Many random processes can be simulated as the output of a deterministic model accepting random inputs. Such a model usually describes a complex mathematical or physical stochastic system and the randomness is introduced in the input variables of the model. When the statistics of the output event are known, these input …
On-device research index
arXiv research
A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
168,742 papers · 148 categories
Trend · papers per month
48 results for “Random inputs”
New method certifies neural network robustness under random input noise.
problem Certifying neural network robustness against random input noise.
method Chance-constrained optimization problem reformulated with input-output samples, convex conditions developed.
result Proposed method certifies robustness against various input noise regimes over larger uncertainty regions.
Bayesian optimization is a powerful tool for expensive stochastic black-box optimization problems such as simulation-based optimization or machine learning hyperparameter tuning. Many stochastic objective functions implicitly require a random number seed as input. By explicitly reusing a seed a user can exploit common …
Random projections improve GP regression performance, reducing high-dimensional inputs to 1D.
problem Gaussian processes struggle with high-dimensional inputs, leading to overfitting and high computational cost.
method Use additive sums of kernels operating on random projections of inputs.
result Predictive performance converges to full-dimensional kernel performance with increasing projections, even in 1D.
Random deep neural networks are robust to adversarial examples, scaling with input size and dimension.
problem Adversarial examples challenge the reliability of deep learning algorithms.
method Analysis of random deep neural networks with Gaussian process equivalence and experiments on MNIST and CIFAR10.
result The distance of adversarial examples scales as norm of the input.
New method enhances neural network robustness against adversarial attacks.
problem Enhancing neural network robustness against adversarial attacks.
method Variational framework with per-sample noise level selector.
result Enhanced empirical robustness and certified robustness.
New method certifies neural network robustness to random input noise.
problem Certifying neural networks' robustness to random input noise.
method Chance-constrained optimization problem reformulated using input-output samples.
result Certifies a uniform infinity-norm uncertainty region with a radius 50 times larger.
DeformRS certifies deep networks against various input deformations.
problem Vulnerability of deep networks to input deformations.
method Randomized smoothing reformulation for general deformations.
result Certifies rich deformations including translations, rotations, scaling, and affine.
Within machine learning, the supervised learning field aims at modeling the input-output relationship of a system, from past observations of its behavior. Decision trees characterize the input-output relationship through a series of nested questions, the testing nodes, leading to a set of predictions, th…
Random feature model approximates PDE solutions efficiently.
problem Approximating solutions to PDEs with high-dimensional inputs and outputs.
method Random feature model applied to infinite-dimensional operators.
result Efficient and accurate approximation of PDE solutions.
Two ANOVA-based algorithms boost random Fourier feature models for function approximation.
problem Approximating high-dimensional functions with low-order interactions.
method Utilizes ANOVA decomposition to learn low-order functions and index sets of important variables.
result Significantly reduces approximation error compared to existing methods.
We consider a neural network architecture with randomized features, a sign-splitter, followed by rectified linear units (ReLU). We prove that our architecture exhibits robustness to the input perturbation: the output feature of the neural network exhibits a Lipschitz continuity in terms of the input perturbation. We fu…
This paper proposes a novel type of random forests called a denoising random forests that are robust against noises contained in test samples. Such noise-corrupted samples cause serious damage to the estimation performances of random forests, since unexpected child nodes are often selected and the leaf nodes that the i…
In this work, a method of random parameters generation for randomized learning of a single-hidden-layer feedforward neural network is proposed. The method firstly, randomly selects the slope angles of the hidden neurons activation functions from an interval adjusted to the target function, then randomly rotates the act…
Input-dependent smoothing mitigates classical issues but suffers from the curse of dimensionality.
problem Certifiably robust classifiers with input-dependent smoothing suffer from the curse of dimensionality.
method Proposed a theoretical and practical framework for input-dependent smoothing under strict restrictions.
result Input-dependent smoothing mitigates some classical issues but is limited by the curse of dimensionality.
Framework combines random features with CDEs for efficient time-series learning.
problem Efficient training of time-series models with strong inductive bias.
method Random Fourier CDEs and Random Rough DEs using continuous-time reservoirs and log-ODE discretization.
result Unified perspective on random-feature reservoirs and path-signature theory.
Free Random Projection enhances reinforcement learning by naturally incorporating hierarchical structure.
problem Improving reinforcement learning algorithms for better generalization and adaptability.
method Introduces Free Random Projection, a method that uses free probability theory to create random orthogonal matrices encoding hierarchical structure.
result Empirically shows consistent improvement in generalization over standard methods on multi-environment benchmarks.
