arXiv research

Productivity and credit limits affect aggregate production in non-monotonic ways.

Study derives new equation for reserves in non-monotone information scenarios.

New risk control method for non-monotonic losses in complex parameters.

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…

GradaGrad adapts learning rate non-monotonically, overcoming AdaGrad's step size decrease.

Study learns a neuron with non-monotonic activation functions.

Study shows rigidity for entropy minimizers in non-monotone cases.

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.

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…

FLOWGEM generates complete datasets from incomplete data with non-monotone MAR missingness.

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.

New algorithm maximizes non-monotone adaptive submodular functions in linear time.

Paper tackles non-monotonic resource utilization in sequential decision-making.

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…

New findings show privacy affects generalization error in a non-monotonic way.

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.

New method speeds up model selection for complex scientific tasks.

The paper analyzes Variable Annuities with surrender charges, providing a pricing formula and optimal exercise boundary.

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-…

Researchers propose a non-monotone quantum natural gradient for quantum systems.

The paper improves PCS approximation for ranking and selection under limited simulation budgets.

Insider trading is reduced when penalized, affecting expected penalties in a non-monotone way.

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…

New algorithms avoid non-monotonic risk curves in statistical learning.

Study tackles criterion collapse in learning criteria, showing conditions for loss minimization.

New method solves nonseparable stochastic control problems.

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…

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…

Paper tackles stochastic $k$-submodular bandits with full feedback, achieving sublinear regret.

The paper explores capital allocation using Euler formula with VaR and ES, revealing non-monotonicity and providing estimation methods.

New method tackles online DR-submodular maximization with improved regret guarantees.

Improved analysis of extragradient methods for structured VIPs.

Gradient descent on neural nets often operates at the Edge of Stability, where loss behavior is complex but loss decreases over time.

In this paper we consider backward stochastic differential equations with time-delayed generators of a moving average type. The classical framework with linear generators depending on $(Y(t),Z(t))$ is extended and we investigate linear generators depending on $(\frac{1}{t}\int_0^tY(s)ds, \frac{1}{t}\int_0^tZ(s)ds)$. We…

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 $h(q)$ -- the fundament…

Large stepsize GD for logistic regression converges faster than expected.

The paper develops algorithms to restore monotonicity in non-monotone functions.

We propose $\textit{Mish}$, a novel self-regularized non-monotonic activation function which can be mathematically defined as: $f(x)=x\tanh(softplus(x))$. As activation functions play a crucial role in the performance and training dynamics in neural networks, we validated experimentally on several well-known benchmarks…

Overview of high-dimensional dynamical systems and their applications to machine learning.

Gradient descent dynamics in quadratic regression models are analyzed, revealing five phases: monotonic, catapult, periodic, chaotic, and divergent.

DR-submodular continuous functions are important objectives with wide real-world applications spanning MAP inference in determinantal point processes (DPPs), and mean-field inference for probabilistic submodular models, amongst others. DR-submodularity captures a subclass of non-convex functions that enables both exact…

The number of trees T in the random forest (RF) algorithm for supervised learning has to be set by the user. It is controversial whether T should simply be set to the largest computationally manageable value or whether a smaller T may in some cases be better. While the principle underlying bagging is that "more trees a…

In this paper we consider a general matrix factorization model which covers a large class of existing models with many applications in areas such as machine learning and imaging sciences. To solve this possibly nonconvex, nonsmooth and non-Lipschitz problem, we develop a non-monotone alternating updating method based o…

In this paper we study the fundamental problems of maximizing a continuous non-monotone submodular function over the hypercube, both with and without coordinate-wise concavity. This family of optimization problems has several applications in machine learning, economics, and communication systems. Our main result is the…

Framework mitigates risk non-monotonicity in high-dimensional predictions.