A new classifier for high-dimensional data with spiked eigenvalues.
problem Classifying high-dimensional data with spiked eigenvalues.
method Distance-based classifier using data transformation and noise reduction.
result The new classifier performs better than existing methods on simulated and real data.
Study eigenvalues and eigenvectors in neural networks, focusing on signal propagation.
problem Characterize signal eigenvalues and eigenvectors in neural networks.
method Characterizes signal eigenvalues and eigenvectors for a nonlinear spiked covariance model.
result Provides precise quantitative characterizations of signal eigenvalues and eigenvectors in neural networks.
PCA can detect a low-rank signal in spiked random matrix models, but not always optimally.
problem Understanding when PCA can detect a low-rank signal in the presence of noise.
method Le Cam's notion of contiguity, analysis of spiked Wishart ensemble, and non-spectral tests.
result PCA is sub-optimal for detection in non-Gaussian Wigner ensembles and certain negative spikes in Gaussian Wishart ensemble.
This paper analyzes generalization for linear models with spiked covariance structures.
problem Understanding the generalization performance of linear models with spiked covariance structures.
method Derives the generalization error for two simple models with spiked covariances using random matrix theory.
result The eigenvector and eigenvalue corresponding to the spike significantly influence the generalization error.
The paper analyzes the risk of a least squares estimator under a spike covariance model.
problem Risk analysis of the least squares estimator under a spike covariance model.
method Assumes spike covariance matrices, studies risk as d/nightarrow∞. result Risk of the minimum norm least squares estimator vanishes compared to the null estimator.
Improves signal detection in non-Gaussian noise using transformed data.
problem Signal detection in rank-one signal-plus-noise data matrices.
method Pre-transforming matrix entries and using linear spectral statistics for hypothesis testing.
result Sharp phase transition of largest eigenvalues in spiked rectangular matrices.
A central problem of random matrix theory is to understand the eigenvalues of spiked random matrix models, in which a prominent eigenvector is planted into a random matrix. These distributions form natural statistical models for principal component analysis (PCA) problems throughout the sciences. Baik, Ben Arous and Pé…
With the development of high-throughput technologies, principal component analysis (PCA) in the high-dimensional regime is of great interest. Most of the existing theoretical and methodological results for high-dimensional PCA are based on the spiked population model in which all the population eigenvalues are equal ex…
Improves detection of low-rank signals from noisy data matrices.
problem Statistical detection of low-rank signals in noisy data matrices.
method Entrywise pre-transforming data matrix for non-Gaussian noise, sharp phase transition thresholds, central limit theorem for linear spectral statistics, hypothesis test.
result Improves detection of low-rank signals from noisy data matrices, generalizing known results.
Consistent model selection for spiked Wigner model via AIC-type criteria.
problem Estimating the number of spiked eigenvalues in the spiked Wigner model.
method AIC-type model selection criteria with parameters γ.
result Strong consistency for γ > 2 and weak consistency for γ = 2 + δ_N.
New estimator for overlapping community detection in graphs.
problem Reconstructing community relations in graphs with overlapping memberships.
method Proposes a new estimator for Mixed-Membership Stochastic Block Model (MMSB) under diverging spiked eigenvalues condition.
result New estimator matches theoretical minimax lower bound on estimation error.
Develops a monitoring procedure to detect changes in large approximate factor models.
problem Detecting structural changes in large approximate factor models.
method Randomises the test statistic to create a sequence of i.i.d. statistics for monitoring changes.
result Very small probability of false detections and tight detection times of change-points.
Study of eigenvalues in nonlinear kernels for classification of separable data.
problem Understanding the applicability of linear equivalents in nonlinearly separable data classification.
method Analysis of conjugate kernels and their quadratic equivalents for a canonical nonlinearly separable dataset (XOR problem).
result Identification of regimes where nonlinear kernels deviate from linear equivalents, leading to label-aligned eigenspaces.
We study the problem of detecting an abrupt change to the signal covariance matrix. In particular, the covariance changes from a "white" identity matrix to an unknown spiked or low-rank matrix. Two sequential change-point detection procedures are presented, based on the largest and the smallest eigenvalues of the sampl…
Adaptive classifier optimizes high-dimensional data with spiked covariance structure.
problem Classification of high-dimensional data with spiked covariance structure.
method Adaptive classifier that whitens data, screens features, and applies Fisher linear discriminant.
result The classifier is Bayes optimal under certain conditions and performs well on real and synthetic data.
