Unsupervised learning with generative adversarial networks (GANs) has proven to be hugely successful. Regular GANs hypothesize the discriminator as a classifier with the sigmoid cross entropy loss function. However, we found that this loss function may lead to the vanishing gradients problem during the learning process…
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48 results for “Least Squares GAN”
This paper explores using SSIM for better image generation in generative models.
problem Improving perceptual quality in generated images using norm.
method Theoretical discussion and practical implementation of SSIM in generative models and autoencoders.
result SSIM can be used in generative models and autoencoders to generate better images.
New method labels GAN-generated faces without stereotyping.
problem Eliminating human bias in AI classification of fictional faces.
method Penalized regression to minimize cost function between realistic and target images.
result Successfully labels GAN-generated images without stereotyping.
New GAN loss functions improve image generation quality and stability.
problem Improving the performance of GANs in generating high-quality images.
method Introducing least kth-order GAN (LGAN) and Rényi-centric GAN loss functions.
result The proposed loss functions lead to better image quality and stability.
A popular heuristic for improved performance in Generative adversarial networks (GANs) is to use some form of gradient penalty on the discriminator. This gradient penalty was originally motivated by a Wasserstein distance formulation. However, the use of gradient penalty in other GAN formulations is not well motivated.…
In this work we propose an adversarial learning approach to generate high resolution MRI scans from low resolution images. The architecture, based on the SRGAN model, adopts 3D convolutions to exploit volumetric information. For the discriminator, the adversarial loss uses least squares in order to stabilize the traini…
Data Interpolants -- That's What Discriminators in Higher-order Gradient-regularized GANs Arestat.ML
Optimized GAN discriminator using polyharmonic interpolation.
problem Optimizing the discriminator in GANs with higher-order gradient regularization.
method Polyharmonic interpolation and variational calculus.
result The optimal discriminator is a polyharmonic radial basis function.
A new GAN framework teaches models to avoid undesirable data.
problem Improving GANs' ability to learn from and avoid negative samples.
method Introducing 'negative samples' to GANs, inspired by Rumi's philosophy.
result The Rumi Framework accelerates GAN learning and improves generalization.
CD converges linearly for MCP/SCAD penalized least squares.
problem Recovering sparse signals from data.
method Coordinate descent for MCP/SCAD penalized least squares.
result CD converges linearly to solutions of MCP/SCAD penalized least squares.
Unsupervised Learning of Solutions to Differential Equations with Generative Adversarial Networkscs.LG
DEQGAN uses GANs to solve differential equations without supervision.
problem Solving differential equations with neural networks.
method Generative Adversarial Networks (GANs) to learn the loss function.
result DEQGAN achieves lower mean squared errors and competitive solution accuracy compared to traditional methods.
Illustrates interleaved learning with Kalman Filter for linear least squares.
problem Improving machine learning algorithms through interleaved learning.
method Simple statistical and optimization framework based on Kalman Filter.
result Demonstrates the effectiveness of interleaved learning.
Iterative Hessian sketch: Fast and accurate solution approximation for constrained least-squaresmath.OC
We study randomized sketching methods for approximately solving least-squares problem with a general convex constraint. The quality of a least-squares approximation can be assessed in different ways: either in terms of the value of the quadratic objective function (cost approximation), or in terms of some distance meas…
Cross validation residuals are well known for the ordinary least squares model. Here leave-M-out cross validation is extended to generalised least squares. The relationship between cross validation residuals and Cook's distance is demonstrated, in terms of an approximation to the difference in the generalised residual …
We compare the risk of ridge regression to a simple variant of ordinary least squares, in which one simply projects the data onto a finite dimensional subspace (as specified by a Principal Component Analysis) and then performs an ordinary (un-regularized) least squares regression in this subspace. This note shows that …
The paper improves Kaczmarz algorithm with momentum for linear least squares.
problem Improving convergence of the Kaczmarz algorithm for linear least squares.
method Integrates geometrically smoothed momentum into the randomized Kaczmarz algorithm.
result Proves expected error reduction in singular vector directions.
