NCC is inefficient in higher dimensions, NCDA improves performance.
problem Inefficiency of NCC in higher dimensions.
method Combining NCC with LDA to create NCDA.
result NCDA outperforms NCC and competes with LDA and QDA.
On-device research index
arXiv research
A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
169,181 papers · 148 categories
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48 results for “cavity analysis”
Cavity Filling: Pseudo-Feature Generation for Multi-Class Imbalanced Data Problems in Deep Learningcs.LG
Method generates pseudo-features to balance imbalanced data.
problem Imbalanced data in deep learning problems.
method Generate pseudo-features from feature maps, augment minor-class data.
result Improves deep learning performance in imbalanced data problems.
Paper introduces a framework for diagnosing Alzheimer's disease using higher-order topological features from fMRI.
problem Diagnosing Alzheimer's disease using brain network topology.
method Persistent homology to extract higher-order features (cycles, cavities) from fMRI data.
result Framework significantly outperforms existing methods in AD classification.
Recently, it was shown that there is a phase transition in the community detection problem. This transition was first computed using the cavity method, and has been proved rigorously in the case of groups. However, analytic calculations using the cavity method are challenging since they require us to understand p…
New method uses cohomology to quantify molecular similarity.
problem Quantifying structural dissimilarity in molecular data.
method Gromov-Hausdorff ultrametric based on simplicial complexes and cohomology.
result Demonstrates effectiveness in clustering organic-inorganic halide perovskite structures.
Statistical physics method analyzes minority game dynamics in financial markets.
problem Analyzing arbitrage dynamics in financial markets with noise.
method Cavity method from statistical physics for linear and time-dependent responses.
result Noise reduces arbitrage, and market dynamics exhibit non-Markovian behavior.
The paper uses belief propagation to analyze rankings and partial orders from partial information.
problem Analyzing rankings and partial orders from incomplete data.
method Continuous spin system and belief propagation algorithm.
result Computes marginal distribution and approximates number of linear extensions.
Sparse Representations, Inference and Learningcond-mat.stat-mech
Statistical physics helps solve complex machine learning problems.
problem Large dimensional inference problems in machine learning.
method Replica symmetric level analysis and cavity methods.
result General framework for solving various problems with weak long-range interactions.
Predicts coherence from quantum heat engine noise using machine learning.
problem Predicting coherence in quantum heat engines from nonequilibrium fluctuations.
method Developed a machine learning protocol using K-Nearest Neighbor (KNN) model.
result Machine learning successfully predicts coherence from quantum heat engine noise.
AI detects oral pre-cancerous lesions with high accuracy.
problem Manual screening of oral cavity cancer is expensive and lacks specialists.
method Deep convolutional neural networks (DCNNs) using transfer learning.
result DCNN models achieve high accuracy in distinguishing between benign and pre-cancerous tongue lesions.
Federated Generalised Variational Inference: A Robust Probabilistic Federated Learning Frameworkcs.LG
FedGVI improves FL robustness to model misspecification.
problem Limited robustness in FL approaches to model misspecification.
method Probabilistic Federated Learning framework that generalizes previous methods.
result FedGVI provides robust and calibrated predictions under model misspecification.
Exponential neural networks store many patterns, mapping cues to targets.
problem Storing many patterns in a neural network efficiently and accurately.
method Introduced an exponential neural network with multiple layers, each storing a dataset.
result The network can store an exponential number of patterns, and it generalizes well to unseen data.
Study on limits of detecting a rank-one perturbation in Wigner matrices.
problem Detecting an additive rank-one perturbation in Wigner matrices.
method Gaussian interpolation methods and rigorous incarnation of the cavity method.
result Established the maximal region of contiguity between planted and null models, marking a phase transition for both estimation and detection.
Belief Propagation outperforms other algorithms in reconstructing binary symmetric channel trees.
problem Reconstructing binary symmetric channel trees with bounded memory.
method Combining recursive reconstruction, information theory, and optimal transport.
result Any recursive algorithm with bounded memory for the reconstruction problem on binary symmetric channel trees has a phase transition strictly below the Belief Propagation threshold.
State Space Expectation Propagation: Efficient Inference Schemes for Temporal Gaussian Processesstat.ML
Unified framework for efficient Gaussian process inference.
problem Efficient inference in non-conjugate Gaussian process models.
method Combines expectation propagation with linearization for improved efficiency.
result Unified view of various inference schemes, including classical smoothers and EP.
