Develops a two-level monotonic multistage recommender system for better user-specific prediction.
problem Leveraging user-item-stage dependencies in a monotonic chain of events for enhanced prediction accuracy.
method A multistage recommender system with a two-level monotonic property, using a large-margin classifier based on a nonnegative additive latent factor model.
result The proposed method outperforms existing methods in simulations and an article sharing dataset.
New analysis of annealing paths in sampling and estimation.
problem Sampling from complex distributions and estimating normalization constants.
method Extending known results on Bregman divergence to quasi-arithmetic means under monotonic embedding.
result Analogous result for quasi-arithmetic means, highlighting the interplay between means, parametric families, and divergence functionals.
Study on identifying AMP chain graph models under known and unknown component decompositions.
problem Identifying AMP chain graph models with known and unknown chain component decompositions.
method Analyzes conditions for identifiability of AMP models and proposes algorithms for structure recovery.
result Conditions for DAG identifiability in AMP models extend equal variance criteria for Bayes nets.
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.
New insights into stochastic methods for solving variational inequalities.
problem Understanding convergence behaviors of stochastic algorithms in variational inequalities.
method Re-casting SEG/SGDA as Markov Chains to analyze their probabilistic structures.
result The average iterate is asymptotically normal with a unique invariant distribution for various VIPs.
Monotonicity of normalized implied-volatility coordinates under no-arbitrage
problem Monotonicity of normalized implied-volatility coordinates under no-arbitrage
method Elementary discrete no-arbitrage proof
result Monotonicity principle extended to Bachelier implied volatility
Let (Mn,g) be simply connected, complete, with non-positive sectional curvatures, and Σ a 2-dimensional closed integral current (or flat chain mod 2) with compact support in M. Let S be an area minimising integral 3-current (resp. flat chain mod 2) such that ∂S=Σ. We use a weak mean curvature flow,…
We present a fully nonparametric method to estimate the value function, via simulation, in the context of expected infinite-horizon discounted rewards for Markov chains. Estimating such value functions plays an important role in approximate dynamic programming and applied probability in general. We incorporate "soft in…
GAttNHP predicts future events in temporal knowledge graphs by encoding long-range dependencies and handling mutual excitation.
problem Forecasting future events in temporal knowledge graphs due to long-range dependencies, mutual excitation, and heavy-tailed inter-arrival times.
method GAttNHP uses a self-attention encoder, semantic soft-grouping, and NCQ regression to address these issues.
result GAttNHP improves entity and time prediction on six benchmark TKG datasets compared to state-of-the-art baselines.
Stein variational gradient descent improves inference in Gaussian process models.
problem Inference in Gaussian process models with non-Gaussian likelihoods and large data volumes is computationally intensive and inaccurate with traditional methods.
method Stein variational gradient descent (SVGD) for non-parametric inference.
result SVGD monotonically decreases the Kullback-Leibler divergence from the sampling distribution to the true posterior.
We propose a new framework for how to use sequential Monte Carlo (SMC) algorithms for inference in probabilistic graphical models (PGM). Via a sequential decomposition of the PGM we find a sequence of auxiliary distributions defined on a monotonically increasing sequence of probability spaces. By targeting these auxili…
We consider the ability of deep neural networks to represent data that lies near a low-dimensional manifold in a high-dimensional space. We show that deep networks can efficiently extract the intrinsic, low-dimensional coordinates of such data. We first show that the first two layers of a deep network can exactly embed…
MLP residual networks implement a selective coarse-graining procedure governed by the spectral structure of the input distribution.
problem Understanding the coarse-graining procedure in MLP residual networks
method Analyzing a pure MLP residual stack on synthetic Markov chain sequences
result MLP residual networks implement a selective coarse-graining procedure governed by the spectral structure of the input distribution
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.
Introducing inequality constraints in Gaussian process (GP) models can lead to more realistic uncertainties in learning a great variety of real-world problems. We consider the finite-dimensional Gaussian approach from Maatouk and Bay (2017) which can satisfy inequality conditions everywhere (either boundedness, monoton…
Probit Monotone BART estimates binary outcomes using monotonic functions.
problem Estimating conditional mean functions for binary outcomes with monotonicity constraints.
method Proposes a new BART variant that incorporates monotonicity constraints for binary outcomes.
result Allows for more precise estimation of monotonic functions in binary outcome models.
Monotone neural networks can approximate and interpolate functions efficiently.
problem Understanding the efficiency and expressiveness of monotone neural networks.
method Solving the monotone interpolation problem using depth-4 networks and comparing size bounds with arbitrary networks.
result Monotone neural networks can approximate and interpolate functions efficiently, but may require exponential size in high dimensions.
Improves k-NN for monotonic data with robustness against noise.
problem Class noise in real-life data violates monotonic constraints in k-NN.
method Monotonic Fuzzy k-NN (MonFkNN) with new fuzzy membership calculation.
result Significant accuracy improvements and robustness against monotonic noise.
Let M be a weakly monotone symplectic manifold, and H be a time-dependent Hamiltonian; we assume that the periodic orbits of the corresponding time-dependent Hamiltonian vector field are non-degenerate. We construct a refined version of the Floer chain complex associated to these data and any regular covering of M, and…
Study examines explainable machine learning for monotonic models, finding Integrated gradients better for strong monotonicity.
problem Applying explainable machine learning to science-informed models.
method Proposed axioms for monotonicity, tested Shapley value and Integrated gradients methods.
result Integrated gradients provides better explanations for strong monotonicity.
