arXiv research

A model order reduction framework reduces financial risk analysis models efficiently.

New method reduces Monte Carlo error in option pricing and Greeks estimation.

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

This paper examines how labeling error affects contrastive learning and proposes data dimensionality reduction methods to mitigate its impact.

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

This paper introduces a new unsupervised method for dimensionality reduction via regression (DRR). The algorithm belongs to the family of invertible transforms that generalize Principal Component Analysis (PCA) by using curvilinear instead of linear features. DRR identifies the nonlinear features through multivariate r…

Novel bounds for logistic regression coreset construction and feature selection.

We consider active maximum a posteriori (MAP) inference problem for Hidden Markov Models (HMM), where, given an initial MAP estimate of the hidden sequence, we select to label certain states in the sequence to improve the estimation accuracy of the remaining states. We develop an analytical approach to this problem for…

Random forests are among the most popular classification and regression methods used in industrial applications. To be effective, the parameters of random forests must be carefully tuned. This is usually done by choosing values that minimize the prediction error on a held out dataset. We argue that error reduction is o…

This work examines consistency issues in Gaussian Mixture Model reduction algorithms.

This paper describes a hierarchical learning strategy for generating sparse representations of multivariate datasets. The hierarchy arises from approximation spaces considered at successively finer scales. A detailed analysis of stability, convergence and behavior of error functionals associated with the approximations…

TD learning reduces prediction error in Markov chain problems.

Paper improves Gumbel-Softmax estimator variance reduction.

Off-policy reinforcement learning aims to leverage experience collected from prior policies for sample-efficient learning. However, in practice, commonly used off-policy approximate dynamic programming methods based on Q-learning and actor-critic methods are highly sensitive to the data distribution, and can make only …

Temporal difference (TD) learning is a popular algorithm for policy evaluation in reinforcement learning, but the vanilla TD can substantially suffer from the inherent optimization variance. A variance reduced TD (VRTD) algorithm was proposed by Korda and La (2015), which applies the variance reduction technique direct…

Framework corrects model form errors in structural dynamics predictions.

This paper corrects errors in UMAP's derivation and explains its properties.

Efficiently reduces rank of non-negative matrices with quadratic time complexity.

CDP reduces point cloud dimensions by preserving detour-induced local non-convexity.

POTD estimates SDR subspace using optimal transport for binary response.

Optimizes MCMC chains with neural control variates.

When learning from a batch of logged bandit feedback, the discrepancy between the policy to be learned and the off-policy training data imposes statistical and computational challenges. Unlike classical supervised learning and online learning settings, in batch contextual bandit learning, one only has access to a colle…

Dimensionality reduction methods are very common in the field of high dimensional data analysis. Typically, algorithms for dimensionality reduction are computationally expensive. Therefore, their applications for the analysis of massive amounts of data are impractical. For example, repeated computations due to accumula…

This work improves tensor decomposition methods, especially for large datasets.

We present local discriminative Gaussian (LDG) dimensionality reduction, a supervised dimensionality reduction technique for classification. The LDG objective function is an approximation to the leave-one-out training error of a local quadratic discriminant analysis classifier, and thus acts locally to each training po…

Data-aware activation function customization reduces neural network error.

Study shows exponential error reduction in multiclass classification without bias-variance trade-off.

New algorithm reduces dimensionality in federated learning.

PredPCA extracts key components for better time series prediction.

A new method reduces dimensionality for better likelihood-free parameter estimation.

We consider the problem of distributed mean estimation (DME), in which $n$ machines are each given a local $d$-dimensional vector $x_v \in \mathbb{R}^d$, and must cooperate to estimate the mean of their inputs $μ= \frac 1n\sum_{v = 1}^n x_v$, while minimizing total communication cost. DME is a fundamental construct in …

We accelerate CNF by reducing ODE truncation errors with polynomial regularization.

While active learning offers potential cost savings, the actual data efficiency---the reduction in amount of labeled data needed to obtain the same error rate---observed in practice is mixed. This paper poses a basic question: when is active learning actually helpful? We provide an answer for logistic regression with t…

Neural operators correct PDE residuals to improve BIP solutions.

The paper provides statistical guarantees for generative models using dimension reduction.

Introduces a continuous version of LWE problem.

Selecting appropriate regularization coefficients is critical to performance with respect to regularized empirical risk minimization problems. Existing theoretical approaches attempt to determine the coefficients in order for regularized empirical objectives to be upper-bounds of true objectives, uniformly over a hypot…

We propose a data-driven approach to solve multiscale elliptic PDEs with random coefficients based on the intrinsic low dimension structure of the underlying elliptic differential operators. Our method consists of offline and online stages. At the offline stage, a low dimension space and its basis are extracted from th…

Method detects insider trading using trading data and dimensionality reduction.

Generative adversarial networks benefit from optimal input dimension and adaptive generator architecture.

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 …

Stochastic gradient Markov Chain Monte Carlo (SG-MCMC) has been developed as a flexible family of scalable Bayesian sampling algorithms. However, there has been little theoretical analysis of the impact of minibatch size to the algorithm's convergence rate. In this paper, we prove that under a limited computational bud…

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

This paper studies a theoretical pruning method for RNNs to reduce computational costs.

To train good supervised and semi-supervised object classifiers, it is critical that we not waste the time of the human experts who are providing the training labels. Existing active learning strategies can have uneven performance, being efficient on some datasets but wasteful on others, or inconsistent just between ru…

New theory shows how multi-head attention reduces variance and decorrelates outputs.

This paper considers the problem of estimating a high-dimensional vector of parameters $\boldsymbolθ \in \mathbb{R}^n$ from a noisy observation. The noise vector is i.i.d. Gaussian with known variance. For a squared-error loss function, the James-Stein (JS) estimator is known to dominate the simple maximum-likelihood (…

CW-EDMD improves prediction accuracy by learning local Koopman models for different state-space regions.