Modeling language as a matrix product state with probability measures.
problem Understanding the structure of natural language.
method Statistical model using complex matrices and matrix product states.
result Language can be represented as a translation invariant matrix product state.
RMCSE improves voltage estimation in low-observability distribution systems.
problem Insufficient measurements in distribution system state estimation.
method Combines matrix completion and power system model, minimizes rank and residual with different weights.
result Robust voltage estimation in low-observability systems without bad data detection.
Sketch Tomography improves quantum state estimation accuracy.
problem Efficiently estimating quantum states, especially MPS states.
method Hybridizes classical shadow protocol with tensor train ansatz.
result Proven convergence with quadratic sample complexity.
A new method for state estimation in state-space models using incomplete data.
problem State estimation in nonlinear state-space models with incomplete observations.
method Statistical analysis of incomplete observations, score function, observed information matrices, EM-gradient-particle filtering.
result Maximum likelihood estimation of state-vector with explicit form of observed information matrix.
Paper introduces OMD for ordered state transitions in SSMs.
problem Modeling ordered latent states in dynamic systems.
method Ordered Matrix Dirichlet (OMD) prior over ordered stochastic matrices.
result OMD models recover interpretable ordered latent structure without sacrificing predictive performance.
New method improves matrix completion with functional maps.
problem Matrix completion with geometric structure.
method Functional map regularization for geometric matrix completion.
result Significant performance improvement over state-of-the-art methods.
The paper explores states of financial markets using correlation matrices and their dynamics.
problem Understanding the states of financial markets based on correlations.
method Revisits previous work and introduces recent developments in practical applications.
result Analysis of trajectories and symbolic dynamics in correlation matrix space.
Two tricks reduce LSTM complexity and speed up training.
problem Training large LSTM networks is computationally expensive.
method Matrix factorization and partitioning of LSTM components.
result Significantly faster training with fewer parameters.
A new method for matrix completion identifies low-rank submatrices.
problem Matrix completion for non-low-rank matrices.
method Targeted framework: extract low-rank submatrices, complete separately.
result Significantly smaller reconstruction errors than classical methods.
Paper introduces MPS for efficient tensor compression and classification.
problem Efficiently compressing and classifying higher-order tensors.
method Matrix Product State (MPS) using successive SVD.
result MPS achieves better classification performance with lower computation cost.
A new model SMPS alleviates the exponential decay of correlations in MPS.
problem Exponential decay of correlations in Matrix Product States (MPS) limits their power in capturing long-range dependences.
method Introducing long-range interactions (shortcuts) to MPS to decrease correlation length while preserving computational efficiency.
result SMPS can decrease significantly the correlation length of MPS, improving its ability to capture long-range dependences.
New proof for knot state-sum formula using bijection between states.
problem Proving a knot state-sum formula for colored Jones polynomial.
method Established bijection between states on arc-graph and bichromatic digraph, used flow property of R-matrix.
result Two state models are essentially the same, extending formula to links.
Efficiently learns sparse low-dimensional Markov chain representations.
problem Learning low-dimensional representations for large-scale Markov chains with sparse structures.
method Formulates as constrained nonnegative matrix factorization and uses gradient descent.
result Proves the effectiveness of the proposed method through convergence analysis.
NIMFA is a Python library for nonnegative matrix factorization.
problem Efficiently factorizing nonnegative matrices for various applications.
method Unified interface, state-of-the-art methods, initialization approaches, quality scoring, supports dense and sparse matrices.
result Unified and efficient implementation of nonnegative matrix factorization methods.
Improved MMWU algorithm achieves instance-optimal regret bound for matrix LEA.
problem Matrix Learning from Expert Advice problem.
method Developed a general potential-based framework for matrix LEA, using a new Jensen's trace inequality.
result Achieved instance-optimal regret bound of O ( T ⋅ S ( X ∣ ∣ d − 1 I d ) ) O(\sqrt{T\cdot S(X||d^{-1}I_d)}) O ( T ⋅ S ( X ∣∣ d − 1 I d ) ) . Researchers developed an algorithm to count all graph mosaics.
problem Defining and counting graph mosaics to represent graph diagrams.
method Using a recursion formula of state matrices and sixteen graph mosaic tiles.
result Produced the exact enumeration of all graph mosaics.
