The paper proves learning-curve monotonicity for maximum likelihood estimators in various parametric settings.
problem Establishing monotonicity guarantees for maximum likelihood estimators.
method Variants of GPT-5.2 Pro were used to derive the results.
result The paper proves monotonicity for maximum likelihood estimators in Gaussian and Gamma variables.
Plotting a learner's average performance against the number of training samples results in a learning curve. Studying such curves on one or more data sets is a way to get to a better understanding of the generalization properties of this learner. The behavior of learning curves is, however, not very well understood and…
Learn2Evaluate uses learning curves to estimate high-dimensional prediction performance.
problem Estimating test performance in high-dimensional data settings is challenging.
method Learn2Evaluate uses learning curves to estimate test performance at the total sample size.
result Learn2Evaluate provides a lower confidence bound for performance estimation.
We use learning curves to analyze deep networks and evaluate model design.
problem Evaluate design choices in deep networks.
method Propose a method to robustly estimate learning curves, abstract their parameters, and evaluate different parameterizations.
result Interesting observations on the effectiveness of different parameterizations.
New model predicts neural network performance from early training epochs, incorporating architecture impact.
problem Predicting neural network performance from early training epochs, neglecting architecture impact.
method Architecture-aware graph ordinary differential equation model.
result Model outperforms state-of-the-art methods for MLP and CNN learning curves.
This work studies learning curves for revenue maximization algorithms.
problem Understanding the performance of revenue-maximizing algorithms as they learn from more data.
method Initiates the study of learning curves for revenue maximization, providing a near-complete characterization of their rate of decay.
result Learning curves for revenue maximization can decay arbitrarily slowly or almost exponentially fast, depending on the distribution and optimal revenue.
Efficiently models learning curves using Gaussian processes with latent Kronecker structure.
problem Joint modeling of machine learning model performance across hyper-parameters and training progress.
method Imposes latent Kronecker structure to leverage efficient product kernels and handle missing values.
result Matches the performance of a Transformer on a learning curve prediction task.
Learning curves show more data doesn't always improve performance.
problem The surprising finding that more data doesn't always lead to better generalization performance.
method A survey of learning curves, focusing on those that indicate more data doesn't necessarily improve performance.
result Learning curves can show that more data doesn't always lead to better generalization performance.
New method saves computational budget by ranking and transferring learning curves.
problem Expensive automated machine learning methods for hyperparameter and neural architecture optimization.
method Tackles as a ranking and transfer learning problem, optimizing a pairwise ranking loss and leveraging learning curves from other datasets.
result Accelerates neural architecture search by a factor of up to 100 without significant performance degradation.
LC-PFN predicts learning curve performance more accurately and faster than MCMC.
problem Bayesian extrapolation of learning curves is computationally expensive and overly restrictive.
method Prior-Data Fitted Neural Networks (PFNs) for approximate Bayesian inference.
result LC-PFN outperforms MCMC in accuracy and is significantly faster.
Study reveals learning curves and benign overfitting in spectral algorithms for large dimensions.
problem Understanding learning curves and benign overfitting in spectral algorithms for large-dimensional data.
method Analysis of learning curves and benign overfitting in spectral algorithms for inner-product kernels on the sphere and general domains.
result Characterization of three distinct regimes: over-regularized, under-regularized, and interpolation regimes, revealing benign overfitting across both under-regularized and interpolation regimes.
A meta-learning approach for efficient algorithm selection in budget-limited scenarios.
problem Efficiently selecting the best-performing machine learning algorithm with limited computational resources.
method A Markov Decision Process framework where an agent decides whether to train, wake up, or start new algorithms based on partial learning curves.
result Meta-learning from learning curves improves algorithm selection, especially when learning curves do not intersect frequently.
We propose probabilistic models that can extrapolate learning curves of iterative machine learning algorithms, such as stochastic gradient descent for training deep networks, based on training data with variable-length learning curves. We study instantiations of this framework based on random forests and Bayesian recur…
Develops a simple model to understand learning curves for arbitrary power laws.
problem Lack of theoretical understanding of scaling laws in machine learning.
method Analyzes a toy model to determine if learning curves are universal or depend on data distribution.
result Determines that learning curves can exhibit n−β for arbitrary power β>0. New combinatorial dimension VCL refines learning curve theory.
problem Explaining the behavior of learning curves for specific distributions.
method Introducing combinatorial dimension VCL to characterize strong minimax lower bounds.
result Learning rate can be decomposed into linear and exponential components.
