Learning ReLU networks to high uniform accuracy requires exponentially many samples.
problem Achieving high uniform accuracy on ReLU networks for security-critical applications.
method Quantified the number of training samples needed for any algorithm to guarantee uniform accuracy.
result The minimal number of training samples scales exponentially with network depth and input dimension.
Linear cost method approximates Gaussian Matérn processes with exponentially convergent accuracy.
problem High computational cost for Gaussian process inference and prediction.
method Optimal rational approximation of spectral density for Gaussian processes on bounded intervals.
result Exponential decrease in covariance error with increasing order of approximation.
We consider a standard binary classification problem. The performance of any binary classifier based on the training data is characterized by the excess risk. We study Bahadur's type exponential bounds on the minimax accuracy confidence function based on the excess risk. We study how this quantity depends on the comple…
Paper evaluates squared-exponential covariance function for Gaussian processes with integral observations.
problem Evaluating double line integrals of the squared exponential covariance function in Gaussian processes.
method Proposes a new approach to reduce double integrals to a single integral using the error function and efficiently computed with numerical techniques.
result Shows superior numerical robustness and accuracy compared to existing methods.
The paper explores the limits of deep neural networks in approximating various function classes.
problem Characterizing the limits of deep neural networks in function approximation.
method Develops a theory relating function complexity and network complexity, using Kolmogorov complexity.
result Deep networks are optimal approximants for various function classes and provide exponential approximation accuracy.
Tensor networks improve integration accuracy for high-dimensional problems.
problem Integration of high-dimensional functions with exponential convergence.
method Regression-free tensor network representations for integration.
result Exponential convergence achieved for non-analytic integrands.
A new topology improves decentralized learning efficiency and accuracy.
problem Finding efficient decentralized learning topologies with fast consensus and low maximum degree.
method Proposed the Base-(k+1) Graph topology for decentralized learning. result The Base-(k+1) Graph enables faster convergence and better communication efficiency than the exponential graph. Efficient method for learning continuous exponential families beyond Gaussian.
problem Learning continuous exponential families with unbounded support.
method Interaction Screening approach for scalable learning of continuous graphical models.
result Our estimator maintains similar accuracy and sample complexity scalings compared to alternative approaches, while improving run-time.
We present and test a sequential learning algorithm for the short-term prediction of human mobility. This novel approach pairs the Exponential Weights forecaster with a very large ensemble of experts. The experts are individual sequence prediction algorithms constructed from the mobility traces of 10 million roaming mo…
Develops a semi-supervised learning method using exponential tilt mixture models.
problem Improves classification accuracy with labeled and unlabeled data.
method Extends logistic regression to exponential tilt modeling, derives maximum likelihood estimation, and proposes regularized estimation.
result Demonstrates improved prediction accuracy compared to existing methods.
High-dimensional neural network manifolds misalign with human perception, causing adversarial examples.
problem Adversarial attacks fool neural networks, but their origin is unclear.
method Defined and analyzed a network's perceptual manifold (PM) for a class concept.
result Neural network PMs have orders of magnitude higher dimensions than natural human concepts, suggesting exponential misalignment.
Optimizes embedding accuracy for data variance and error.
problem Efficiently embedding data while minimizing distortion.
method Uses Johnson-Lindenstrauss embeddings with orthogonal matrices and singular-value latent variables.
result Achieves best accuracy in variance, mean-squared error, and length distortion.
Improved Gibbs sampler speeds up Bayesian exponential smoothing model.
problem Computational inefficiency of original NUTS sampler.
method Modifications to the original model and a bespoke Gibbs sampler.
result Significant improvement in sampling time by an order of magnitude.
We consider the problem of learning a forest of nonlinear decision rules with general loss functions. The standard methods employ boosted decision trees such as Adaboost for exponential loss and Friedman's gradient boosting for general loss. In contrast to these traditional boosting algorithms that treat a tree learner…
EFDA extends LDA to non-Gaussian models using exponential families.
problem Classifying non-Gaussian data with LDA's limitations.
method EFDA uses exponential families to derive closed-form estimators for natural parameters and a linear decision rule.
result EFDA matches LDA's accuracy while reducing ECE by 2-6x, proving asymptotic calibration and efficiency.
Methodology selects best activation functions for DNN layers.
problem Challenging to choose the best activation function for each DNN layer.
method Identifies Evaluation Points and dropout rates for each layer.
result Average 7% to 15% Relative Error Reduction on benchmarks.
