arXiv research

This paper analyzes how errors accumulate in PCA's deflation method.

Score matching errors are not sufficient for measuring diffusion model quality.

New geometric analysis shows $L^2$ score error is flawed for diffusion models.

A new method for fair PCA ensures balanced error across groups.

The paper decomposes unsupervised learning's generalization error into model, data, and variance components.

Two derivations of PCA for distributional data.

This paper tackles fairness in PCA by balancing it with reconstruction error.

A hybrid loss framework improves time series forecasting by balancing global and component errors.

We propose a fair principal component analysis method that balances reconstruction error and subgroup fairness.

In this paper, in following of the first part (which ADF tests using ACI evaluation) has conducted, Time Series (TSs) are analyzed using decomposition analysis. In fact, TSs are composed of four components including trend (long term behavior or progression of series), cyclic component (non-periodic fluctuation behavior…

The paper introduces COAR to estimate component attributions and enable model editing.

We introduce a new approach to unsupervised estimation of feature-rich semantic role labeling models. Our model consists of two components: (1) an encoding component: a semantic role labeling model which predicts roles given a rich set of syntactic and lexical features; (2) a reconstruction component: a tensor factoriz…

New method optimizes PCA for better prediction and variance.

Principal component analysis (PCA) has been a prominent tool for high-dimensional data analysis. Online algorithms that estimate the principal component by processing streaming data are of tremendous practical and theoretical interests. Despite its rich applications, theoretical convergence analysis remains largely ope…

The paper analyzes CycleGAN's error components for unpaired data generation.

QAPCA uses quantum annealing for robust PCA.

Paper analyzes online tensorial ICA convergence with stochastic approximation.

New DMEM models forecast volatility combining low- and high-frequency data.

Data science relies on pipelines that are organized in the form of interdependent computational steps. Each step consists of various candidate algorithms that maybe used for performing a particular function. Each algorithm consists of several hyperparameters. Algorithms and hyperparameters must be optimized as a whole …

Proposes a new model for mixed membership in Gaussian mixture.

We consider the mixed regression problem with two components, under adversarial and stochastic noise. We give a convex optimization formulation that provably recovers the true solution, and provide upper bounds on the recovery errors for both arbitrary noise and stochastic noise settings. We also give matching minimax …

Estimates surface count with prescribed foliations.

Principal Component Analysis (PCA) is the most common nonparametric method for estimating the volatility structure of Gaussian interest rate models. One major difficulty in the estimation of these models is the fact that forward rate curves are not directly observable from the market so that non-trivial observational e…

Researchers propose a new SSL risk decomposition method to evaluate and improve self-supervised learning models.

Principal component analysis (PCA) is often used to reduce the dimension of data by selecting a few orthonormal vectors that explain most of the variance structure of the data. L1 PCA uses the L1 norm to measure error, whereas the conventional PCA uses the L2 norm. For the L1 PCA problem minimizing the fitting error of…

We propose a new sparse regression method called the component lasso, based on a simple idea. The method uses the connected-components structure of the sample covariance matrix to split the problem into smaller ones. It then solves the subproblems separately, obtaining a coefficient vector for each one. Then, it uses n…

New PCA method detects faults using occupation kernels.

Principal Component Analysis (PCA) is a very successful dimensionality reduction technique, widely used in predictive modeling. A key factor in its widespread use in this domain is the fact that the projection of a dataset onto its first $K$ principal components minimizes the sum of squared errors between the original …

Study shows MDA's effectiveness even when more components are assumed than in actual data.

We show that for links with at most 5 components, the only finite type homotopy invariants are products of the linking numbers. In contrast, we show that for links with at least 9 components, there must exist finite type homotopy invariants which are not products of the linking numbers. This corrects previous errors of…

We present a new method for the separation of superimposed, independent, auto-correlated components from noisy multi-channel measurement. The presented method simultaneously reconstructs and separates the components, taking all channels into account and thereby increases the effective signal-to-noise ratio considerably…

Gradient descent with growing learning rate enables learning non-linear features in neural networks.

Boosting variational inference (BVI) approximates an intractable probability density by iteratively building up a mixture of simple component distributions one at a time, using techniques from sparse convex optimization to provide both computational scalability and approximation error guarantees. But the guarantees hav…

Probabilistic Autoencoder learns latent space weights' distribution.

Enhanced time series forecasting with improved trend and seasonal components.

We informally call a stochastic process learnable if it admits a generalization error approaching zero in probability for any concept class with finite VC-dimension (IID processes are the simplest example). A mixture of learnable processes need not be learnable itself, and certainly its generalization error need not de…

Study on reducing dimensionality in high-dimensional regression with kernel methods and stability analysis.

We identify and validate a model for PCR in high dimensions, improving prediction guarantees.

Recent advances in Capsule Networks (CapsNets) have shown their superior learning capability, compared to the traditional Convolutional Neural Networks (CNNs). However, the extremely high complexity of CapsNets limits their fast deployment in real-world applications. Moreover, while the resilience of CNNs have been ext…

New method calibrates asynchronous, error-prone covariates for longitudinal data.

Efficient private matrix analysis algorithms for recent variants.

A method for noise reduction in functional time series using FPCA.

Improved spectral convergence bounds for diffusion maps on tori.

Gradient descent recovers principal components of overparametrized asymmetric matrices without explicit regularization.

The study characterizes diffusion model generalization using data-dependent ridge manifolds.

This paper proposes a simple approach to derive efficient error bounds for learning multiple components with sparsity-inducing regularization. We show that for such regularization schemes, known decompositions of the Rademacher complexity over the components can be used in a more efficient manner to result in tighter b…

This paper extends robust principal component analysis (RPCA) to nonlinear manifolds. Suppose that the observed data matrix is the sum of a sparse component and a component drawn from some low dimensional manifold. Is it possible to separate them by using similar ideas as RPCA? Is there any benefit in treating the mani…

Linear Transformer Block combines MLP and linear attention for near-optimal ICL in linear regression.