Topological comparison of some dimension reduction methods using persistent homology on EEG datamath.GT
Paper compares dimension reduction methods using topological analysis on EEG data.
problem Comparing dimension reduction methods on EEG data.
method Topological data analysis, including persistent homology, Wasserstein distance, and hypothesis tests.
result Different dimension reduction methods show significant qualitative differences across topological homologies.
We analyse the matrix factorization problem. Given a noisy measurement of a product of two matrices, the problem is to estimate back the original matrices. It arises in many applications such as dictionary learning, blind matrix calibration, sparse principal component analysis, blind source separation, low rank matrix …
ResNets converge to a limit model with improved error rates.
problem Understanding convergence of ResNets in the large-scale limit.
method Combining cavity method and propagation of chaos arguments on skeleton maps.
result Convergence rate of O(1/sqrt(D)) for ResNets in the large-scale limit.
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.
Study investigates learning performance in inverse Ising problems with sparse teacher couplings.
problem Learning performance in inverse Ising problems with sparse teacher couplings.
method Pseudolikelihood maximization method, replica and cavity methods from statistical mechanics.
result Perfect inference of teacher's couplings is possible in the thermodynamic limit for certain conditions.
A discrete diffusion model learns denoising, scoring, and bridging in different coordinates.
problem Understanding what a discrete diffusion model learns in different coordinate systems.
method Rigorous derivation of continuous-time Markov chain ELBO, Oracle Distance theorem, and exact coordinates for optimizer.
result The negative ELBO is exactly equal to the data entropy plus the path KL from the oracle reverse process to the learned one.
This paper introduces a method for efficiently inferring a high-dimensional distributed quantity from a few observations. The quantity of interest (QoI) is approximated in a basis (dictionary) learned from a training set. The coefficients associated with the approximation of the QoI in the basis are determined by minim…
Sharp thresholds and contiguity for community detection in contextual SBM.
problem Community detection in graphs with high-dimensional node-covariates.
method Contextual Stochastic Block Model, non-rigorous cavity method, information theory.
result Established the sharp threshold for detection and weak recovery in the contextual SBM.
This paper details the techniques and algorithms implemented in Kahler, a Python library that implements discrete exterior calculus on arbitrary Hermitian manifolds. Borrowing techniques and ideas first implemented in PyDEC, Kahler provides a uniquely general framework for computation using discrete exterior calculus. …
Belief Propagation (BP) is one of the most popular methods for inference in probabilistic graphical models. BP is guaranteed to return the correct answer for tree structures, but can be incorrect or non-convergent for loopy graphical models. Recently, several new approximate inference algorithms based on cavity distrib…
Phase transitions and optimal algorithms for semi-supervised classifications on graphs: from belief propagation to graph convolution networkcond-mat.stat-mech
Optimal algorithms identified for semi-supervised classification on graphs.
problem Clustering and classification on graphs with relational and feature information.
method Bayesian inference and belief propagation, extended to graph convolution neural networks.
result Identification of a phase transition and asymptotically optimal algorithms.
The future predictive performance of a Bayesian model can be estimated using Bayesian cross-validation. In this article, we consider Gaussian latent variable models where the integration over the latent values is approximated using the Laplace method or expectation propagation (EP). We study the properties of several B…
Recent experimental advances in neuroscience have opened new vistas into the immense complexity of neuronal networks. This proliferation of data challenges us on two parallel fronts. First, how can we form adequate theoretical frameworks for understanding how dynamical network processes cooperate across widely disparat…
Method designs lightweight, structurally robust shell objects.
problem Designing lightweight, structurally robust shell objects under external forces.
method Shape parametrization based on Laplace's equation for smooth, intersection-free boundaries; gradient-free optimization algorithm.
result Practical solution to structural design of hollow objects with single inner cavity.
Enhanced quantum synchronization achieved using quantum machine learning.
problem Quantum synchronization between two systems with different loss/decoherence mechanisms.
method Digital-analog decomposition of the master equation, quantum machine learning protocol with projective measurements and reinitialization.
result Quantum machine learning protocol enhances synchronization even with different loss/decoherence mechanisms.
Using methods of statistical physics, we analyse the error of learning couplings in large Ising models from independent data (the inverse Ising problem). We concentrate on learning based on local cost functions, such as the pseudo-likelihood method for which the couplings are inferred independently for each spin. Assum…
Predicting labels of nodes in a network, such as community memberships or demographic variables, is an important problem with applications in social and biological networks. A recently-discovered phase transition puts fundamental limits on the accuracy of these predictions if we have access only to the network topology…
Disordered Dynamics in High Dimensions: Connections to Random Matrices and Machine Learningcond-mat.dis-nn
Overview of high-dimensional dynamical systems and their applications to machine learning.
problem Characterizing behavior of high-dimensional dynamical systems driven by random matrices.
method Cavity method arguments, path integrals, dynamical mean field theory (DMFT), and random matrix resolvents.
result Connections between random matrix resolvents and DMFT response, and non-monotonic loss curves in training.