A new method for estimating sparse inverse covariance matrices.
problem Recovering the connectivity and non-connectivity graph of covariates.
method Adaptive thresholding in a transformed domain of the inverse covariance matrix.
result The proposed method outperforms state-of-the-art methods in accuracy.
Greedy pruning reduces neural networks by a logarithmic number of tickets, improving accuracy.
problem Pruning large neural networks to reduce size while maintaining accuracy.
method Greedy optimization-based pruning method with exponential decay guarantee.
result The discrepancy between pruned and original networks decays exponentially with network size.
Paper proposes a new e-exponentiated transformation to make convex loss functions more robust to outliers.
problem Making convex loss functions robust to outliers in the presence of label noise.
method Introduces a novel e-exponentiated transformation for loss functions and proves its effectiveness through theoretical and empirical analysis. result The transformed loss function achieves tighter generalization error bounds and higher accuracy in noisy datasets.
Study reveals how initialization scale affects training accuracy in linear networks.
problem Understanding implicit bias in linear classification models.
method Asymptotic analysis of gradient flow trajectories and training loss minimization.
result Implicit bias is more complex at reasonable initialization scales and training accuracies.
Quantum algorithm speeds up learning from big data exponentially.
problem Scalable learning from big data with optimized random features.
method Quantum algorithm for sampling optimized random features.
result Exponential speedup in runtime compared to classical algorithms.
The accuracy of least squares calibration using option premiums and particle filtering of price data to find model parameters is determined. Derivative models using exponential Lévy processes are calibrated using regularized weighted least squares with respect to the minimal entropy martingale measure. Sequential impor…
Proposes a new classification model using extended exponential functions.
problem Improving classification accuracy in binary linear classification problems.
method Developed a Bregman-Tweedie classification model based on extended exponential functions.
result The H-Bregman and L-Bregman sub-models outperform traditional methods in ranking and classification accuracy.
Probabilistic solvers improve stability for stiff systems.
problem Performance penalties for small steps in stiff systems.
method Probabilistic exponential integrators that include fast linear dynamics in the prior.
result Proven L-stability and probabilistic error accounting.
New CFNN architecture approximates functions with machine accuracy.
problem Function approximation with high precision.
method Chebyshev Feature Neural Network (CFNN) with learnable frequencies.
result Achieves machine accuracy in function approximation.
Study compares local and global models for hierarchical forecasting accuracy.
problem Challenges in hierarchical time series forecasting, especially in accuracy and information utilisation.
method Developed and evaluated local and global forecasting models (GFMs) to exploit cross-series and cross-hierarchies information.
result Global Forecasting Models (GFMs) outperform local models in hierarchical forecasting accuracy and computational efficiency.
AUC (area under ROC curve) is an important evaluation criterion, which has been popularly used in many learning tasks such as class-imbalance learning, cost-sensitive learning, learning to rank, etc. Many learning approaches try to optimize AUC, while owing to the non-convexity and discontinuousness of AUC, almost all …
We show that there is a simple (approximately radial) function on Rd, expressible by a small 3-layer feedforward neural networks, which cannot be approximated by any 2-layer network, to more than a certain constant accuracy, unless its width is exponential in the dimension. The result holds for virtually all kn…
Efficiently learns exponential family distributions with i.i.d. samples.
problem Learning natural parameters of truncated exponential families efficiently.
method Proposes a novel loss function and computationally efficient estimator.
result Achieves optimal sample complexity and asymptotic normality.
Novel method for estimating currency option parameters with improved accuracy.
problem Improving currency option pricing accuracy and calibration process.
method Develops approximate formulas for two parameters in stochastic volatility models with exponentially-affine characteristic functions.
result Superior accuracy in parameter estimation for currency options.
The aim of this work is to provide fast and accurate approximation schemes for the Monte Carlo pricing of derivatives in LIBOR market models. Standard methods can be applied to solve the stochastic differential equations of the successive LIBOR rates but the methods are generally slow. Our contribution is twofold. Firs…
Optimal estimator for discrete distributions from faulty batches.
problem Estimating discrete distributions from batches, some of which may be unreliable.
method First polynomial-time estimator achieving optimal accuracy in number of batches.
result Optimal estimation accuracy in polynomial time.
