New algorithm extends Greville's method for partitioned matrices efficiently and stably.
problem Efficiently compute pseudoinverse of partitioned matrices without retraining.
method Incorporates inverse Cholesky factorization to reduce computational complexity and improve stability.
result 1 iteration to compute pseudoinverse of whole matrix from first part, addressing all cases.
Improved BLS by reducing pseudoinverse complexity for added inputs.
problem High computational complexity in pseudoinverse for incremental learning.
method Used inverse of a sum of matrices to reduce matrix inversion size.
result Significant reduction in computational complexity (1.24 - 1.30 speedups).
Paper introduces a new method to compute pseudoinverse for ELM with large datasets.
problem Efficient computation of pseudoinverse for ELM with large datasets.
method Rank-based matrix decomposition of the hidden layer matrix.
result Optimal training time and reduced computational complexity for large hidden nodes.
InfiniteWalk connects deep network embeddings to spectral graph theory with a nonlinear transformation.
problem Learning node representations from networks with deep learning methods.
method Study of the DeepWalk objective in the limit as window size goes to infinity, linking to spectral graph embeddings with a nonlinear transformation.
result Simple binary thresholding of the Laplacian pseudoinverse can approximate DeepWalk embeddings.
In this work, a non-gradient descent learning (NGDL) scheme was proposed for deep feedforward neural networks (DNN). It is known that an autoencoder can be used as the building blocks of the multi-layer perceptron (MLP) DNN, the MLP is taken as an example to illustrate the proposed scheme of pseudoinverse learning algo…
A new GCN variant tackles large eigengaps in dense graphs and hypergraphs.
problem Large eigengaps in dense graphs and hypergraphs hinder popular GCN architectures.
method Uses pseudoinverse of the Laplacian and low-rank approximation for efficient computation.
result Improves runtime and accuracy in various experiments with real-world datasets.
In this paper, we briefly review the basic scheme of the pseudoinverse learning (PIL) algorithm and present some discussions on the PIL, as well as its variants. The PIL algorithm, first presented in 1995, is a non-gradient descent and non-iterative learning algorithm for multi-layer neural networks and has several adv…
Gaussian Processes (GPs) are a popular approach to predict the output of a parameterized experiment. They have many applications in the field of Computer Experiments, in particular to perform sensitivity analysis, adaptive design of experiments and global optimization. Nearly all of the applications of GPs require the …
ZORB speeds up neural network training without sacrificing accuracy.
problem Slow and strenuous training of neural networks using gradient descent.
method Uses pseudoinverse of targets instead of gradients for backpropagation.
result ZORB converges 300 times faster than Adam on MNIST without hyperparameter tuning.
In this paper we consider the training of single hidden layer neural networks by pseudoinversion, which, in spite of its popularity, is sometimes affected by numerical instability issues. Regularization is known to be effective in such cases, so that we introduce, in the framework of Tikhonov regularization, a matricia…
We present a non-parametric method to estimate the discount curve from market quotes based on the Moore-Penrose pseudoinverse. The discount curve reproduces the market quotes perfectly, has maximal smoothness, and is given in closed-form. The method is easy to implement and requires only basic linear algebra operations…
As a type of pseudoinverse learning, extreme learning machine (ELM) is able to achieve high performances in a rapid pace on benchmark datasets. However, when it is applied to real life large data, decline related to low-convergence of singular value decomposition (SVD) method occurs. Our study aims to resolve this issu…
New invariant for special alternating links based on graph Laplacian.
problem Developing an invariant for special alternating links.
method Using the Laplacian matrix of the Tait graph, invariant is defined.
result A specific quadratic trace expression is invariant under flype moves.
We propose Very Simple Classifier (VSC) a novel method designed to incorporate the concepts of subsampling and locality in the definition of features to be used as the input of a perceptron. The rationale is that locality theoretically guarantees a bound on the generalization error. Each feature in VSC is a max-margin …
Enhances sequence memory capacity in neural networks.
problem Limited sequence capacity in Hopfield-like neural networks.
method Introducing a nonlinear interaction term and a generalized pseudoinverse rule.
result Significantly increased sequence capacity with novel scaling laws.
Recently, Mahoney and Orecchia demonstrated that popular diffusion-based procedures to compute a quick \emph{approximation} to the first nontrivial eigenvector of a data graph Laplacian \emph{exactly} solve certain regularized Semi-Definite Programs (SDPs). In this paper, we extend that result by providing a statistica…
New estimator reduces risk in slate bandits by leveraging Bayes risk criterion.
problem Evaluating slate policies using logged data when policies factorize over slots.
method Developed a new estimator using a control variate approach, showing risk improvement over existing methods.
result The new estimator has lower risk than the pseudoinverse estimator in slate bandit problems.
New method differentiates square-root Kalman filters robustly.
problem Gradient calculation issues in square-root Kalman filters.
method Closed-form chain rule derived from Gramian identity, resolves non-orthogonal and rank-deficient issues.
result Robust automatic differentiation for Kalman filters, resolving numerical stability and gradient issues.
Double descent in condition number shows peak at equal dimensions.
problem Estimating function from random measurements.
method Analyzing the condition number of random matrices.
result Condition number is highest when d=n. Enhances robustness of BLS using MCC criterion.
problem Outliers sensitivity in standard BLS.
method Adopting maximum correntropy criterion (MCC) for training output weights.
result C-BLS achieves excellent robustness to outliers.
The use of improved covariance matrix estimators as an alternative to the sample estimator is considered an important approach for enhancing portfolio optimization. Here we empirically compare the performance of 9 improved covariance estimation procedures by using daily returns of 90 highly capitalized US stocks for th…
A new estimator reduces variance in slate bandit OPE.
problem Large action spaces in slate bandits cause high variance in OPE.
method Develops Latent IPS (LIPS) to optimize slate abstractions for low variance and bias.
result LIPS substantially outperforms existing estimators in scenarios with non-linear rewards and large slate spaces.
New methods improve solving linear systems and preconditioning with reduced complexity.
problem Efficiently solving linear systems and preconditioning matrices.
method Developed structured semidefinite programming algorithms.
result Improved runtimes for preconditioning and solving linear systems.
One-step learning in crosspoint memory reduces computation time.
problem Real-time AI at the edge requires fast, low-energy computing.
method Crosspoint resistive memory with feedback configures linear and logistic regression.
result Linear and logistic regression can be computed in one step.
New curvature tensor and matrices for connection graphs derived from Bakry-Émery curvature.
problem Deriving Buser-type bounds on eigenvalues of connection Laplacians.
method Reformulation of Bakry-Émery curvature through curvature matrices and tensor representations.
result Extension of curvature matrices to connection graphs, addressing eigenfunction challenges.
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.
Study shows how optimization affects deep neural network performance as model size increases.
problem Understanding the performance of deep neural networks as model size increases.
method Careful study of learning dynamics for least squares scenario, providing an excess risk bound.
result Excess risk bound depends on the smallest non-zero eigenvalue of the covariance matrix of input features, showing double descent behavior.
Robotic grasping improved using evolutionary computing and deep reinforcement learning.
problem Developing a robot capable of grasping objects as skillfully as humans.
method Position estimation using Genetic Algorithm and regression, orientation learning using deep reinforcement learning.
result Deep reinforcement learning model outperforms traditional methods for orientation learning.