Unified theory for neural scaling laws in hierarchically compositional data.
problem Understanding neural scaling laws in hierarchically compositional data.
method Probabilistic context-free grammars and power-law distributed production rules.
result Unified learning curve behavior for classification and next-token prediction tasks.
The paper analyzes learning curves for kernel ridge regression with dot-product kernels.
problem Understanding the learning curves for different scaling regimes of data and model.
method Precise formulas for mean test error, bias, and variance in the mo∞ with m/dr constant regime. result A peak in the learning curve at m≈dr/r! for any integer r. Slice Tuner optimizes data acquisition for accurate and fair machine learning models.
problem Acquiring enough data for all slices of data to ensure accurate and fair models.
method Selective data acquisition using convex optimization and iterative learning curve updates.
result Significantly outperforms baselines in model accuracy and fairness.
Theory and method for reducing prediction variance in noisy feature-subsampled ridge ensembles.
problem Reduction of prediction variance in noisy data with feature bagging.
method Developed analytical learning curves for noisy ridge ensembles, introduced heterogeneous feature ensembling.
result Subsampling shifts the double-descent peak, leading to improved performance over a single linear predictor.
New benchmarks provide full training data for NAS research.
problem Limited training data on popular benchmarks restricts multi-fidelity techniques.
method SVD and noise modeling to create surrogate benchmarks with full training info.
result Learning curve extrapolation framework improves single-fidelity algorithms.
We study the average case performance of multi-task Gaussian process (GP) regression as captured in the learning curve, i.e. the average Bayes error for a chosen task versus the total number of examples n for all tasks. For GP covariances that are the product of an input-dependent covariance function and a free-form …
We analyze learning curves of RF models with convex regularization and derive precise asymptotic expressions.
problem Understanding the learning curves of RF models with general convex regularization.
method Novel multi-level application of the convex Gaussian min max theorem (CGMT) to compute precise asymptotic expressions.
result Precise asymptotic expressions for learning curves of RF models with separable strongly convex regularization or ℓ1 regularization. We consider learning on graphs, guided by kernels that encode similarity between vertices. Our focus is on random walk kernels, the analogues of squared exponential kernels in Euclidean spaces. We show that on large, locally treelike, graphs these have some counter-intuitive properties, specifically in the limit of lar…
Study when to replace machine learning models with new data.
problem When to switch machine learning models with new data sources.
method Unified economic and statistical framework linking learning-curve dynamics, data-acquisition, and retraining costs.
result Look-ahead sequential method outperforms other methods and approaches optimal value.
Paper generalizes teacher-student model for realistic data.
problem Capturing learning curves for realistic datasets.
method Introduces a Gaussian covariate generalization of the teacher-student model.
result Generalized model captures learning curves for various realistic data sets.
Paper explores universal rates of ERM in machine learning.
problem Understanding universal learning rates for ERM.
method Analyzes realizable concept classes and ERM principles.
result Four possible universal learning rates by ERM.
The paper introduces a new learning model that explains practical aspects of machine learning.
problem Understanding how quickly a concept class can be learned from examples in practical scenarios.
method Introducing a new learning model that considers fixed data sources and varying number of training examples.
result There are only three possible rates of universal learning: exponential, linear, or arbitrarily slow.
New insights on how weight structure affects generalization in deep Gaussian feature models.
problem Understanding how weight structure impacts generalization in deep learning models.
method Using the replica trick from statistical physics to derive learning curves for models with structured Gaussian features.
result Allowing correlations between the rows of the first layer of features can aid generalization, while structure in later layers is generally detrimental.
Automated algorithm selection and hyperparameter tuning facilitates the application of machine learning. Traditional multi-armed bandit strategies look to the history of observed rewards to identify the most promising arms for optimizing expected total reward in the long run. When considering limited time budgets and c…
New study shows how model complexity affects test risk, challenging classical theory.
problem Understanding how test risk scales with model complexity for large over-parametrized deep networks.
method Developed norm-based capacity measures for random features based estimators, providing precise characterization of estimator's norm concentration and test error.
result Predicted learning curve shows a phase transition from under- to over-parameterization, confirming classical U-shaped behavior with appropriate capacity measures.
Locality helps in learning from high-dimensional data.
problem Understanding how convolutional neural networks learn from high-dimensional data.
method Teacher-student framework for kernel regression with convolutional kernels.
result Locality is key to determining the learning curve exponent in high-dimensional data.