Generative adversarial networks (GANs) are effective in generating realistic images but the training is often unstable. There are existing efforts that model the training dynamics of GANs in the parameter space but the analysis cannot directly motivate practically effective stabilizing methods. To this end, we present …
New algorithm improves online binary classification with constant time complexity.
problem Online binary classification with rebalancing.
method Non-iteratively reweighted recursive least-squares.
result Exacts converges to batch formulation and outperforms existing algorithms.
Reduced-rank method improves least-squares regression under output regularity.
problem Least-squares regression with infinite dimensional outputs.
method Reduced-rank method for solving least-squares problems with output regularity assumptions.
result Learning bounds and improved statistical performance compared to full-rank method.
Generative adversarial networks (GANs) are highly effective unsupervised learning frameworks that can generate very sharp data, even for data such as images with complex, highly multimodal distributions. However GANs are known to be very hard to train, suffering from problems such as mode collapse and disturbing visual…
Proposes a partitioned least squares model for feature grouping.
problem Modeling with feature groups to assess variable importance.
method Two methods: alternating least squares and exact reformulation.
result Exact method provides better results in less time.
ESNs trained with Tikhonov least squares approximate ergodic dynamical systems in L2(μ) norm.
problem Approximating ergodic dynamical systems using ESNs.
method Tikhonov least squares regression on ESNs trained on observations from an ergodic dynamical system.
result ESNs trained with Tikhonov least squares approximate the target function in the L2(μ) norm.
The kernel least mean squares (KLMS) algorithm is a computationally efficient nonlinear adaptive filtering method that "kernelizes" the celebrated (linear) least mean squares algorithm. We demonstrate that the least mean squares algorithm is closely related to the Kalman filtering, and thus, the KLMS can be interpreted…
A new algorithm solves nonnegative least squares faster with nonnegative data.
problem Nonnegative least squares problems with nonnegative data.
method Primal-dual perspective accelerated algorithm with adaptive restart.
result Oracle complexity independent of matrix constants, solvable to multiplicative error.
The paper identifies saddlepoints in unsupervised auto-encoding neural nets.
problem The risk landscape of unsupervised least squares in auto-encoding neural nets.
method Established an equivalence between unsupervised least squares and principal manifolds, discussed regularization strategies for auto-encoders.
result All non-trivial critical points in auto-encoding are saddlepoints, which are degenerate in overcomplete auto-encoding.
New methods improve insurance data quality for catastrophic events.
problem Improving precision and size of insurance data for catastrophic events.
method Bootstrap, bootknife, and GAN algorithms.
result Compared MSE and MAE of simulated outputs, direct algorithm for fuzzy expert opinion.
The paper proposes a least squares method for binary compressive sampling with low intrinsic dimension signals.
problem Recovering signals from binary measurements with noise and sign flips.
method Least squares decoder for signals with low generative intrinsic dimension.
result The least squares decoder achieves a sharp estimation error of under certain conditions.
This paper studies an unsupervised deep learning-based numerical approach for solving partial differential equations (PDEs). The approach makes use of the deep neural network to approximate solutions of PDEs through the compositional construction and employs least-squares functionals as loss functions to determine para…
We propose a new forward-backward stochastic differential equation solver for high-dimensional derivatives pricing problems by combining deep learning solver with least square regression technique widely used in the least square Monte Carlo method for the valuation of American options. Our numerical experiments demonst…
We introduce a novel semi-supervised version of the least squares classifier. This implicitly constrained least squares (ICLS) classifier minimizes the squared loss on the labeled data among the set of parameters implied by all possible labelings of the unlabeled data. Unlike other discriminative semi-supervised method…
New method speeds up solving L0-regularized least-squares problems.
problem Solving L0-regularized least-squares problems efficiently.
method Safe peeling for Branch-and-Bound algorithm.
result Significant gains in solving time and node exploration.
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 .
result Risk of the minimum norm least squares estimator vanishes compared to the null estimator.
Least squares estimator fails to achieve optimal risk in bounded distributions, but non-linear predictors can.
problem Optimal risk in bounded distributions for constrained least squares.
method Comparison of least squares and non-linear predictors.
result Non-linear predictors can achieve optimal risk in bounded distributions.
