Learning performance can show non-monotonic behavior. That is, more data does not necessarily lead to better models, even on average. We propose three algorithms that take a supervised learning model and make it perform more monotone. We prove consistency and monotonicity with high probability, and evaluate the algorit…
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48 results for “non-monotonic behavior”
New algorithms avoid non-monotonic risk curves in statistical learning.
problem Non-monotonic behavior of risk curves in statistical learning.
method Derive risk-monotonic algorithms under weak assumptions.
result Risk monotonicity does not necessarily lead to worse excess risk rates.
We present a heuristic based algorithm to induce \textit{nonmonotonic} logic programs that will explain the behavior of XGBoost trained classifiers. We use the technique based on the LIME approach to locally select the most important features contributing to the classification decision. Then, in order to explain the mo…
Gradient descent on neural nets often operates at the Edge of Stability, where loss behavior is complex but loss decreases over time.
problem Understanding the optimization dynamics of neural networks at the Edge of Stability.
method Empirical demonstration of gradient descent behavior in neural network training.
result Gradient descent on neural networks typically occurs at the Edge of Stability, where loss behavior is non-monotonic but loss decreases over time.
The paper improves PCS approximation for ranking and selection under limited simulation budgets.
problem Improving finite sample performance in Ranking and Selection.
method Develops a Bahadur-Rao type expansion for PCS, proposes a novel FCBA policy.
result FCBA policy achieves superior PCS performance compared to traditional methods.
Empirical time series of inter-event or waiting times are investigated using a modified Multifractal Detrended Fluctuation Analysis operating on fluctuations of mean detrended dynamics. The core of the extended multifractal analysis is the non-monotonic behavior of the generalized Hurst exponent -- the fundament…
New findings show privacy affects generalization error in a non-monotonic way.
problem Privacy and robustness in distributed learning.
method Theoretical analysis and matching lower/upper bounds on algorithmic stability.
result Generalization error is non-monotonically affected by privacy, depending on noise level.
Framework mitigates risk non-monotonicity in high-dimensional predictions.
problem Risk non-monotonicity in high-dimensional predictions.
method Model-agnostic framework using cross-validation and data-driven methodologies (zero- and one-step).
result Modified prediction procedures achieve monotonic asymptotic risk behavior.
Productivity and credit limits affect aggregate production in non-monotonic ways.
problem Understanding how aggregate production is influenced by individual characteristics and financial constraints.
method Analytical proof of non-monotonic effects of productivity and credit limits on aggregate production in a general equilibrium model.
result Equilibrium aggregate production can be non-monotonic in both individual productivity and credit limit.
Study derives new equation for reserves in non-monotone information scenarios.
problem Modeling reserves in situations where information is not always increasing.
method Infinitesimal approach to derive generalized stochastic Thiele equation.
result New equation allows for information discarding and solves open problems.
New risk control method for non-monotonic losses in complex parameters.
problem Controlling risk for non-monotonic losses with multidimensional parameters.
method Stability-based guarantees for generic algorithms applied to non-monotonic losses.
result Guarantees depend on algorithm stability, with looser guarantees for unstable algorithms.
GradaGrad adapts learning rate non-monotonically, overcoming AdaGrad's step size decrease.
problem Fixed learning rate in AdaGrad leads to step size decrease over time.
method Introduces GradaGrad, which grows or shrinks the learning rate based on a different accumulation in the denominator.
result GradaGrad achieves similar convergence rates as AdaGrad and demonstrates non-monotone adaptation.
Study learns a neuron with non-monotonic activation functions.
problem Learning a single neuron with non-monotonic activation functions.
method Gradient descent (GD) with conditions on activation function and input distribution.
result Learnability of non-monotonic activation functions is established without monotonicity assumption.
We propose , a novel self-regularized non-monotonic activation function which can be mathematically defined as: . As activation functions play a crucial role in the performance and training dynamics in neural networks, we validated experimentally on several well-known benchmarks…
New insights into Nadaraya-Watson interpolators show varied generalization behaviors.
problem Understanding generalization of interpolating predictors, especially in noisy data.
method Revisiting Nadaraya-Watson estimator with a single hyperparameter.
result Multiple overfitting behaviors exist, ranging from catastrophic to tempered.
Study shows rigidity for entropy minimizers in non-monotone cases.
problem Rigidity of entropy minimizers in non-monotone settings.
method Elementary proofs in non-monotone situations.
result Showed rigidity for minimizers of generalized Colding-Minicozzi entropies.
