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.
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…
We propose an algorithm for a family of optimization problems where the objective can be decomposed as a sum of functions with monotonicity properties. The motivating problem is optimization of hyperparameters of machine learning algorithms, where we argue that the objective, validation error, can be decomposed as mono…
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.
Paper establishes NE existence and efficient algorithms for weakly monotone GMFGs.
problem Existence and efficient learning of Nash Equilibrium in λ-regularized GMFGs. method Establishes existence of NE for any λ-regularized GMFGs. Proposes efficient algorithms for weakly monotone GMFGs. result Efficient algorithms for weakly monotone GMFGs with provable convergence.
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.
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 1/e−ε approximation ratio with O(nε−2logε−1) value oracle queries. Monotone adversarial corruptions degrade optimal learning algorithms.
problem Optimal learning algorithms' reliance on exchangeability and independence is challenged.
method Introduces a monotone adversarial corruption model where an adversary adds monotone corruptions to a clean dataset.
result Optimal learning algorithms achieve suboptimal expected error on new test points.
Paper tackles stochastic k-submodular bandits with full feedback, achieving sublinear regret.
problem Online optimization of k-submodular functions with full-bandit feedback. method Proposes online algorithms for various k-submodular stochastic combinatorial multi-armed bandit problems. result Achieves sublinear α-regret bounds for multiple k-submodular stochastic combinatorial multi-armed bandit problems. 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.
New algorithms solve monotone inclusions and convex-concave minimax problems.
problem Solving maximally monotone equations and inclusions.
method Developed new accelerated algorithms based on Halpern-type fixed-point iteration and Popov's past extra-gradient method.
result Achieved O(1/k) convergence rates for various problems. 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.
Efficient algorithms find optimal monotone transforms for calibration under strictly convex losses.
problem Calibrating estimations to improve performance with monotone transforms.
method Proposed linear-time and space algorithm for finding optimal monotone transforms for specific loss functions. Also proposed an anytime algorithm with linear space and pseudo-linearithmic time complexity.
result Optimal monotone transforms are unique and can be found efficiently for various strictly convex loss functions.
Monotonicity helps in safely optimizing unknown functions.
problem Sequentially maximizing an unknown function with safety constraints.
method Gaussian process with monotonicity assumption, inspired by GP-UCB and SafeOpt.
result The proposed M-SafeUCB algorithm achieves theoretical guarantees and safety.
When training data is sparse, more domain knowledge must be incorporated into the learning algorithm in order to reduce the effective size of the hypothesis space. This paper builds on previous work in which knowledge about qualitative monotonicities was formally represented and incorporated into learning algorithms (e…
Additive Gaussian process framework handles monotonicity constraints in high dimensions.
problem Handling monotonicity constraints in high-dimensional data.
method Additive Gaussian process framework with MaxMod algorithm for dimension reduction.
result Framework enables to satisfy monotonicity constraints everywhere in the input space.
In this paper, we consider first-order convergence theory and algorithms for solving a class of non-convex non-concave min-max saddle-point problems, whose objective function is weakly convex in the variables of minimization and weakly concave in the variables of maximization. It has many important applications in mach…
We prove that any arc-presentation of the unknot admits a monotonic simplification by elementary moves; this yields a simple algorithm for recognizing the unknot. We obtain similar results for split links and composite links.
Improved algorithms for convex-concave min-max optimization and monotone variational inequalities.
problem Efficiently solving constrained convex-concave min-max problems and monotone variational inequalities.
method Higher-order methods achieving iteration complexities of O(1/T^{ rac{p+1}{2}}) for p-th order derivatives.
result Achieved improved convergence rates for min-max and monotone variational inequalities.
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.
Non-affine aggregation rules cannot preserve monotonicity in convex learning.
problem Designing non-affine aggregation rules that maintain monotonicity in convex learning.
method Proving that monotonicity of aggregated gradients is preserved only if the aggregation rule is positively affine.
result Non-affine aggregation prevents steady convergence and substantially degrades algorithmic stability.
Paper investigates monotonicity issues in AI preference learning.
problem AI models may violate monotonicity when learning preferences.
method Investigates root causes of non-monotonicity in comparison-based preference learning.
result Proves local pairwise monotonicity under mild assumptions.
New models ensure monotonicity in preference learning, improving accuracy especially with limited data.
problem Failure of widely used preference learning models to maintain monotonicity.
method Proposed Linear Generalized Bradley-Terry models with Diffusion Priors.
result New models improve accuracy, especially with limited data.
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…
It is common to encounter large-scale monotone inclusion problems where the objective has a finite sum structure. We develop a general framework for variance-reduced forward-backward splitting algorithms for this problem. This framework includes a number of existing deterministic and variance-reduced algorithms for fun…
This paper analyzes and improves monotonic accelerated algorithms like M-NAG and M-FISTA.
problem Establishing linear convergence of M-NAG and M-FISTA under strong convexity.
method Lyapunov analysis and modified Lyapunov functions.
result Linear convergence of M-NAG and M-FISTA is guaranteed without full NAG iterates.