Detects corruption in agentic models during execution.
problem Inconsistent context, retrieval errors, or adversarial inputs corrupt intermediate steps of reasoning chains.
method Analyzes token graphs induced by attention and computes spectral statistics to emit accept/reject signals.
result A single threshold on the high frequency energy ratio optimally detects context inconsistency in agentic models.
Formula proves monotonicity for anisotropic minimal hypersurfaces.
problem Understanding anisotropic minimal hypersurfaces.
method Proved a monotonicity formula under a sign assumption on the Minkowski norm.
result Monotonicity formula for anisotropic minimal hypersurfaces.
New example of manifolds with monotonic heat kernels found.
problem Understanding monotonicity of heat kernels on manifolds.
method Analyzing new examples and classifying flat tori.
result Generic metrics fail monotonicity at large times.
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.
problem Non-monotone solutions from heuristic algorithms need to be corrected.
method Develops algorithms to restore monotonicity with limited queries.
result Restores monotonicity while degrading the function value by at most ε.
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.
problem Enforcing monotonicity constraints in neural networks for real-world tasks.
method Counterexample-guided learning technique for ReLU neural networks.
result COMET achieves state-of-the-art results and improves model quality.
Monotonic differentiable sorting networks improve upon previous methods.
problem Non-monotonicity in differentiable sorting networks.
method Relaxation of conditional swap operations using sigmoid functions to ensure monotonicity.
result 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.
problem Monotonicity of parabolic frequency on manifolds.
method Analyzes parabolic frequency function on manifolds, proving monotonicity without curvature assumptions.
result Monotonicity of parabolic frequency on all manifolds, no curvature assumption needed.
Paper introduces algorithms for explaining monotonic classifiers.
problem Need for explanations of monotonic classifiers.
method Polynomial algorithms for formal explanations of monotonic classifiers.
result Efficient model-agnostic algorithm for enumerating explanations.
Develops monotone tree-based GAMI models using XGBoost.
problem Incorporating monotonicity into GAMI models based on boosted trees.
method Adapting XGBoost algorithm to fit monotone GAMI-Tree models, filtering interactions, and parsing results.
result Fits monotone GAMI-Tree models that are directly interpretable and visualizable.
The paper evaluates the importance of monotonicity in AI fairness across various fields.
problem Ensuring fairness in AI applications across criminology, education, health care, and finance.
method Theoretical reasoning, simulation, and extensive empirical analysis of monotonic neural additive models (MNAMs).
result Monotonicity is essential for fairness in AI ethics and society, especially in criminology, education, health care, and finance.
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.
problem Properties of biharmonic heat kernel and extrinsic biharmonic map heat flow.
method Derived an entropy type quantity exhibiting monotonicity behaviors.
result Monotonicity formula for extrinsic biharmonic map heat flow.
A local monotonicity formula for the Yang-Mills-Higgs flow on G-bundles over Rn (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.
problem Aligning machine learning model behavior with domain knowledge in credit risk.
method Benchmarked monotone-constrained versus unconstrained gradient boosting models across five datasets and three libraries, defining the Price of Monotonicity (PoM) as the relative change in AUC.
result Monotonicity constraints are almost costless on large datasets and most costly on smaller datasets, with PoM ranging from essentially zero to about 2.9 percent.
Study on pairwise counter-monotonicity, a type of negative dependence.
problem Understanding and quantifying extremal negative dependence structures.
method Established stochastic representation and invariance property; showed implications and connections.
result Pairwise counter-monotonicity implies negative association and joint mix dependence.
We propose a new framework for imposing monotonicity constraints in a Bayesian nonparametric setting based on numerical solutions of stochastic differential equations. We derive a nonparametric model of monotonic functions that allows for interpretable priors and principled quantification of hierarchical uncertainty. W…
Classical Hurwitz numbers count branched covers of the Riemann sphere with prescribed ramification data, or equivalently, factorisations in the symmetric group with prescribed cycle structure data. Monotone Hurwitz numbers restrict the enumeration by imposing a further monotonicity condition on such factorisations. In …
This paper introduces a novel monotone curve estimation framework based on convex duality.
problem Estimating smooth, continuous, and monotonic curves in data.
method Convex duality and optimal transport theories.
result Established statistical guarantees for monotone curve estimates.
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.
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.
In this paper we generalize the monotonicity formulas of [C] for manifolds with nonnegative Ricci curvature. Monotone quantities play a key role in analysis and geometry; see, e.g., [A], [CM1] and [GL] for applications of monotonicity to uniqueness. Among the applications here is that level sets of Green's function on …
The paper investigates quantitative rigidity using Colding's monotonicity formulas for Ricci curvature.
problem Quantifying rigidity in manifolds with nonnegative Ricci curvature.
method Investigates pinching of Colding's monotone functionals and constructs k-splitting functions. result Quantitative control of splitting functions by pinching at independent points controls the distance to the nearest cone.
We propose learning deep models that are monotonic with respect to a user-specified set of inputs by alternating layers of linear embeddings, ensembles of lattices, and calibrators (piecewise linear functions), with appropriate constraints for monotonicity, and jointly training the resulting network. We implement the l…
Investigates polar tangential angles of curves and their monotonicity.
problem Behavior of polar tangential angles of plane curves.
method Proof of monotonicity for certain curves of monotone curvature.
result Nonexistence results for an obstacle problem involving free elasticae.