Diminishing-returns (DR) submodular optimization is an important field with many real-world applications in machine learning, economics and communication systems. It captures a subclass of non-convex optimization that provides both practical and theoretical guarantees. In this paper, we study the fundamental problem of…
Study non-monotonic loss functions in CRC, achieving valid risk control with large calibration samples.
problem Non-monotonic loss functions in CRC, violating existing theory's monotonicity assumption.
method Finite grid selection, calibration sample size analysis, Lipschitz continuity, monotonicity, distribution shift.
result Valid CRC achieved with large calibration samples, optimal excess risk rate of .
The information dynamics in finance and insurance applications is usually modeled by a filtration. This paper looks at situations where information restrictions apply such that the information dynamics may become non-monotone. A fundamental tool for calculating and managing risks in finance and insurance are martingale…
Generative Modeling under Non-Monotone MAR Missingness via Approximate Wasserstein Gradient Flowsstat.ML
FLOWGEM generates complete datasets from incomplete data with non-monotone MAR missingness.
problem Dealing with non-monotone Missing at Random (MAR) missingness in data.
method Iterative particle evolution of Wasserstein Gradient Flow, approximated by local linear estimators of density ratio.
result FLOWGEM achieves state-of-the-art performance across various settings, including non-monotone MAR mechanisms.
In this work we construct Calabi quasi-morphisms on the universal cover of the group Ham(M) of Hamiltonian diffeomorphisms for some non-monotone symplectic manifolds. This complements a result by Entov and Polterovich which applies in the monotone case. Moreover, in contrast to their work, we show that these quasi-morp…
Study finds non-monotonic Value of Information in dynamic multi-market monopoly.
problem Investigates non-monotonicity in Value of Information for a price-setting monopolist.
method Uses a Bayesian inverse problem with Kalman-Bucy-Stratonovich filter in a dynamic discrete model.
result Non-monotonic relationship between signal variance and Value of Information.
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…
Disordered Dynamics in High Dimensions: Connections to Random Matrices and Machine Learningcond-mat.dis-nn
Overview of high-dimensional dynamical systems and their applications to machine learning.
problem Characterizing behavior of high-dimensional dynamical systems driven by random matrices.
method Cavity method arguments, path integrals, dynamical mean field theory (DMFT), and random matrix resolvents.
result Connections between random matrix resolvents and DMFT response, and non-monotonic loss curves in training.
New algorithm maximizes non-monotone adaptive submodular functions in linear time.
problem Maximizing non-monotone adaptive submodular functions subject to a cardinality constraint.
method Developed a linear-time algorithm for non-monotone adaptive submodular maximization.
result Achieved a approximation ratio with value oracle queries.
Adapts safe policies for exploration in high-risk settings.
problem Balancing safety and exploration in high-risk environments.
method Uses conformal calibration on a safe reference policy to determine aggressive action limits.
result Safe exploration improves performance without requiring model class identification or hyperparameter tuning.
Paper tackles non-monotonic resource utilization in sequential decision-making.
problem Sequential decision-making under uncertainty with resource constraints.
method Introduces a new MDP policy with constant regret against LP relaxation.
result Develops a learning algorithm with logarithmic regret for unknown outcome distributions.
In this paper, we study fundamental problems of maximizing DR-submodular continuous functions that have real-world applications in the domain of machine learning, economics, operations research and communication systems. It captures a subclass of non-convex optimization that provides both theoretical and practical guar…
A mathematical analysis of the distribution of voting power in the Council of the European Union operating according to the Treaty of Lisbon is presented. We study the effects of Brexit on the voting power of the remaining members, measured by the Penrose--Banzhaf Index. We note that the effects in question are non-mon…
Study on MMV in jump-diffusion models resolves MV's non-monotonicity issues.
problem Non-monotonicity and free cash flow stream problems in MV preferences.
method Explicit solution for MMV preferences in jump-diffusion models, proving non-negative potential measures.
result MMV resolves MV's non-monotonicity and free cash flow stream issues.
New method speeds up model selection for complex scientific tasks.
problem Exhaustive model selection is computationally infeasible for large model spaces.
method Branch-and-bound algorithm with non-monotonic criteria.
result Guaranteed identification of optimal models with significant computational speedups.
The paper analyzes Variable Annuities with surrender charges, providing a pricing formula and optimal exercise boundary.
problem Analyzing Variable Annuities with surrender charges and early termination rights.
method Formulated as an optimal stopping problem with a discontinuous payoff, non-monotonic optimal stopping boundaries are proven continuous and regular.
result A rigorous pricing formula and optimal exercise boundary for surrender options are derived.
Study optimal control strategy for hedge funds managers with PSAHARA utility family.
problem Optimizing risk and reward in incomplete markets with non-monotone risk aversion and convex compensation.
method Introduced PSAHARA utility family to model non-monotone risk aversion and convex compensation. Proved concavification techniques for non-concave utility functions. Derived explicit optimal control strategy.
result PSAHARA utility induces risk-taking behavior even with convex compensation, leading to high returns and volatility.
