A method uses neural networks to approximate sampling distributions of test statistics.
problem Accurate modeling of p-value functions or cdfs for correct confidence set coverage.
method Uses neural networks to model the cdf of test statistics, approximating sampling distributions.
result Neural network approximations of sampling distributions are effective and simple.
Develops statistical guarantees for neural networks with regularization.
problem Lack of comprehensive mathematical theories for neural networks.
method General statistical guarantee for least-squares with regularizers.
result Prediction error increases sub-linearly in layers, logarithmically in parameters.
NN-Turb generates turbulent velocity statistics using neural networks.
problem Creating a 1D field with turbulent velocity statistics.
method Fully-convolutional neural network (NN-Turb) to generate the field.
result NN-Turb generates a 1D field that satisfies Kolmogorov's 2/3 and 4/5 laws, exhibiting intermittency.
Study enhances neural network interpretability through statistical methods.
problem Complexity and interpretability challenges in neural networks.
method Theoretical framework, statistical tests, dimensionality reduction algorithms.
result Developed bootstrapping technique and statistical tests for ANN performance.
Approximate Bayesian Computation is widely used in systems biology for inferring parameters in stochastic gene regulatory network models. Its performance hinges critically on the ability to summarize high-dimensional system responses such as time series into a few informative, low-dimensional summary statistics. The qu…
Statistical uncertainty of different filtration techniques for market network analysis is studied. Two measures of statistical uncertainty are discussed. One is based on conditional risk for multiple decision statistical procedures and another one is based on average fraction of errors. It is shown that for some import…
Paper tackles complex risk in deep neural networks.
problem Complex risk in deep neural networks.
method Developed new approach for complex risk statistics.
result Derived dual representation for complex risk.
FNNs can be made more interpretable with statistical methods.
problem FNNs lack interpretability and are often used as black-box models.
method Supplement FNNs with statistical inference and covariate-effect visualizations.
result FNNs can be made more like traditional statistical models.
The paper provides statistical guarantees for sparse deep learning.
problem Understanding the potential and limitations of sparse deep learning.
method Develops statistical guarantees for different types of sparsity in sparse deep learning.
result Statistical guarantees for sparse deep learning with mild dependence on network widths and depths.
Statistical analysis reveals pitfalls in climate network construction.
problem Uncertainty in correlation estimates affects network characteristics.
method Simulated isotropic random fields and resampling procedures.
result Spurious link bundles and high-degree clusters are common.
Networks are ubiquitous in science and have become a focal point for discussion in everyday life. Formal statistical models for the analysis of network data have emerged as a major topic of interest in diverse areas of study, and most of these involve a form of graphical representation. Probability models on graphs dat…
Consider observing an undirected network that is `noisy' in the sense that there are Type I and Type II errors in the observation of edges. Such errors can arise, for example, in the context of inferring gene regulatory networks in genomics or functional connectivity networks in neuroscience. Given a single observed ne…
We consider a two-sample hypothesis testing problem, where the distributions are defined on the space of undirected graphs, and one has access to only one observation from each model. A motivating example for this problem is comparing the friendship networks on Facebook and LinkedIn. The practical approach to such prob…
We develop the necessary theory in computational algebraic geometry to place Bayesian networks into the realm of algebraic statistics. We present an algebra{statistics dictionary focused on statistical modeling. In particular, we link the notion of effiective dimension of a Bayesian network with the notion of algebraic…
Interneurons improve learning in neural networks by accelerating convergence.
problem Rapid adaptation to changing input statistics in neural networks.
method Two mathematically tractable recurrent linear neural networks were compared: one with direct recurrent connections and the other with interneurons that mediate recurrent communication.
result The network with interneurons converges more quickly than the network with direct recurrent connections, scaling logarithmically with initialization spectrum.
We describe convolutional networks using harmonic functions.
problem Understanding the function space and smoothness of convolutional networks.
method Using reproducing kernel Hilbert spaces and functional ANOVA decomposition.
result Convolutional networks can be decomposed into a sum of elementary functions.