Proves depth 2 neural networks can't approximate certain functions as well as depth 3 networks.
problem Approximating functions with depth 2 networks in high dimensions.
method Lower bound proof using worst-to-average-case random self-reducibility.
result Proves depth 2 networks can't approximate certain functions as well as depth 3 networks, resolving an open problem.
Sparse attention model reduces long-context inference time with exponential accuracy guarantees.
problem Efficiently processing long-context queries in large language models.
method Formalizes attention as a projection onto key vectors, analyzes entropic relaxation, and introduces Vashista Sparse Attention.
result Sparse attention concentrates on a constant-size active face, leading to exponential decay of inactive tokens' mass and linear scaling of active face error.
New ensemble method improves model stability exponentially.
problem Improving model stability for discontinuous base learners.
method Selecting the most frequently generated model from subsamples.
result Exponentially decaying tails for excess risk.
Many fits of Hawkes processes to financial data look rather good but most of them are not statistically significant. This raises the question of what part of market dynamics this model is able to account for exactly. We document the accuracy of such processes as one varies the time interval of calibration and compare t…
Greedy AutoAugment improves accuracy with less computation.
problem Finding effective data augmentation policies to cover the search space.
method Greedy approach to reduce the number of trials from exponential to linear growth.
result Greedy AutoAugment increases accuracy by 360 times with fewer resources.
This paper operationalizes the Exponential Mechanism using Normalizing Flows for private optimization.
problem Improving privacy in machine learning while maintaining accuracy and efficiency.
method Using Normalizing Flows to approximate sampling from the Exponential Mechanism for private optimization.
result ExpM+NF provides more privacy than non-private SGD but not as much as DPSGD.
We analyze how an observer synchronizes to the internal state of a finite-state information source, using the epsilon-machine causal representation. Here, we treat the case of exact synchronization, when it is possible for the observer to synchronize completely after a finite number of observations. The more difficult …
Mean Field Variational Bayes (MFVB) is a popular posterior approximation method due to its fast runtime on large-scale data sets. However, it is well known that a major failing of MFVB is its (sometimes severe) underestimates of the uncertainty of model variables and lack of information about model variable covariance.…
We propose a novel probabilistic method for detection of objects in noisy images. The method uses results from percolation and random graph theories. We present an algorithm that allows to detect objects of unknown shapes in the presence of random noise. The algorithm has linear complexity and exponential accuracy and …
Paper proposes GEG to enhance fairness in binary and multi-class classification.
problem Fairness in multi-class classification tasks is under-explored.
method Formulates multi-objective problem between effectiveness and fairness constraints, proposes GEG algorithm.
result GEG improves fairness up to 92% and decreases accuracy up to 14%.
We present a theoretical analysis of Maximum a Posteriori (MAP) sequence estimation for binary symmetric hidden Markov processes. We reduce the MAP estimation to the energy minimization of an appropriately defined Ising spin model, and focus on the performance of MAP as characterized by its accuracy and the number of s…
Bayesian approach generalizes ADMM for federated learning.
problem Improving federated learning efficiency and accuracy.
method Integrates Bayesian duality with ADMM for optimization.
result New extensions of ADMM for various distributions.
New bounds on majority voting's accuracy for multi-class classification problems.
problem Determining the accuracy of majority voting for multi-class classification.
method Analyzing the majority voting function under different voter conditions and distributions.
result The error rate of majority voting exponentially decays or grows with the number of voters under certain conditions.
VISTA learns causal structures by integrating local subgraphs, improving accuracy and efficiency.
problem Efficiently learning causal structures from high-dimensional observational data.
method VISTA decomposes the global causal structure learning problem into local subgraphs based on Markov Blankets, integrating them via a weighted voting mechanism.
result VISTA achieves notable improvements in accuracy and efficiency over existing methods.
A deep network classifies images by scattering and dictionary learning.
problem Classifying images with high accuracy using deep learning.
method Sparse scattering transform followed by ℓ1 dictionary learning in a deep convolutional network. result Higher classification accuracy than AlexNet on ImageNet dataset.
The paper proposes a method to optimize rule-based models for better accuracy and interpretability.
problem Developing rule-based models for regression and classification with better accuracy and interpretability.
method Column generation to optimize over an exponentially large space of rules, using integer programming or a heuristic.
result The proposed methods achieve better accuracy-complexity trade-offs than existing rule ensemble algorithms.