We propose non-stationary spectral kernels for Gaussian process regression. We propose to model the spectral density of a non-stationary kernel function as a mixture of input-dependent Gaussian process frequency density surfaces. We solve the generalised Fourier transform with such a model, and present a family of non-…
Neural networks generalize well despite overfitting due to high capacity.
problem Understanding why deep neural networks generalize well in overparameterized settings.
method High-dimensional asymptotic analysis of generalization under kernel regression with Neural Tangent Kernel.
result Test error exhibits non-monotonic behavior and can have additional peaks and descents in the overparameterized regime.
Researchers propose a non-monotone quantum natural gradient for quantum systems.
problem Applying natural gradient methods to quantum systems without monotonicity.
method Introducing a non-monotone quantum natural gradient (QNG) and demonstrating its superiority over conventional QNG.
result Non-monotone QNG outperforms conventional QNG in terms of convergence speed.
Insider trading is reduced when penalized, affecting expected penalties in a non-monotone way.
problem Reducing insider trading behavior when insiders face legal penalties.
method Characterized via a backward stochastic differential equation (BSDE) with a non-linear operator.
result The insider's expected penalties are non-monotone in the fee structure and determined by relative entropy.
The theory of monotone Riemannian metrics on the state space of a quantum system was established by Denes Petz in 1996. In a recent paper he argued that the scalar curvature of a statistically relevant - monotone - metric can be interpreted as an average statistical uncertainty. The present paper contributes to this su…
New insights into how randomization affects greedy model selection.
problem Understanding the impact of feature subsampling on greedy model selection.
method Investigated greedy forward selection with feature subsampling, proving effects on bias and variance.
result Ensembling with feature subsampling reduces both bias and variance, unlike convex base learners.
Induction of Non-Monotonic Rules From Statistical Learning Models Using High-Utility Itemset Miningcs.LG
We present a fast and scalable algorithm to induce non-monotonic logic programs from statistical learning models. We reduce the problem of search for best clauses to instances of the High-Utility Itemset Mining (HUIM) problem. In the HUIM problem, feature values and their importance are treated as transactions and util…
Deep learning models can have low bias and variance, contrary to classical theory.
problem Understanding the performance of deep learning models at high complexity.
method Developed a fine-grained bias-variance decomposition for random feature kernel regression, analyzing the effects of sampling, initialization, and labels.
result The variance terms exhibit non-monotonic behavior and can diverge at the interpolation boundary, even in the absence of label noise.
Study tackles criterion collapse in learning criteria, showing conditions for loss minimization.
problem Criterion collapse in optimization, focusing on error probability minimizers.
method Analyzes various learning criteria, including DRO, OCE risks, and non-monotonic criteria.
result Non-monotonic criteria can avoid collapse, while monotonic ones cannot.
New method solves nonseparable stochastic control problems.
problem Nonseparable and non-monotonic stochastic control problems.
method Scenario-decomposition solution framework using progressive hedging algorithm.
result Extends reach of stochastic optimal control.
Standard sequential generation methods assume a pre-specified generation order, such as text generation methods which generate words from left to right. In this work, we propose a framework for training models of text generation that operate in non-monotonic orders; the model directly learns good orders, without any ad…
Study privacy and accuracy in high-dimensional LASSO with perturbation mechanisms.
problem Privacy-preserving sparse linear regression in high dimensions.
method Analyzes output and objective perturbation mechanisms using AMP.
result Sparsity affects privacy-accuracy trade-off; stronger regularization improves privacy.
Paper tackles stochastic -submodular bandits with full feedback, achieving sublinear regret.
problem Online optimization of -submodular functions with full-bandit feedback.
method Proposes online algorithms for various -submodular stochastic combinatorial multi-armed bandit problems.
result Achieves sublinear -regret bounds for multiple -submodular stochastic combinatorial multi-armed bandit problems.
The paper explores capital allocation using Euler formula with VaR and ES, revealing non-monotonicity and providing estimation methods.
problem Non-monotonicity in VaR-based capital allocation and the need for consistent risk measures.
method Use of Euler formula, Value-at-Risk (VaR), Expected shortfall (ES), simulation, and Markov chain Monte Carlo.
result Capital allocation with VaR is not monotonous, and consistent risk measures are crucial.
Upper-Linearizability of Online Non-Monotone DR-Submodular Maximization over Down-Closed Convex Setscs.LG
New method tackles online DR-submodular maximization with improved regret guarantees.
problem Online maximization of non-monotone DR-submodular functions over down-closed convex sets.
method 1/e-linearization through exponential reparametrization, surrogate potential, and reduction to online linear optimization.
result Achieves static regret with single gradient query per round, improving state of the art.