New ELM algorithms reduce computation time and complexity.
problem Efficient computation of extreme learning machine (ELM) algorithms.
method Developed inverse-free ELM algorithms using recursive matrix inverse and inverse LDL' factorization.
result Proposed algorithms significantly reduce computational complexity.
Efficient algorithm removes redundant nodes and obsolete samples in machine learning.
problem Pruning redundant nodes and removing obsolete training samples in machine learning.
method Deduced decremented learning algorithms from incremental learning algorithms, using inverse Cholesterol factor and unitary transformation.
result Proposed decremented learning algorithms efficiently prune redundant nodes and remove obsolete training samples.
Two efficient ridge solutions improve BLS for new inputs, enhancing accuracy and speed.
problem Improving BLS for new added inputs in a learning system.
method Proposes recursive and square-root BLS algorithms using inverse and inverse Cholesky factor updates.
result Both proposed ridge solutions improve BLS accuracy and speed, especially with larger lambda.
Two new inverse-free ELM algorithms for incremental and decremental learning are proposed.
problem Efficiently updating and removing multiple hidden nodes in ELM.
method Improved inverse-free recursive algorithms for Tikhonov regularization.
result Inverse-free algorithms for ELM with multiple hidden nodes and redundant nodes.
Develops a fast algorithm for fitting multilevel factor models.
problem Fitting multilevel factor models with covariance structure.
method Novel expectation-maximization algorithm tailored for multilevel factor models.
result Shows efficient computation of inverse of positive definite MLR matrix.
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 develops efficient methods for estimating Hessian inverses in stochastic optimization.
problem Estimating the inverse Hessian for convex function minimization.
method Robbins-Monro procedure for recursive estimation of the inverse Hessian.
result Develops universal stochastic Newton methods with improved efficiency.
New method for PKM inverse dynamics second derivatives efficiently.
problem Efficient computation of PKM inverse dynamics second derivatives.
method Recursive Lie-group formulation for serial robots adapted to PKM topology.
result Efficient computation of second time derivatives for PKM.
Efficient optimization method reduces Full AdaGrad complexity.
problem Computational challenges in Full AdaGrad for large-scale applications.
method Recursive method and streaming variant for parameter updates.
result Significant reduction in complexity and resource demands.
This text investigates relations between two well-known family of algorithms, matrix factorisations and recursive linear filters, by describing a probabilistic model in which approximate inference corresponds to a matrix factorisation algorithm. Using the probabilistic model, we derive a matrix factorisation algorithm …
Paper improves RLS for sparse outlier detection in linear models.
problem Outliers contaminate linear regression models infrequently.
method Hierarchical-optimization recursive least squares with sparsity-inducing regularization.
result The method robustly estimates linear filters/systems with outliers.
New recursion formula for non-orientable surfaces resolves divergences.
problem Computing volumes of moduli spaces for non-orientable surfaces.
method Generalization of Mirzakhani's recursion to non-orientable surfaces, handling divergences with integral kernels.
result Regularized volumes can be computed with a cutoff on crosscap size.
Develops inverse extended Kalman filter for predicting adversarial steps.
problem Predicting adversarial Kalman filter estimates from limited information.
method Proposes inverse extended Kalman filter (I-EKF) for non-linear systems with unknown inputs.
result Derives I-EKF with theoretical stability guarantees and consistency proofs.
The problem at the heart of this tutorial consists in modeling the path choice behavior of network users. This problem has been extensively studied in transportation science, where it is known as the route choice problem. In this literature, individuals' choice of paths are typically predicted using discrete choice mod…
LASER compresses recursive model activations by exploiting their low-dimensional structure.
problem Understanding and optimizing the geometric structure of recursive reasoning trajectories.
method Dynamic low-rank basis tracking via matrix-free subspace tracking with a fidelity-triggered reset mechanism.
result Recursive activations occupy a linear, low-dimensional subspace that can be compressed efficiently.
Paper improves ML estimation from incomplete data with robust M-estimator.
problem Estimating parameters from incomplete data with improved accuracy.
method Developed a robust M-estimator and a sandwich estimator for standard errors.
result Improved estimation accuracy with smaller standard errors than ML estimates.