New method improves submodular maximization for machine learning applications.
problem Inexact monotonicity in submodular functions limits traditional algorithms' performance.
method Introduces monotonicity ratio as a continuous version of monotonicity, leading to improved approximation guarantees.
result Improved approximation ratios for movie recommendation, quadratic programming, and image summarization.
Differentially private algorithms for submodular maximization under various constraints.
problem Maximizing decomposable submodular functions under constraints while preserving privacy.
method Designing differentially private algorithms for both monotone and non-monotone decomposable submodular maximization under general matroid constraints.
result Improved utility guarantees and competitive performance compared to non-private algorithms.
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.
The paper addresses fairness issues in screening classifiers, proposing within-group monotonicity to avoid unfair treatment of qualified candidates.
problem Within-group unfairness in screening classifiers using calibrated models.
method Introducing within-group monotonicity as a property to avoid unfair treatment and developing an efficient post-processing algorithm based on dynamic programming.
result Within-group monotonicity can be achieved efficiently and often at a small cost, improving fairness without significantly compromising prediction accuracy.
New algorithm solves maximal monotone inclusion problems.
problem Solving maximal monotone inclusion problems.
method Bregman Douglas-Rachford splitting method and variants.
result Convergence of algorithms under certain assumptions.
Applications in machine learning, optimization, and control require the sequential selection of a few system elements, such as sensors, data, or actuators, to optimize the system performance across multiple time steps. However, in failure-prone and adversarial environments, sensors get attacked, data get deleted, and a…
Extends conformal prediction for controlling expected risk of monotone loss functions.
problem Controlling expected risk of monotone loss functions.
method Generalizes split conformal prediction with coverage guarantee, extending to distribution shift, quantile risk, multiple, adversarial, and expectations of U-statistics.
result Tight up to an O(1/n) factor, with worked examples in computer vision and natural language processing. We consider the learning algorithms under general source condition with the polynomial decay of the eigenvalues of the integral operator in vector-valued function setting. We discuss the upper convergence rates of Tikhonov regularizer under general source condition corresponding to increasing monotone index function. T…
A new algorithm finds minimizers in dueling optimization with a monotone adversary.
problem Finding minimizers in dueling optimization with a monotone adversary.
method Introduces and studies dueling optimization with a monotone adversary, designs an efficient randomized algorithm.
result Efficient algorithm incurs cost O(d) and iteration complexity O(dlog(1/ε)2), asymptotically optimal. Algorithm reduces regret in safe Bayesian optimization with monotonicity constraints.
problem Sequentially maximize unknown function with safety constraints.
method Sequential algorithms using Gaussian processes with safety constraints modeled as monotonicity.
result Sublinear regret achieved for expanding safe region and finding optimal s. A new stochastic primal--dual algorithm for solving a composite optimization problem is proposed. It is assumed that all the functions/operators that enter the optimization problem are given as statistical expectations. These expectations are unknown but revealed across time through i.i.d. realizations. The proposed al…
Survey of methods for solving smooth stochastic variational inequalities.
problem Solving smooth (strongly) monotone stochastic variational inequalities.
method Deterministic foundation, general stochastic formulation, finite sum setup, recent advances.
result Review of various methods for solving smooth stochastic variational inequalities.
Kleinberg introduced three natural clustering properties, or axioms, and showed they cannot be simultaneously satisfied by any clustering algorithm. We present a new clustering property, Monotonic Consistency, which avoids the well-known problematic behaviour of Kleinberg's Consistency axiom, and the impossibility resu…
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…
The paper tackles online learning problems with monotone arm sequences, achieving optimal or near-optimal regret bounds.
problem Online learning problems with ordinal and monotone arm sequences, such as dynamic pricing and clinical trials.
method Proposes algorithms for continuum-armed bandit problems with monotone arm sequences, achieving optimal or near-optimal regret bounds.
result Achieves optimal or near-optimal regret bounds for monotone arm sequences, differing from the continuous-armed bandit literature.
EPEM efficiently estimates parameters for monotone missing data.
problem Efficiently estimating parameters for monotone missing data.
method Derive exact formulas and propose EPEM algorithm for multiple class, monotone missing datasets.
result EPEM reduces error rates significantly and is faster than other methods.
New work shows FP potential monotonicity equals low-degree polynomial estimators limits.
problem Establishing a precise mathematical relationship between statistical physics and polynomial estimators limits.
method Analyzing Gaussian additive models (GAMs) to show FP potential monotonicity equals low-degree polynomial estimators limits.
result For a broad family of Gaussian additive models, the power of low-degree polynomials is equivalent to the monotonicity of the annealed FP potential.
Submodular functions have many applications. Matchings have many applications. The bitext word alignment problem can be modeled as the problem of maximizing a nonnegative, monotone, submodular function constrained to matchings in a complete bipartite graph where each vertex corresponds to a word in the two input senten…
Monotonic policy improvement and off-policy learning are two main desirable properties for reinforcement learning algorithms. In this paper, by lower bounding the performance difference of two policies, we show that the monotonic policy improvement is guaranteed from on- and off-policy mixture samples. An optimization …