New algorithms improve transduction accuracy with low-rank data matrices.
problem Improving transduction accuracy with low-rank data matrices.
method Proposes two new algorithms using Smoothed Rank Function for transduction with Matrix Completion.
result Proposed methods outperform state-of-the-art methods in accuracy, especially in low observation rates.
Method forecasts market states using sparse precision matrix and penalized Mahalanobis distance.
problem Forecasting market states and distinguishing bull and bear markets.
method Identifies market states via sparse precision matrix and expectation values. Uses penalized Mahalanobis distance for clustering and forecasting.
result Successfully clusters market states and forecasts future market conditions with significant accuracy.
Quantum-inspired model generates samples from data efficiently.
problem Unsupervised generative modeling from data.
method Matrix product states for efficient learning and direct sampling.
result Efficient direct sampling approach for generative tasks.
AMP algorithm for matrix tensor product model provides recovery conditions.
problem Generalization of standard spiked matrix models with multiple pairwise observations.
method Approximate message passing with optimal weighing and combining of estimates.
result Asymptotically exact performance description and necessary/sufficient recovery conditions.
Solves steering problem with continuous time, Hilbert-Schmidt cost, and matrix ODEs.
problem Fixed horizon linear quadratic covariance steering in continuous time with a specific terminal cost.
method Formulates necessary conditions as a coupled matrix ODE two-point boundary value problem, designs a matricial recursive algorithm, and proves convergence.
result Proposes and proves the convergence of a matricial recursive algorithm for solving the steering problem.
A new state-space approach improves NMF for dynamic data.
problem Modeling time series with strong temporal dependencies.
method Probabilistic framework with state-space approach and multi-lag N-VAR model.
result D-NMF outperforms static NMF and other state-of-the-art methods.
An ADRC-incorporated SGD algorithm improves latent factor analysis speed and accuracy.
problem Slow convergence in standard SGD for HDI matrix analysis.
method Incorporates ADRC principles to refine historical and future learning error states.
result Empirically outperforms state-of-the-art LFA models in HDI matrix prediction.
Polynomial-time algorithm learns latent-state systems without spectral radius assumptions.
problem Learning latent-state linear dynamical systems without spectral radius assumptions.
method Spectral filtering technique with a novel convex relaxation.
result Efficient identification of phases for general transition matrices.
New method learns quantum states using neural networks, revealing hidden dynamics.
problem High-precision ground state estimation of quantum many-body problems.
method Stochastic reconfiguration method with neural network Ansatz states.
result Learning landscape modes with least entanglement have largest eigenvalues, suggesting correlations are encoded in large flat valleys.
Deep neural network model extends matrix completion to unseen data.
problem Limited extendability of neural-network-based matrix completion models.
method Two-branch neural network model that can predict and extend to unseen data.
result Model outperforms state-of-the-art in accuracy and extendability.
In this paper, we review the problem of matrix completion and expose its intimate relations with algebraic geometry, combinatorics and graph theory. We present the first necessary and sufficient combinatorial conditions for matrices of arbitrary rank to be identifiable from a set of matrix entries, yielding theoretical…
This paper identifies and estimates the label noise transition matrix without ground truth labels.
problem Learning with noisy labels and identifying the noise transition matrix.
method Building on Kruskal's identifiability results, the paper characterizes the identifiability of the label noise transition matrix for the generic case at the instance level.
result The necessity of multiple noisy labels in identifying the noise transition matrix for the generic case at the instance level.
Matrix Chernoff bound for Markov chains applied to co-occurrence matrices.
problem Analyzing the behavior of co-occurrence statistics in sequential data.
method Proved a matrix Chernoff-type bound for sums of matrix-valued random variables sampled via a regular Markov chain.
result Achieved exponentially fast convergence rate and sample complexity analysis for co-occurrence matrices.
We study the projected gradient descent method on low-rank matrix problems with a strongly convex objective. We use the Burer-Monteiro factorization approach to implicitly enforce low-rankness; such factorization introduces non-convexity in the objective. We focus on constraint sets that include both positive semi-defi…
Paper proposes a new Markov model for efficient PLC system design.
problem Efficient estimation of Markov model parameters for bursty error channels.
method Introduced a Block Diagonal Markov model and a modified Baum-Welch algorithm.
result Efficient estimation of state transition matrix Λ Λ Λ for PLC system design. We analyze the relationship between the covering of the Jacobi group and the squeezed states. We attach some nonclassical states to the Jacobi group. The matrix elements of the Jacobi group are presented.
