arXiv research

Non-affine aggregation rules cannot preserve monotonicity in convex learning.

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

Monotone aggregation of dependent random vectors has an absolutely continuous distribution under certain conditions.

Study online monotone density estimation with expert aggregation and log-optimal calibration.

Develops a method to efficiently compute Wasserstein barycenters with variational distributions.

The paper examines the unexpected losses and risk ratios for co-monotonic alternatives in large portfolios.

CAOS aggregates multiple one-shot predictors for efficient uncertainty quantification.

Improves quantile regression models by aggregating multiple models.

Study causal inference under specific sampling methods with monotonicity assumptions.

The paper examines risk aggregation under mixtures of marginals, finding that more homogeneous distributions lead to larger uncertainty.

Learning new tasks with few samples using related task evaluations.

AEA dynamically aggregates ensemble targets for actor-critic learning.

The paper addresses fairness in online learning by extending auditing schemes and presenting efficient algorithms.

Learning the true ordering between objects by aggregating a set of expert opinion rank order lists is an important and ubiquitous problem in many applications ranging from social choice theory to natural language processing and search aggregation. We study the problem of unsupervised rank aggregation where no ground tr…

The paper studies risk-sharing allocations for risk-seeking agents using a common distortion risk measure.

We propose a data aggregation-based algorithm with monotonic convergence to a global optimum for a generalized version of the L1-norm error fitting model with an assumption of the fitting function. The proposed algorithm generalizes the recent algorithm in the literature, aggregate and iterative disaggregate (AID), whi…

This study examines how financial tick data becomes more random with time aggregation.

The financial crisis has dramatically demonstrated that the traditional approach to apply univariate monetary risk measures to single institutions does not capture sufficiently the perilous systemic risk that is generated by the interconnectedness of the system entities and the corresponding contagion effects. This has…

We propose learning flexible but interpretable functions that aggregate a variable-length set of permutation-invariant feature vectors to predict a label. We use a deep lattice network model so we can architect the model structure to enhance interpretability, and add monotonicity constraints between inputs-and-outputs.…

Framework for online resource allocation using social welfare functions.

New method improves transductive learning predictions with multiplicative oracle inequalities.

LOO prediction method improves generalization guarantees for arbitrary datasets.

This paper considers a simulation-based estimator for a general class of Markovian processes and explores some strong consistency properties of the estimator. The estimation problem is defined over a continuum of invariant distributions indexed by a vector of parameters. A key step in the method of proof is to show the…

The paper addresses monotonicity in machine learning models for fairness and accountability.

Individual risk models need to capture possible correlations as failing to do so typically results in an underestimation of extreme quantiles of the aggregate loss. Such dependence modelling is particularly important for managing credit risk, for instance, where joint defaults are a major cause of concern. Often, the d…

Probit Monotone BART estimates binary outcomes using monotonic functions.

CB-APM uses analyst consensus as a bottleneck to interpret stock returns.

Monotone neural networks can approximate and interpolate functions efficiently.

Improves k-NN for monotonic data with robustness against noise.

Study examines explainable machine learning for monotonic models, finding Integrated gradients better for strong monotonicity.

Formula proves monotonicity for anisotropic minimal hypersurfaces.

New example of manifolds with monotonic heat kernels found.

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…

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

Nonnegative matrix factorization (NMF) factorizes a non-negative matrix into product of two non-negative matrices, namely a signal matrix and a mixing matrix. NMF suffers from the scale and ordering ambiguities. Often, the source signals can be monotonous in nature. For example, in source separation problem, the source…

In [S. Basu, A. Gabrielov, N. Vorobjov, Semi-monotone sets. arXiv:1004.5047v2 (2011)] we defined semi-monotone sets, as open bounded sets, definable in an o-minimal structure over the reals, and having connected intersections with all translated coordinate cones in R^n. In this paper we develop this theory further by d…

COMET learns monotonic neural networks by incorporating counterexamples.

Monotonic differentiable sorting networks improve upon previous methods.

We prove three new monotonicity formulas for manifolds with a lower Ricci curvature bound and show that they are connected to rate of convergence to tangent cones. In fact, we show that the derivative of each of these three monotone quantities is bounded from below in terms of the Gromov-Hausdorff distance to the neare…

Proves monotonicity of parabolic frequency on all manifolds without curvature assumptions.

Paper introduces algorithms for explaining monotonic classifiers.

Develops monotone tree-based GAMI models using XGBoost.

The paper evaluates the importance of monotonicity in AI fairness across various fields.

We introduce large scale analogues of topological monotone and light maps, which we call coarsely monotone and coarsely light maps respectively. We show that these two classes of maps constitute a factorization system on the coarse category. We also show how coarsely monotone maps arise from a reflection in a similar w…

Study on biharmonic map heat flow with monotonicity formula.

The ERI is a new index for measuring exam readiness.

A local monotonicity formula for the Yang-Mills-Higgs flow on $G$-bundles over $\mathbb{R}^{n}$ ($n>4$) is proved. It is shown that the monotone quantity coïncides on certain self-similar solutions with that appearing in existing non-local monotonicity formulæ for the Yang-Mills and Yang-Mills-Higgs flows.

This paper benchmarks monotone-constrained models for credit PD across datasets and finds constraints are mostly costless.