For the supervised least squares classifier, when the number of training objects is smaller than the dimensionality of the data, adding more data to the training set may first increase the error rate before decreasing it. This, possibly counterintuitive, phenomenon is known as peaking. In this work, we observe that a s…
The study investigates how data variability impacts the generalization of neural networks.
problem Understanding the impact of data variability on neural network generalization.
method Developed a field-theoretic formalism to compute generalization properties of neural networks, focusing on data variability.
result Data variability leads to non-Gaussian action, affecting the learning curve and generalization properties of neural networks.
Inspired by the unsupervised learning or self-organization in the machine learning context, here we attempt to draw `learning curve' for the collective behavior of job-seeking `zero-intelligence' labors in successive job-hunting processes. Our labor market is supposed to be opened especially for university graduates in…
In biospectroscopy, suitably annotated and statistically independent samples (e. g. patients, batches, etc.) for classifier training and testing are scarce and costly. Learning curves show the model performance as function of the training sample size and can help to determine the sample size needed to train good classi…
The performance of deep neural networks (DNN) is very sensitive to the particular choice of hyper-parameters. To make it worse, the shape of the learning curve can be significantly affected when a technique like batchnorm is used. As a result, hyperparameter optimization of deep networks can be much more challenging th…
Unified analysis of generalization curves in large models using gradient flow.
problem Analyzing generalization error curves in simple learning models.
method Gradient flow in the Gaussian covariate model, using random matrix theory.
result Unified understanding of multiple descent structures in learning curves.
Statistical physics approaches can be used to derive accurate predictions for the performance of inference methods learning from potentially noisy data, as quantified by the learning curve defined as the average error versus number of training examples. We analyse a challenging problem in the area of non-parametric inf…
We use variational Gaussian approximations to analyze parametric models with unknown data-generating distributions.
problem Analyzing inference and learning in parametric models with unknown or intractable data-generating distributions.
method Replica method with variational Gaussian approximation in grand canonical formalism.
result Stationarity conditions adaptively determine parameters of the trial Hamiltonian for each dataset.
Online field experiments are the gold-standard way of evaluating changes to real-world interactive machine learning systems. Yet our ability to explore complex, multi-dimensional policy spaces - such as those found in recommendation and ranking problems - is often constrained by the limited number of experiments that c…
The recent advent of automated neural network architecture search led to several methods that outperform state-of-the-art human-designed architectures. However, these approaches are computationally expensive, in extreme cases consuming GPU years. We propose two novel methods which aim to expedite this optimization prob…
New algorithms improve performance guarantees for multi-armed bandits problems.
problem Allocating effort under uncertainty in scenarios like investing research effort.
method Proposed two new families of bandit algorithms with stronger guarantees.
result Achieved optimal dependence on k with additional properties of arm reward curves.
We introduce a new algorithm named WGAN, an alternative to traditional GAN training. In this new model, we show that we can improve the stability of learning, get rid of problems like mode collapse, and provide meaningful learning curves useful for debugging and hyperparameter searches. Furthermore, we show that the co…
MACE uses higher-order messages to create fast, accurate force fields.
problem Creating fast and accurate force fields in computational chemistry and materials science.
method Introducing MACE, an equivariant MPNN model that uses four-body messages.
result MACE reduces the required number of message passing iterations to just two, achieving state-of-the-art accuracy.
Study on neural networks' performance in sequential task learning.
problem Understanding the performance of neural networks in sequential task learning.
method Theoretical analysis of generalization performance in continual learning using statistical mechanical analysis of kernel ridge-less regression.
result Characteristic transitions from positive to negative transfer observed in neural networks.
Study finds that only a fraction of data is needed for accurate patient-level prediction models.
problem Developing predictive models for patient-level outcomes using large observational data.
method Empirical assessment of sample size effects on model performance and complexity using learning curves.
result A median reduction of 9.5% to 78.5% in the number of observations and 8.6% to 68.3% in the number of predictors can be achieved with adequate sample size.
Study derives error decay rates for kernel classification under source and capacity conditions.
problem Understanding prediction error decay rates for real data sets.
method Derived decay rates for misclassification error under Gaussian design for SVM and ridge classification.
result Rates accurately describe learning curves for data sets satisfying source and capacity conditions.
The paper addresses monotonicity in machine learning models for fairness and accountability.
problem Ensuring fairness and accountability in transparent machine learning models.
method Study of three types of monotonicity (individual, weak pairwise, strong pairwise) and propose monotonic groves of neural additive models.
result Monotonic groves of neural additive models maintain transparency, accountability, and fairness.