Enzyme sequences and structures are routinely used in the biological sciences as queries to search for functionally related enzymes in online databases. To this end, one usually departs from some notion of similarity, comparing two enzymes by looking for correspondences in their sequences, structures or surfaces. For a…
New method identifies network structure without regularization for sparse teacher couplings.
problem Identifying network structure in inverse Ising problems with model mismatch.
method Ridge linear regression with two-stage estimator.
result Perfect identification of network structure possible without regularization for sparse teacher couplings.
Develops panoramic gastroscopy for automatic polyp detection.
problem Missed diagnosis of gastric polyps during endoscopy.
method Panoramic reconstruction method and end-to-end multi-object detection.
result Average error of panorama less than 2 mm, polyp detection accuracy 95%, recall rate 99%.
The study examines knot probabilities in confined lattice polygons.
problem Determining the relative knotting probabilities in confined lattice knots.
method Used Monte Carlo algorithms to enumerate conformations of lattice knots in a confined volume.
result Relative knotting probabilities are small, with the model dominated by unknots.
Ensemble-based Topological Entropy Calculation (E-tec)physics.comp-ph
E-tec calculates topological entropy of chaotic systems using an ensemble of trajectories.
problem Quantifying the complexity of chaotic dynamics in two-dimensional systems.
method E-tec uses an ensemble of trajectories and a rubber band to estimate topological entropy.
result E-tec provides a computationally efficient method to estimate topological entropy.
Deep adaptive sampling improves surrogate modeling for complex systems.
problem Statistical errors in random sampling for high-dimensional problems.
method DAS^2 method, using deep generative models to refine training sets.
result Reduces statistical errors in approximating solutions for low-regularity problems.
Semi-supervised learning classifies cardiac pathology using motion features from cine MRI.
problem Classifying cardiac pathology based on motion features from cine MRI.
method Semi-supervised learning of apparent flow to generate motion features from non-segmented images.
result The model achieves 95% classification accuracy on ACDC test set.
Analyzes bias-variance in overparameterized linear models using random features.
problem Understanding bias-variance trade-off in overparameterized models.
method Zero-temperature cavity method and random matrix theory.
result Three phase transitions in the linear random features model.
We consider a random sparse graph with bounded average degree, in which a subset of vertices has higher connectivity than the background. In particular, the average degree inside this subset of vertices is larger than outside (but still bounded). Given a realization of such graph, we aim at identifying the hidden subse…
A benchmark evaluates ioUS-to-MR synthesis methods for brain tumor surgery.
problem Difficult interpretation of ioUS images for brain tumor surgery.
method Six generators trained under four inference regimes and two targets on public data.
result SynDiff-2.5D best preserved downstream segmentation (U_Dice=0.55).
Physics-informed neural networks improve surrogate modeling of turbulent Rayleigh-Bénard convection.
problem Modeling turbulent Rayleigh-Bénard convection with high accuracy and efficiency.
method Physics-informed neural networks (PINNs) with novel padding and regularization techniques.
result Significantly improved predictive accuracy of surrogate models at high Rayleigh numbers Ra = 2 × 10^9.
Efficient private matrix analysis algorithms for recent variants.
problem Private analysis of recent matrix updates.
method Identifying sufficient conditions on positive semidefinite matrices.
result First efficient differentially private algorithms for various matrix analysis tasks.
Lecture notes on analysis tools for X-ray tomography.
problem Understanding X-ray tomography using mathematical analysis.
method Overview of analysis tools and ideas, minimal assumptions.
result Broad overview of analysis tools for X-ray tomography.
The paper explores machine learning in mobile big data analysis.
problem Challenges in mobile big data analysis.
method Discussion and review of existing methods.
result Identification of main challenges and future directions.
Accounting statement analysis at industry level. A gentle introduction to the compositional approachq-fin.ST
This paper introduces compositional data analysis for financial ratios, improving industry-level analysis.
problem Statistical issues with standard financial ratios at industry level.
method Compositional data analysis techniques for financial ratios.
result Improved analysis of financial ratios using compositional data methods.