Paper optimizes private PCA for covariance estimation in statistics.
problem Private estimation of covariance matrices and principal components.
method Developed differentially private estimators for spiked covariance model.
result Established minimax rates of convergence for principal components and covariance matrix estimation.
Single-spike neurons can approximate as well as multi-spike neurons.
problem Limitation of single-spike neurons in spiking neural networks.
method Comparison of single-spike and multi-spike neural networks.
result Single-spike and multi-spike neural networks are equivalent in approximation capabilities.
New theory for eigenvectors of generalized Laplacian matrices, addressing dependency issues.
problem Dependency in random matrix theory hinders eigenvector analysis for latent embeddings.
method Introduces generalized Laplacian matrices and a new asymptotic theory framework.
result Established asymptotic normalities for spiked eigenvectors and eigenvalues.
Much of studies on neural computation are based on network models of static neurons that produce analog output, despite the fact that information processing in the brain is predominantly carried out by dynamic neurons that produce discrete pulses called spikes. Research in spike-based computation has been impeded by th…
Paper trains SNNs for classification using first-to-spike decoding.
problem Training SNNs for classification under GLM model.
method Proposes first-to-spike decoding method for SNNs.
result Improves accuracy and efficiency of SNN classification.
The paper examines how spike strengths and alignments affect overfitting in linear regression models.
problem The impact of spike strengths and alignments on overfitting in linear regression models.
method Characterization of generalization error through exact expressions and analysis of spike strengths, aspect ratio, and target alignment.
result Increasing spike strength can lead to catastrophic overfitting before benign overfitting, especially in well-specified aligned problems.
New method improves neural spike train models by minimizing divergence directly, leading to better performance.
problem Poor performance and divergence issues in spike train models using maximum likelihood estimation.
method Directly minimize maximum mean discrepancy using spike train kernels and stochastic optimization.
result The proposed method generates well-behaved models with better control over feature trade-offs.
SNNs enhance high-frequency price spike forecasting in HFT environments.
problem Conventional financial models fail to capture fine temporal structure in high-frequency price spikes.
method Application of Spiking Neural Networks (SNNs) with hyperparameter tuning via Bayesian Optimization (BO).
result SNN models optimized with PSA achieve significantly higher cumulative returns in backtesting.
Neurons perform computations, and convey the results of those computations through the statistical structure of their output spike trains. Here we present a practical method, grounded in the information-theoretic analysis of prediction, for inferring a minimal representation of that structure and for characterizing its…
Bayesian method detects neuron spike activities from noisy fluorescence data.
problem Detecting neuron spike activities from noisy fluorescence data.
method Random finite set (RFS) based Bayesian approach.
result Gains 12% extra detection accuracy compared to MLSpike method.
Accurate statistical models of neural spike responses can characterize the information carried by neural populations. But the limited samples of spike counts during recording usually result in model overfitting. Besides, current models assume spike counts to be Poisson-distributed, which ignores the fact that many neur…
Algorithm detects and estimates correlated signals in spiked matrices.
problem Detect and estimate correlated signals in spiked matrices.
method Proposes an efficient algorithm based on counting edge-decorated cycles.
result Algorithm succeeds under certain signal-to-noise ratio conditions.
Develops generic spike-and-slab priors for high-dimensional linear regression.
problem Bayesian high-dimensional linear regression challenges.
method Proposes a class of generic spike-and-slab priors and a unified framework for theoretical assessment.
result Achieves nearly-optimal posterior contraction rate and model selection consistency under general conditions.
Develops path integral for spiked tensor model dynamics.
problem Dynamics of spiked tensor model with random initial conditions.
method Path integral approach applied to partial differential equations.
result Large-N saddle point equations dominated by melonic diagrams. SEF-M improves spiking neural network classification accuracy by 14%.
problem Improving spiking neural network classification accuracy.
method Meta-neuron based learning algorithm with time-varying weight model.
result Time-varying weight model improves classification accuracy by 14%.
New algorithm speeds up spike sorting for large datasets.
problem Numerical complexity limits processing large scale neuroscience datasets.
method Windowed active set Lasso algorithm for convolutional spike sorting.
result Linear complexity ensures scalability and opens online sorting.
Study on detecting a single spike in high-dimensional data matrices.
problem Detecting a single unknown spike in high-dimensional rectangular data matrices.
method Analysis of likelihood ratio between spiked and null models, using Gaussian fluctuations and Talagrand's interpretation of cavity method.
result Asymptotic Gaussian fluctuations of the likelihood ratio below the BBP threshold, with open maximal parameter region.