UA-LQE improves value function learning by selectively erasing uncertain entries in Q-matrix.
problem Improving value function learning in complex reinforcement learning tasks.
method Uncertainty-aware low-rank Q-matrix estimation (UA-LQE) algorithm.
result UA-LQE selectively erases uncertain entries in Q-matrix to improve value function approximation.
Global stability bounds for matrix frames in phase retrieval problems.
problem Phase retrieval for matrix frames in various applications.
method Computable global stability bounds for the quasi-linear analysis map β, using Whitney stratification of positive semidefinite matrices of low rank.
result Novel conditions for a frame to be generalized phase retrievable.
We explicitly test if the reliability of credit ratings depends on the total number of admissible states. We analyse open access credit rating data and show that the effect of the number of states in the dynamical properties of ratings change with time, thus giving supportive evidence that the ideal number of admissibl…
Efficient algorithm estimates low-rank matrices from noisy measurements.
problem Estimating low-rank matrices from noisy linear measurements.
method Stochastic variance-reduced gradient descent algorithm.
result Algorithm converges to the unknown low-rank matrix at a linear rate up to the minimax optimal statistical error.
The study explores how Matrix Product States can represent boolean and continuous functions.
problem Representing arbitrary boolean and continuous functions using Matrix Product States.
method Developed a construction method for MPS to represent boolean gates and proved density in continuous function space.
result MPS can accurately represent arbitrary boolean functions and continuous functions densely.
Deep model tackles matrix completion issues.
problem Matrix completion problems in signal processing and machine learning.
method Deep matrix factorization model with a generic discretization operator.
result Efficacy demonstrated on a real movie rating dataset.
The paper analyzes stability of random matrix products with Markovian noise.
problem Analyzing stability of random matrix products with Markovian noise.
method Using a super-Lyapunov drift condition and controlled growth of matrix-valued functions, the paper provides an exponential stability result for the p-th moment of random matrix product.
result Finite-time p-th moment bounds for linear stochastic approximation and TD learning algorithms.
New statistical model improves protein alignment accuracy.
problem Improving accuracy in protein sequence alignment.
method Inferred a time-dependent Markov process from protein sequences.
result Developed a new optimal matrix (MMLSUM) for protein alignment.
Study on Neural Tangent Kernel of Matrix Product States and their convergence.
problem Understanding the convergence of Neural Tangent Kernel of Matrix Product States.
method Analyzing the Neural Tangent Kernel of Matrix Product States and proving its convergence in the infinite bond dimensional limit.
result The Neural Tangent Kernel of Matrix Product States converges to a constant matrix during training.
We extend kernelized matrix factorization with a fully Bayesian treatment and with an ability to work with multiple side information sources expressed as different kernels. Kernel functions have been introduced to matrix factorization to integrate side information about the rows and columns (e.g., objects and users in …
A hierarchical Gaussian prior model improves low-rank matrix completion.
problem Low-rank matrix completion with improved structure exploitation.
method Hierarchical Gaussian prior model with GAMP embedded variational Bayesian inference.
result The proposed method outperforms state-of-the-art matrix completion methods.
Improved covariance estimation for various metrics outperforms existing methods.
problem Estimating covariance and precision matrices for a wide range of metrics.
method Random matrix theory for improved estimation.
result Significantly outperforms sample covariance matrix and state-of-the-art methods.
Tensor networks and RNNs are equivalent, improving wave function encoding.
problem Efficiently encoding quantum states in neural networks.
method Generalized RNN architecture for tensor networks, supporting polynomial time wave function evaluation.
result Tensorial RNNs can encode quantum states with lower bond dimensions and higher accuracy.
A fast optimization method for matrix completion with side information.
problem Matrix completion with and without side information.
method fastImpute based on non-convex gradient descent.
result fastImpute converges to a global minimum and recovers the matrix accurately.
Algorithm uses matrix estimation to impute and forecast time series data.
problem Impute and forecast time series data with missing values and noise.
method Transform time series into a matrix, use matrix estimation for missing values and de-noise, perform linear regression for predictions.
result Established a rigorous link between time series analysis and matrix estimation, providing finite sample analysis and asymptotic consistency.
New algorithm speeds up matrix learning with nonconvex regularizers.
problem Efficiently learn low-rank matrices using nonconvex regularizers.
method Developed an efficient proximal gradient algorithm with inexact proximal splitting.
result Achieved a convergence rate of O(1/T) and nearly linear speedup.