We propose a novel framework for the differentially private ERM, input perturbation. Existing differentially private ERM implicitly assumed that the data contributors submit their private data to a database expecting that the database invokes a differentially private mechanism for publication of the learned model. In i…
We consider derivative-free black-box global optimization of expensive noisy functions, when most of the randomness in the objective is produced by a few influential scalar random inputs. We present a new Bayesian global optimization algorithm, called Stratified Bayesian Optimization (SBO), which uses this strong depen…
New framework models neural systems with random architecture on manifolds.
problem Complex, uncertain systems with non-Gaussian outputs.
method Latent random field on compact manifold generates neural architecture and weights.
result Synthetic neural systems can produce stochastic outputs for deterministic inputs.
Randomized smoothing reduces accuracy in ML models, especially at higher noise levels.
problem Adversarial attacks on ML models, especially randomized smoothing's accuracy drop.
method Theoretical and empirical analysis of randomized smoothing's effect on feasible hypotheses space.
result For some noise levels, randomized smoothing shrinks the set of feasible hypotheses, leading to accuracy drops.
Study shows perceptrons with random labels perform similarly to Gaussian data.
problem The assumption of Gaussian input data is often seen as a limitation in machine learning.
method Analyzed generalized linear classification (perceptron model) with random labels.
result Minimum training loss is independent of data covariance for high-dimensional input data.
In linear regression we wish to estimate the optimum linear least squares predictor for a distribution over -dimensional input points and real-valued responses, based on a small sample. Under standard random design analysis, where the sample is drawn i.i.d. from the input distribution, the least squares solution for…
Global sensitivity analysis for stochastic simulators based on generalized lambda surrogate modelsstat.CO
The paper develops methods to analyze sensitivity in stochastic models using surrogate models.
problem Quantifying the impact of input variability on stochastic simulators with randomness.
method The authors propose using generalized lambda models to emulate response distributions of stochastic simulators and estimate sensitivity indices.
result The proposed method can estimate sensitivity indices even with strong heteroskedasticity and small signal-to-noise ratio.
New BO method optimizes multiple objectives under input noise.
problem Optimizing multiple performance metrics in manufacturing processes subject to random input noise.
method Formalizes optimization of multivariate value-at-risk (MVaR) using random scalarizations.
result Significantly outperforms alternative methods in identifying robust designs.
Tensorized random projections reduce high-dimensional tensor size efficiently.
problem Efficiently reducing the dimension of very high-dimensional tensors.
method Proposes two tensorized random projection maps using TT and CP decompositions.
result TT format offers superior performance in terms of required random projection size.
Random projections are able to perform dimension reduction efficiently for datasets with nonlinear low-dimensional structures. One well-known example is that random matrices embed sparse vectors into a low-dimensional subspace nearly isometrically, known as the restricted isometric property in compressed sensing. In th…
Random feature matrices' singular values concentrate near their full expectation in high dimensions.
problem Characterizing the spectra of random feature matrices for regression problems.
method Analyzing two settings of input variables (random or well-separated) with conditions on dimension, complexity ratio, and sampling variance.
result The singular values of random feature matrices concentrate near their full expectation and near one with high probability.
Recurrent neural networks (RNNs) have drawn interest from machine learning researchers because of their effectiveness at preserving past inputs for time-varying data processing tasks. To understand the success and limitations of RNNs, it is critical that we advance our analysis of their fundamental memory properties. W…
Reservoir computing's success depends on mapping different input time series to separable states.
problem Quantifying the ability of random linear reservoirs to map different input time series.
method Mathematical framework using spectral properties of the connectivity matrix.
result Separation capacity is fully characterized by the spectral properties of the connectivity matrix.
Overparametrized models are vulnerable to adversarial perturbations, affecting robust generalization.
problem Understanding how overparametrization impacts robustness in adversarial training.
method Analyzing random features regression models with a precise asymptotic formula.
result High overparametrization can hurt robust generalization in adversarially trained models.
A new method optimizes robustness measures under input uncertainty using randomized Gaussian process upper confidence bound.
problem Optimizing robustness measures under input uncertainty.
method Randomized robustness measure GP-UCB (RRGP-UCB) that samples β from a chi-squared-based distribution.
result RRGP-UCB provides tight bounds on expected regret.