Method reconstructs neuron models from spike times efficiently.
problem Reconstructing neuron models from spike times in degenerate populations.
method Combining deep learning with DICs to map spike times to DIC densities and generate degenerate CBM populations.
result Fast and scalable reconstruction of degenerate populations from spike recordings.
Develops a new point process model for detecting neural spike sequences.
problem Detecting sparse sequences of neural spikes in high-dimensional spike trains.
method A point process model that represents sequence occurrences as marked events in continuous time, with learnable time warping parameters.
result Demonstrates improved detection and modeling of neural spike sequences.
Synthesizes images from audio and visual data using spike-based autoencoders.
problem Extracting meaningful information from spatio-temporal data for image synthesis.
method Spike-based autoencoders trained to learn spatio-temporal representations of audio and visual data.
result Synthesized images from audio samples with high fidelity, achieving competitive performance.
This paper investigates the effect of leak in spiking neural networks.
problem Comparative analysis of leaky and non-leaky spiking neuron models.
method Experimental and frequency domain analysis of spiking neural networks.
result Leaky spiking neuron models provide improved robustness and generalization but decrease sparsity of computation.
A spiking neural network model for probabilistic inference of binary Markov random fields.
problem Implementing probabilistic inference in spiking neural networks.
method Designing a spiking recurrent neural network and proving its equivalence to mean-field inference of binary Markov random fields.
result The spiking neural network model can implement inference of arbitrary binary Markov random fields.
SNNs as first-to-spike policies improve energy efficiency in RL control.
problem Reducing energy consumption in RL control systems.
method Policy gradient approach with GLM for spiking neurons.
result Online trained SNNs outperform ANN conversion in energy efficiency and control performance.
A new method improves fitting neural data with spiking network models.
problem Fitting spiking network models to neural activity does not produce realistic data.
method Augment log-likelihood with dissimilarity terms measured by summary statistics and optimized via back-propagation.
result The new method generates more realistic neural activity statistics and improves network connectivity inference.
Paper proposes a new method for Bayesian linear regression using spike-and-slab priors.
problem Identifying predictors with similar relationships in linear regression models.
method Hierarchical Bayesian models with spike-and-slab priors and a Gibbs sampler.
result The proposed method outperforms previous methods in simulations and real data analysis.
This research bridges binary and spiking neural networks for efficient on-chip AI.
problem Reducing compute requirements in machine learning frameworks.
method Training Spiking Neural Networks in extreme quantization regime and utilizing standard training techniques for conversion.
result Training Spiking Neural Networks in extreme quantization regime achieves near full precision accuracies.
This paper suggests a learning-theoretic perspective on how synaptic plasticity benefits global brain functioning. We introduce a model, the selectron, that (i) arises as the fast time constant limit of leaky integrate-and-fire neurons equipped with spiking timing dependent plasticity (STDP) and (ii) is amenable to the…
A new method using negative-shifted gradient descent improves overparameterized linear regression by avoiding structural limitations of negative ridge endpoints.
problem Structural limitations of negative ridge endpoints in overparameterized linear regression.
method Negative-shifted gradient descent, which avoids the pole constraint of negative ridge endpoints.
result The method improves over all admissible endpoints by a polynomial factor in risk under explicit conditions.
SGD recovers multiple signal vectors in noisy tensor PCA.
problem Estimating multiple signal vectors from noisy tensor observations.
method Online stochastic gradient descent (SGD) in high dimensions with detailed analysis of correlations.
result Sequential elimination of correlations allows recovery of all spikes from Np−2 samples. Neurons in cortical circuits exhibit coordinated spiking activity, and can produce correlated synchronous spikes during behavior and cognition. We recently developed a method for estimating the dynamics of correlated ensemble activity by combining a model of simultaneous neuronal interactions (e.g., a spin-glass model)…
Study detects signals in spiked Wigner models using log likelihood ratio.
problem Detecting signals in rank-one spiked Wigner models with non-Gaussian noise.
method Proved asymptotic normality of log likelihood ratio and computed error thresholds.
result Optimal signal-to-noise ratio threshold for reliable detection.
Spiking-YOLO improves object detection with low power and fast convergence.
problem Challenging object detection tasks with spiking neural networks.
method Channel-wise normalization and signed neuron with imbalanced threshold.
result Spiking-YOLO achieves comparable results to Tiny YOLO but with significantly less energy consumption.
Study of spiked matrix models with generative priors.
problem Performance enhancement in signal processing and statistical inference.
method Analysis of spiked matrix models with generative priors, using Bayes-optimal performance and enhanced spectral algorithms.
result Approximate message passing algorithm reaches optimal performance.