A neural network approach unifies Lasso for variable selection.
problem Combining statistical and machine learning techniques for variable selection.
method Representing Lasso through a neural network and developing a new optimization algorithm.
result The new optimization algorithm achieves better performance than previous methods.
Enhanced Markov chain sampler learns network statistics faster.
problem Learning network statistics efficiently.
method Integrates graph Forman curvature into Markov chain transition probabilities and stationary distribution.
result Curved Markov chain Monte Carlo achieves faster convergence.
Lectures on deep learning properties in infinite and large-width networks.
problem Understanding deep neural networks in extreme width conditions.
method Analysis of random deep neural networks, connections to linear models, kernels, and Gaussian processes, perturbative and non-perturbative treatments.
result Properties and behaviors of deep neural networks in the infinite-width limit and large-width regime.
The paper validates a centrality measure for financial networks during financial distress.
problem Systemic risk and shock propagation in financial networks.
method Statistical validation method for network centrality measures.
result The proposed centrality measure increases significantly during financial distress.
Paper presents a WiFi-based indoor sensor localization technique.
problem Indoor localization in wireless sensor networks.
method Zoning-based localization using statistical learning.
result Efficient sensor zone determination in indoor environments.
Paper compares neural networks and classical statistics for dementia prediction, highlighting interpretability of classical methods.
problem Tackles the challenge of interpreting risk factors for dementia prediction.
method Compares neural networks and classical statistics for dementia prediction.
result Classical statistics provide clearer interpretation of risk factors compared to neural networks.
The network jackknife provides conservative variance estimates for network statistics.
problem Estimating the variance of network statistics.
method Leave-node-out jackknife procedure for network data under the sparse graphon model.
result The network jackknife leads to conservative estimates of the variance for network functionals invariant to node permutation.
New method identifies diffusion sources on networks with statistical confidence.
problem Identifying sources of diffusion on networks without restrictive assumptions.
method Statistical framework and confidence set inference approach based on hypothesis testing.
result Efficiently produces a small subset of nodes covering the source node with any confidence level.
Network-assisted regression uses conformal prediction for valid inference.
problem Predicting node attributes using network and conventional covariates with valid statistical inference.
method Network analog of conformal prediction under mild joint exchangeability assumption.
result Achieves finite sample validity and asymptotic conditional validity for various network covariates.
Jan Tinbergen, the first recipient of the Nobel Memorial Prize in Economics in 1969, obtained his PhD in physics at the University of Leiden under the supervision of Paul Ehrenfest in 1929. Among many achievements as an economist after his training as a physicist, Tinbergen proposed the so-called Gravity Model of inter…
Statistical mechanics explains learning in large neural networks near interpolation.
problem Understanding the learning dynamics of large neural networks near interpolation.
method Statistical physics analysis of a two-layer network with generic weight distribution and activation function.
result Learning transitions and feature learning emerge as the number of data increases.
Method measures weight similarity in neural networks using normalization and statistical inference.
problem Quantifying weight similarity in non-convex neural networks.
method Chain normalization rule and hypothesis-training-testing statistical inference.
result Weights of identical neural networks converge to similar local solutions.
Study uses complex networks and machine learning to predict soccer match outcomes.
problem Predicting soccer match outcomes with complex networks and machine learning.
method Complex network metrics and match statistics were used to build machine learning models.
result Models based on passing networks were as effective as traditional models using match statistics.
Proposes a new normalization method using convolutional neural networks.
problem Slow and inefficient training of deep neural networks.
method Uses depth-wise convolutional neural networks to approximate statistics.
result Learned coefficients improve the approximation of statistics.
Flexible framework for deep distributional regression models.
problem Learning conditional distributions from semi-structured data.
method Combines additive regression models with deep networks using TensorFlow.
result State-of-the-art predictive performance with interpretability.
Unified framework for network model assessment using maximum entropy.
problem Statistical inference for network models.
method Constrained entropy-maximization problem, Lagrange multipliers.
result Consistent goodness-of-fit and two-sample tests for network models.