In this paper, we study the nonnegative matrix factorization problem under the separability assumption (that is, there exists a cone spanned by a small subset of the columns of the input nonnegative data matrix containing all columns), which is equivalent to the hyperspectral unmixing problem under the linear mixing mo…
Advanced optimization algorithms such as Newton method and AdaGrad benefit from second order derivative or second order statistics to achieve better descent directions and faster convergence rates. At their heart, such algorithms need to compute the inverse or inverse square root of a matrix whose size is quadratic of …
In this paper, we consider the Graphical Lasso (GL), a popular optimization problem for learning the sparse representations of high-dimensional datasets, which is well-known to be computationally expensive for large-scale problems. Recently, we have shown that the sparsity pattern of the optimal solution of GL is equiv…
Develops a novel ML smoothing method for incomplete data in state-space models.
problem Estimating states in stochastic systems with incomplete information.
method Introduces score function and conditional observed information matrices for incomplete data, and uses them to derive the ML smoother.
result The ML smoother provides more accurate state estimates with lower standard errors compared to the standard ML state estimator.
The reduction problem of the chiral field equation on symmetric spaces is studied. It is shown that the symmetric chiral field has infinitely many local conservation laws. A recursive formula for these conservation laws is derived and the first associated integral of motion are given explicitly. Furthermore, the Zakhar…
We extend topological recursion to twisted Higgs bundles with singularities.
problem Computing Taylor expansions of period matrices for twisted Higgs bundles.
method We introduce a twisted topological recursion on the spectral curve of a twisted Higgs bundle, encoding singularities and performing the recursion explicitly.
result The g=0 twisted Eynard-Orantin differentials compute the Taylor expansion of the spectral curve's period matrix, independent of the ambient space. The paper explores continuous inverse ambiguous functions on various Lie groups.
problem Existence of continuous inverse ambiguous functions on Lie groups.
method Investigation of continuous inverse ambiguous functions on specific Lie groups.
result Existence of continuous inverse ambiguous functions on various Lie groups.
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.
Method estimates sparse inverse covariance and partial correlation matrices efficiently.
problem Sparse high-dimensional inverse covariance and partial correlation matrix estimation.
method Two-stage estimation method using partial regression with positive semi-definiteness.
result Efficient estimation of inverse covariance and partial correlation matrices with derived non-asymptotic rates.
We use the explicit relation between genus filtrated s-loop means of the Gaussian matrix model and terms of the genus expansion of the Kontsevich--Penner matrix model (KPMM), which is the generating function for volumes of discretized (open) moduli spaces Mg,sdisc (discrete volumes), to express Gaussian means…
We present a formula for the trace of any symmetric power of a n×n matrix (with coefficients in a field) in terms of the ordinary powers of the matrix, an arbitrarily chosen linear function which vanishes on the identity matrix, and n−2 polynomial functions defined recursively.
The graphical lasso (glasso) is a widely-used fast algorithm for estimating sparse inverse covariance matrices. The glasso solves an L1 penalized maximum likelihood problem and is available as an R library on CRAN. The output from the glasso, a regularized covariance matrix estimate a sparse inverse covariance matrix e…
In this paper, we develop an approach to recursively estimate the quadratic risk for matrix recovery problems regularized with spectral functions. Toward this end, in the spirit of the SURE theory, a key step is to compute the (weak) derivative and divergence of a solution with respect to the observations. As such a so…
NGD improves multivariate Gaussian inference by optimizing Fisher information.
problem Efficiently optimizing multivariate Gaussian models.
method Natural Gradient Descent applied to multivariate Gaussian parameters.
result NGD updates are more efficient for symmetric covariance matrices.
Paper shows how sparse inversion speeds up log determinant derivatives.
problem Deriving log determinant derivatives for sparse matrices.
method Sparse inversion, selected inversion, accelerates computation.
result Derivative of log determinant can be computed faster with sparse inversion.
We investigate the special Kähler geometry of the base of the Hitchin integrable system in terms of spectral curves and topological recursion. The Taylor expansion of the special Kähler metric about any point in the base may be computed by integrating the g=0 Eynard-Orantin invariants of the corresponding spectral …
New method identifies latent treatment effects from proxy models.
problem Identifying heterogeneous treatment effects under unobserved confounding.
method Compressed observable operator and spectral analysis of treatment effects.
result Eigenvalues of the operator represent latent treatment effects.