We propose a new method for input variable selection in nonlinear regression. The method is embedded into a kernel regression machine that can model general nonlinear functions, not being a priori limited to additive models. This is the first kernel-based variable selection method applicable to large datasets. It sides…
Extends randomized smoothing to certify robustness against various threat models and adversarial perturbations.
problem Certifying robustness of classifiers against adversarial perturbations.
method Develops a method to certify robustness against any () minimized adversarial perturbation.
result Randomized smoothing suffers from the curse of dimensionality, reducing effective radius as increases.
Develops a framework to quantify uncertainties in multiple ML models.
problem Uncertainty in ML model predictions and model inputs.
method Develops a theoretical framework to decouple and transform uncertainties.
result Generates joint distribution of ML predictions considering uncertainties.
Generalizes Hoeffding's decomposition for dependent inputs under mild conditions.
problem Performing global sensitivity analysis on black-box models with dependent inputs.
method Proposes a novel framework based on probability theory, functional analysis, and combinatorics to handle dependencies.
result Any square-integrable, real-valued function of random elements with mild dependence assumptions can be uniquely additively decomposed.
We propose reinforcement learning on simple networks consisting of random connections of spiking neurons (both recurrent and feed-forward) that can learn complex tasks with very little trainable parameters. Such sparse and randomly interconnected recurrent spiking networks exhibit highly non-linear dynamics that transf…
Traditional GANs use a deterministic generator function (typically a neural network) to transform a random noise input to a sample that the discriminator seeks to distinguish. We propose a new GAN called Bayesian Conditional Generative Adversarial Networks (BC-GANs) that use a random generator function…
Enhances random forests by smoothing predictions for better performance.
problem Suboptimal performance due to piecewise constant predictions in random forests.
method Kernel-based smoothing mechanism to introduce local regularity.
result Smoothed random forest model consistently improves predictive performance.
Hashing is a basic tool for dimensionality reduction employed in several aspects of machine learning. However, the perfomance analysis is often carried out under the abstract assumption that a truly random unit cost hash function is used, without concern for which concrete hash function is employed. The concrete hash f…
This paper analyzes the interpolation error of nonlinear Attention compared to linear regression.
problem Understanding the interpolation error of nonlinear Attention in high-dimensional settings.
method Derives explicit expressions for mean-squared interpolation error using signal-plus-noise model and random matrix theory.
result Nonlinear Attention generally incurs a larger interpolation error than linear regression, but this gap can be reversed with structured signals.
Random Forests are reinterpreted as generative models to handle missing data and detect outliers.
problem Handling missing features and detecting outliers in Random Forests.
method Interpreting Random Forests as Probabilistic Circuits and applying marginalisation for missing data.
result GeDTs and GeFs can handle missing data and detect outliers under certain assumptions.
Random forests are a statistical learning method widely used in many areas of scientific research because of its ability to learn complex relationships between input and output variables and also its capacity to handle high-dimensional data. However, current random forest approaches are not flexible enough to handle he…
RFMs transition from linear to nonlinear under specific input-label correlation.
problem Understanding the transition from linear to nonlinear behavior in RFMs.
method Analyzing RFMs under spiked covariance designs, characterizing the interaction between anisotropy and input-label correlation.
result The RFM generalization error is governed by the strength of input-label correlation, leading to a clear nonlinear advantage above a specific boundary.
Matrix completion is a well-studied problem with many machine learning applications. In practice, the problem is often solved by non-convex optimization algorithms. However, the current theoretical analysis for non-convex algorithms relies heavily on the assumption that every entry is observed with exactly the same pro…
Deep Regression Ensemblesstat.ML
DRE combines DNN with random feature regression for efficient neural network design.
problem Designing and training deep neural networks (DNN) efficiently and effectively.
method DRE architecture with two-layer neural networks, randomly drawn input and output weights trained with linear ridge regression.
result DRE outperforms state-of-the-art DNN in many data sets with lower computational cost.
AgraSSt assesses graph generators using Stein operators and kernel discrepancies.
problem Assessing the quality of graph generators that are implicit or not in explicit form.
method AgraSSt uses Stein operators and kernel discrepancies to assess graph generators, providing interpretable criticisms.
result Theoretical guarantees and empirical validation for various graph models.
Standard sparse pseudo-input approximations to the Gaussian process (GP) cannot handle complex functions well. Sparse spectrum alternatives attempt to answer this but are known to over-fit. We suggest the use of variational inference for the sparse spectrum approximation to avoid both issues. We model the covariance fu…