Sparse linear regression, which entails finding a sparse solution to an underdetermined system of linear equations, can formally be expressed as an -constrained least-squares problem. The Orthogonal Least-Squares (OLS) algorithm sequentially selects the features (i.e., columns of the coefficient matrix) to greedil…
Paper predicts EEG features from acoustic features using RNN and GAN.
problem Predicting EEG features from acoustic features.
method Recurrent Neural Network (RNN) and Generative Adversarial Network (GAN).
result Lower RMSE and normalized RMSE values compared to generating acoustic features from EEG features.
We introduce the implicitly constrained least squares (ICLS) classifier, a novel semi-supervised version of the least squares classifier. This classifier minimizes the squared loss on the labeled data among the set of parameters implied by all possible labelings of the unlabeled data. Unlike other discriminative semi-s…
We prove the statistical consistency of kernel Partial Least Squares Regression applied to a bounded regression learning problem on a reproducing kernel Hilbert space. Partial Least Squares stands out of well-known classical approaches as e.g. Ridge Regression or Principal Components Regression, as it is not defined as…
This paper uses GAN and ERMSE to improve stock price movement prediction accuracy.
problem Predicting stock price movement direction is challenging due to complex, incomplete, and fuzzy information.
method The paper proposes a deep learning model using GAN and ERMSE to forecast stock market trends.
result The GAN model outperformed LSTM in predicting stock price movement direction with a 4.35% improvement.
GANs can learn hierarchical distributions in real-world images efficiently.
problem Understanding and efficiently learning complex, real-world distributions with GANs.
method Formally studying how GANs can learn hierarchically generated distributions close to real-life image distributions using SGDA.
result Training GANs via SGDA can efficiently learn distributions with a 'forward super-resolution' structure, both in sample and time complexities.
Randomized matrix compression techniques, such as the Johnson-Lindenstrauss transform, have emerged as an effective and practical way for solving large-scale problems efficiently. With a focus on computational efficiency, however, forsaking solutions quality and accuracy becomes the trade-off. In this paper, we investi…
A simple modification improves GAN performance by discarding bad samples.
problem Improving GAN performance with minimal computational cost.
method Top-k update procedure: zero out gradient contributions from least realistic elements.
result Significant improvement in FID score for conditional generation on CIFAR-10.
This book introduces linear models and their theories rigorously.
problem Understanding linear models and their theories.
method Explains linear models from three perspectives, introduces maximum likelihood estimation, and proves least squares is the best unbiased linear model.
result Least squares is the best unbiased linear model in terms of mean squared error.
The ratio of two probability densities can be used for solving various machine learning tasks such as covariate shift adaptation (importance sampling), outlier detection (likelihood-ratio test), and feature selection (mutual information). Recently, several methods of directly estimating the density ratio have been deve…
The least-squares support vector machine is a frequently used kernel method for non-linear regression and classification tasks. Here we discuss several approximation algorithms for the least-squares support vector machine classifier. The proposed methods are based on randomized block kernel matrices, and we show that t…
Efficiently estimates private least squares with linear error growth.
problem Private estimation of ordinary least squares with bounded residuals and leverage.
method Scaled noise added to a stable nonprivate estimator of the regression vector.
result Near-optimal accuracy guarantee with linear error growth in dimension.
Here, we provide a supplementary material for Takayuki Osogami, "Uncorrected least-squares temporal difference with lambda-return," which appears in {\it Proceedings of the 34th AAAI Conference on Artificial Intelligence} (AAAI-20).
Least squares estimation for the subcritical Heston model based on continuous time observationsmath.ST
We prove strong consistency and asymptotic normality of least squares estimators for the subcritical Heston model based on continuous time observations. We also present some numerical illustrations of our results.
Improved Least-Squares Monte Carlo with finite-difference ansatz.
problem Improving accuracy and stability in option pricing.
method Constructing an ansatz using finite-difference solution for conditional expected continuation payoffs.
result Reduces mean squared error and final pricing error.
We study asymptotic properties of some (essentially conditional least squares) parameter estimators for the subcritical Heston model based on discrete time observations derived from conditional least squares estimators of some modified parameters.