A new method for unfolding histograms without matrix inversion.
problem Matrix inversion in experimental physics, especially in high-energy particle physics.
method Sampling many distributions, folding them through the response matrix, and choosing the closest one to the data.
result Performs as well as traditional methods in well-defined inverse problems and outperforms them in ill-defined ones.
The paper computes a knot's Kauffman bracket polynomial using recursive concatenation of a 4-tangle shadow.
problem Computing the Kauffman bracket polynomial for complex knots.
method Recursive concatenation of a 4-tangle shadow, followed by a closure operation and polynomial computation.
result A method to compute the Kauffman bracket polynomial for knots formed from 4-tangle shadows.
Guichard's transformations generate Voss surfaces from sine-Gordon solutions.
problem Generating Voss surfaces from sine-Gordon solutions.
method Using Guichard transformations and recursion operators for sine-Gordon symmetries.
result Explicit derivation of Voss nets and length of Guichard sequences.
New filters improve radar target inference in complex scenarios.
problem Improving radar target inference in highly non-linear system models.
method Developed inverse cubature Kalman filter (I-CKF), inverse quadrature Kalman filter (I-QKF), and inverse cubature-quadrature Kalman filter (I-CQKF) for non-linear systems.
result Numerical experiments show improved estimation accuracy compared to existing methods.
Non-negative matrix factorization (NMF) approximates a non-negative matrix X by a product of two non-negative low-rank factor matrices W and H. NMF and its extensions minimize either the Kullback-Leibler divergence or the Euclidean distance between X and WTH to model the Poisson noise or the Gaussian noise.…
Paper presents novel online MTL methods using WRLS and OSLSSVR.
problem Online Multi-Task Learning (MTL) Regression Problems
method Develops recursive versions of WRLS and OSLSSVR for MTL.
result Achieves exact and approximate recursions with quadratic cost.
We propose an algorithmic framework for convex minimization problems of a composite function with two terms: a self-concordant function and a possibly nonsmooth regularization term. Our method is a new proximal Newton algorithm that features a local quadratic convergence rate. As a specific instance of our framework, w…
Paper proposes a generalized precision matrix for t-Student distributions to improve portfolio optimization.
problem Limitations of inverse covariance matrix in non-Gaussian settings.
method Exploits local dependence function to define generalized precision matrix (GPM) for multivariate t-Student distribution.
result GPM leads to statistically significant lower out-of-sample variances in minimum-variance portfolios.
Paper analyzes AIRL in high-dimensional spaces using random matrix theory.
problem AIRL's performance challenges in high-dimensional environments.
method Examined the rank of the matrix derived from transition matrix, applied random matrix theory.
result High-dimensional scenarios reveal transfer limitations not inherent to AIRL framework.
The Darboux-Egoroff system of PDEs with any number n≥3 of independent variables plays an essential role in the problems of describing n-dimensional flat diagonal metrics of Egoroff type and Frobenius manifolds. We construct a recursion operator and its inverse for symmetries of the Darboux-Egoroff system and des…
Matrix completion is a modern missing data problem where both the missing structure and the underlying parameter are high dimensional. Although missing structure is a key component to any missing data problems, existing matrix completion methods often assume a simple uniform missing mechanism. In this work, we study ma…
In distributed optimization and distributed numerical linear algebra, we often encounter an inversion bias: if we want to compute a quantity that depends on the inverse of a sum of distributed matrices, then the sum of the inverses does not equal the inverse of the sum. An example of this occurs in distributed Newton's…
Proves conjecture about integer sums of torus knot torsions.
problem Integrality of sums of (g-1)st powers of adjoint Reidemeister torsions for torus knots.
method Introduced Verlinde numbers from modular S-matrix, proved integrality through recursion formulas.
result Proven integrality of sums of (g-1)st powers of adjoint Reidemeister torsions for all torus knots and non-negative g.
A new method for estimating adversarial strategies in nonlinear systems.
problem Inferring an intelligent adversarial agent's strategy in highly nonlinear systems.
method Formulated inverse cognition as a nonlinear Gaussian state-space model and developed an inverse UKF (IUKF) system.
result The estimation error of IUKF converges and closely follows the recursive Cramér-Rao lower bound.
New method for mixed memberships using symmetrized Laplacian inverse matrix.
problem Mixed memberships in community detection.
method Spectral clustering on symmetrized Laplacian inverse matrix.
result Mixed-SLIM methods outperform state-of-the-art methods.