Unified statistical framework for LSTM model selection.
problem Model selection and hyperparameter tuning in LSTM networks is heuristic and computationally expensive.
method Proposes a statistical framework extending classical model selection ideas to LSTM networks.
result Improved performance of the proposed framework demonstrated on biomedical data.
Approximate Bayesian Computation (ABC) methods are used to approximate posterior distributions in models with unknown or computationally intractable likelihoods. Both the accuracy and computational efficiency of ABC depend on the choice of summary statistic, but outside of special cases where the optimal summary statis…
Electric vehicles (EVs) have been gaining popularity due to their environmental friendliness and efficiency. EV charging station networks are scalable solutions for supporting increasing numbers of EVs within modern electric grid constraints, yet few tools exist to aid the physical configuration design of new networks.…
Neural networks help create summary statistics for complex models.
problem Creating summary statistics for models with intractable likelihood functions.
method Infomax learning with neural networks to maximize mutual information.
result Improves performance of approximate Bayesian computation and neural likelihood methods.
GANs improve event generation in physics experiments.
problem Improving statistical precision in event generation.
method Used generative adversarial networks (GANs) to generate events.
result GANs amplify the statistical precision of the training sample.
Paper provides Edgeworth expansions for network moments, improving accuracy of sampling distributions.
problem Accurate descriptions of sampling distributions of network moment statistics.
method Edgeworth expansion applied to studentized network moment statistics.
result Higher-order accurate approximation to sampling CDF of network moment statistics.
Paper proposes a method to prune neural networks, reducing storage and computation costs.
problem Reduction of storage and computational costs for deep neural networks.
method Statistical analysis of component significance using F-statistic-based screening technique.
result Pruned models are highly competitive with state-of-the-art approaches.
Analyzes unsupervised neural networks using statistical mechanics and Monte Carlo simulations.
problem Understanding computational capabilities of unsupervised neural networks.
method Statistical mechanics approach and Monte Carlo simulations.
result Obtained a phase diagram summarizing network performance.
The paper extends hypothesis testing to non-diagonalizable matrices, improving network statistics inference.
problem Testing on non-diagonalizable matrices for network statistics.
method Generalizes Wald and t-tests to non-symmetric matrices, controlling convergence rates.
result Improved inference on network statistics from directed networks.
Paper addresses statistical inference for GANs and minimax problems.
problem Statistical properties of GANs and minimax problems.
method Consistent estimation and confidence sets for GAN parameters.
result Confidence sets for GAN parameters contain the population solutions with desired coverage probability.
A new test statistic counts tree co-occurrences to detect edge correlation between networks.
problem Detecting edge correlation between networks using latent vertex correspondence.
method The test statistic is based on counting co-occurrences of signed trees for a family of non-isomorphic trees.
result The test runs in n2+o(1) time and succeeds with high probability for large n. A test for neural networks identifies genetic associations.
problem Testing complex associations in neural networks.
method Sieve quasi-likelihood ratio test for neural networks with one hidden layer.
result The test statistic has an asymptotic chi-squared distribution.
This work analyzes statistical properties of SAM, showing it outperforms GD.
problem Improving deep neural network generalization through flatter solutions.
method Directly studies statistical performance of Sharpness-Aware Minimization (SAM).
result SAM has smaller prediction error than Gradient Descent (GD) under certain conditions.
Neural networks can learn from higher-order cumulants efficiently, requiring quadratic samples.
problem Learning from higher-order cumulants in high-dimensional data.
method Spiked cumulant model, polynomial time algorithms, neural networks, random features.
result Neural networks require quadratic samples to learn from higher-order cumulants efficiently, while random features require more samples.
Deep learning used for parameter estimation in hard-to-infer models.
problem Parameter estimation in intractable models like max-stable processes.
method Train deep neural networks on simulated data to estimate parameters.
result Deep learning provides accurate and faster parameter estimation.
In a number of disciplines, the data (e.g., graphs, manifolds) to be analyzed are non-Euclidean in nature. Geometric deep learning corresponds to techniques that generalize deep neural network models to such non-Euclidean spaces. Several recent papers have shown how convolutional neural networks (CNNs) can be extended …