the function class can be identified with kernels of reproducing kernel Hilbert spaces, whereas in the asymmetric case the function class can be identified with kernels of reproducing kernel Banach spaces. Finally, these approximation results are applied to analyzing the attention mechanism underlying Transformers, showing that any retrieval mechanism defined by an abstract preorder can be approximated by attention through its inner product relations. This result uses the Debreu representation theorem in economics to represent preference relations in terms of utility functions.
We present an information-theoretic lower bound for the problem of parameter estimation with time-uniform coverage guarantees. Via a new a reduction to sequential testing, we obtain stronger lower bounds that capture the hardness of the time-uniform setting. In the case of location model estimation, logistic regression, and exponential family models, our $\Omega(\sqrt{n^{-1}\log \log n})$ lower bound is sharp to within constant factors in typical settings.
We study the problem of training diffusion models to sample from a distribution with a given unnormalized density or energy function. We benchmark several diffusion-structured inference methods, including simulation-based variational approaches and off-policy methods (continuous generative flow networks). Our results shed light on the relative advantages of existing algorithms while bringing into question some claims from past work. We also propose a novel exploration strategy for off-policy methods, based on local search in the target space with the use of a replay buffer, and show that it improves the quality of samples on a variety of target distributions. Our code for the sampling methods and benchmarks studied is made public at //github.com/GFNOrg/gfn-diffusion as a base for future work on diffusion models for amortized inference.
We adopt the integral definition of the fractional Laplace operator and study an optimal control problem on Lipschitz domains that involves a fractional elliptic partial differential equation (PDE) as state equation and a control variable that enters the state equation as a coefficient; pointwise constraints on the control variable are considered as well. We establish the existence of optimal solutions and analyze first and, necessary and sufficient, second order optimality conditions. Regularity estimates for optimal variables are also analyzed. We develop two finite element discretization strategies: a semidiscrete scheme in which the control variable is not discretized, and a fully discrete scheme in which the control variable is discretized with piecewise constant functions. For both schemes, we analyze the convergence properties of discretizations and derive error estimates.
In 2012 Chen and Singer introduced the notion of discrete residues for rational functions as a complete obstruction to rational summability. More explicitly, for a given rational function f(x), there exists a rational function g(x) such that f(x) = g(x+1) - g(x) if and only if every discrete residue of f(x) is zero. Discrete residues have many important further applications beyond summability: to creative telescoping problems, thence to the determination of (differential-)algebraic relations among hypergeometric sequences, and subsequently to the computation of (differential) Galois groups of difference equations. However, the discrete residues of a rational function are defined in terms of its complete partial fraction decomposition, which makes their direct computation impractical due to the high complexity of completely factoring arbitrary denominator polynomials into linear factors. We develop a factorization-free algorithm to compute discrete residues of rational functions, relying only on gcd computations and linear algebra.
In this study, we explore data assimilation for the Stochastic Camassa-Holm equation through the application of the particle filtering framework. Specifically, our approach integrates adaptive tempering, jittering, and nudging techniques to construct an advanced particle filtering system. All filtering processes are executed utilizing ensemble parallelism. We conduct extensive numerical experiments across various scenarios of the Stochastic Camassa-Holm model with transport noise and viscosity to examine the impact of different filtering procedures on the performance of the data assimilation process. Our analysis focuses on how observational data and the data assimilation step influence the accuracy and uncertainty of the obtained results.
We introduce a novel continual learning method based on multifidelity deep neural networks. This method learns the correlation between the output of previously trained models and the desired output of the model on the current training dataset, limiting catastrophic forgetting. On its own the multifidelity continual learning method shows robust results that limit forgetting across several datasets. Additionally, we show that the multifidelity method can be combined with existing continual learning methods, including replay and memory aware synapses, to further limit catastrophic forgetting. The proposed continual learning method is especially suited for physical problems where the data satisfy the same physical laws on each domain, or for physics-informed neural networks, because in these cases we expect there to be a strong correlation between the output of the previous model and the model on the current training domain.
We derive information-theoretic generalization bounds for supervised learning algorithms based on the information contained in predictions rather than in the output of the training algorithm. These bounds improve over the existing information-theoretic bounds, are applicable to a wider range of algorithms, and solve two key challenges: (a) they give meaningful results for deterministic algorithms and (b) they are significantly easier to estimate. We show experimentally that the proposed bounds closely follow the generalization gap in practical scenarios for deep learning.
Artificial neural networks thrive in solving the classification problem for a particular rigid task, acquiring knowledge through generalized learning behaviour from a distinct training phase. The resulting network resembles a static entity of knowledge, with endeavours to extend this knowledge without targeting the original task resulting in a catastrophic forgetting. Continual learning shifts this paradigm towards networks that can continually accumulate knowledge over different tasks without the need to retrain from scratch. We focus on task incremental classification, where tasks arrive sequentially and are delineated by clear boundaries. Our main contributions concern 1) a taxonomy and extensive overview of the state-of-the-art, 2) a novel framework to continually determine the stability-plasticity trade-off of the continual learner, 3) a comprehensive experimental comparison of 11 state-of-the-art continual learning methods and 4 baselines. We empirically scrutinize method strengths and weaknesses on three benchmarks, considering Tiny Imagenet and large-scale unbalanced iNaturalist and a sequence of recognition datasets. We study the influence of model capacity, weight decay and dropout regularization, and the order in which the tasks are presented, and qualitatively compare methods in terms of required memory, computation time, and storage.
注冊地址： 北京市海淀區羊坊店路18號2幢3層301-191