Study optimal policies under budget and coverage constraints.
problem Optimal policy learning with budget and coverage constraints.
method Combination of knapsack structure, affine threshold rule, linear programming relaxation, Greedy-Lagrangian (GLC), and rank-and-cut (RC) algorithms.
result GLC closely approximates the optimal solution and achieves near-optimal performance in finite samples; RC is approximately optimal under certain conditions.
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.
No policy can simultaneously be fully autonomous, optimally calibrated, and helpful, proving a trilemma.
problem Proving impossibility of a policy achieving maximum helpfulness, optimal calibration, and full autonomy.
method Geometric proof showing that adding any non-affine autonomy incentive to a strictly proper scoring rule destroys strict properness.
result The Behavioral Credibility Trilemma: no policy can achieve all three goals simultaneously.
Paper proves fair classification can be done via simple thresholding.
problem Achieving fair binary classification subject to group fairness constraints.
method Proves Bayes optimal fair learning rule is a group-wise thresholding rule over the Bayes regressor with randomization.
result Proposes an efficient unconstrained optimization algorithm for post-processing fair classification.
The study classifies singularities in discrete improper affine spheres.
problem Classifying singularities in discrete improper affine spheres.
method Analysis of discrete improper affine spheres based on asymptotic nets, distinguishing singular edges and vertices.
result First step in classifying singularities of discrete nets.
Defines CAMC discrete nets and their properties.
problem Understanding CAMC discrete nets and their properties.
method Defining CAMC discrete nets and proving properties.
result Properties of CAMC discrete nets are equivalent to properties of compatible interpolating quadrics.
Improved bounds on combining hypothesis classes for binary functions.
problem Understanding how to combine hypothesis classes for binary functions.
method Established upper bounds on Littlestone and threshold dimensions for combined classes.
result Upper bounds are nearly tight and give exponential improvements.
Prior-weighted logistic regression has become a standard tool for calibration in speaker recognition. Logistic regression is the optimization of the expected value of the logarithmic scoring rule. We generalize this via a parametric family of proper scoring rules. Our theoretical analysis shows how different members of…
Critiques binary classification evaluation methods, advocating for proper scoring rules.
problem The dominance of top-K metrics and fixed-threshold evaluations in machine learning.
method Introduces a decision-theoretic framework mapping evaluation metrics to their use cases, and implements a clipped Brier score variant.
result Demonstrates the clinical utility of proper scoring rules through a Python package, exttt{briertools}.
Majority bit estimation in noisy random recursive DAGs.
problem Estimating the majority bit in a noisy random recursive DAG.
method Majority rule among nodes, with bit flipping and noisy channel.
result Identification of the threshold for p at which majority rule yields errors. Optimal classification rules control error rates in multiclass mixture models.
problem Classifying observations in multiclass mixture models while controlling error rates.
method Finding optimal classification rules by searching an optimal region in the observation space, using Maximum A Posteriori (MAP) rule and heuristic computation.
result The FDR-like optimal rule can be significantly less conservative than thresholded MAP rules.
Binary classification rules based on covariates typically depend on simple loss functions such as zero-one misclassification. Some cases may require more complex loss functions. For example, individual-level monitoring of HIV-infected individuals on antiretroviral therapy (ART) requires periodic assessment of treatment…
The Kelly rule fails to maximize growth in a time-changed return setting.
problem Performance of the Kelly rule in a time-changed return process.
method Investigated the Kelly rule in a semi-martingale setting with a time change process.
result The Kelly rule does not maximize average growth rate in a non-normal log-return setting.
Basic aspects of the equiaffine geometry of level sets are developed systematically. As an application there are constructed families of 2n-dimensional nondegenerate hypersurfaces ruled by n-planes, having equiaffine mean curvature zero, and solving the affine normal flow. Each carries a symplectic structure with r…
We give a geometric description of the fusion rules of the affine Lie algebra su(2)_k at a positive integer level k in terms of the k-th power of the basic gerbe over the Lie group SU(2). The gerbe can be trivialised over conjugacy classes corresponding to dominant weights of su(2)_k via a 1-isomorphism. The fusion-rul…
The purpose of this paper relies on the study of long term affine yield curves modeling. It is inspired by the Ramsey rule of the economic literature, that links discount rate and marginal utility of aggregate optimal consumption. For such a long maturity modelization, the possibility of adjusting preferences to new ec…
Paper connects rejection learning to Bhattacharyya divergence.
problem Learning models to abstain from predictions.
method Developed a link between rejection and thresholding different statistical divergences, focusing on Bhattacharyya divergence.
result Rejector obtained by joint ideal distribution corresponds to thresholding of skewed Bhattacharyya divergence.
Develops RES metrics for stable rare-event forecasting evaluation.
problem Challenges in evaluating forecasts of rare events.
method Rare-event-stable (RES) metrics designed to maintain stable thresholds under extreme rarity.
result RES metrics maintain stable thresholds, consistent model rankings, and near-complete prevalence invariance.
We consider relative normalizations of ruled surfaces with non-vanishing Gaussian curvature K in the Euclidean space R3, which are characterized by the support functions (α)q=∣K∣α for α∈R (Manhart's relative normalizations). All ruled surfaces for…
Paper proposes a new method for SP with covariates using PADR and ERM.
problem Stochastic programming with covariate information.
method Empirical risk minimization (ERM) with nonconvex piecewise affine decision rules (PADR).
result The method provides theoretical consistency and computational tractability for nonconvex SP problems.
This paper gives two methods for constructing associative 3-folds in R^7, based around the fundamental idea of evolution equations, and uses these methods to construct examples of these geometric objects. The paper is a generalisation of the work by Joyce in math.DG/0008021, math.DG/0008155, math.DG/0010036 and math.DG…
Unified framework for shrinkage, thresholding, and regularization in normal mean estimation and linear regression.
problem Estimation of normal mean in multivariate settings with correlated observations.
method Approximate risk minimization over a functional class of shrinkage-thresholding rules.
result Unified estimator NOMAD for shrinkage, thresholding, and regularization.
MLShrink integrates machine learning with wavelet shrinkage for denoising.
problem Denoising signals with uncertain magnitudes
method Combines wavelet shrinkage with machine learning
result Preserves simplicity for signal coefficients while allowing data-adaptive decisions for ambiguous coefficients
The paper explores affine geometry of line congruences using singularity theory.
problem Understanding the affine geometry of line congruences and their focal sets.
method Use of singularity theory to describe generic phenomena and singularities.
result Identification of a key projective quadric in the tangent space.
Optimal regression with reject option using conditional variance thresholding.
problem Regression with reject option to handle uncertain predictions.
method Derive optimal rule based on thresholding conditional variance, semi-supervised estimation using labeled and unlabeled data.
result The predictor with reject option is almost as good as the optimal predictor in terms of risk and rejection rate.
Estimates fat-shattering dimension of aggregated function classes.
problem Understanding the complexity of aggregated function classes.
method Analyzes fat-shattering dimension of k-fold aggregations of real-valued function classes. result Provides upper and lower bounds on fat-shattering dimension for linear and affine function classes.
We consider the sparse inverse covariance regularization problem or graphical lasso with regularization parameter ρ. Suppose the co- variance graph formed by thresholding the entries of the sample covariance matrix at ρ is decomposed into connected components. We show that the vertex-partition induced by the thresh…
We consider the problem of clustering noisy high-dimensional data points into a union of low-dimensional subspaces and a set of outliers. The number of subspaces, their dimensions, and their orientations are unknown. A probabilistic performance analysis of the thresholding-based subspace clustering (TSC) algorithm intr…
Paper proposes robust methods for estimating optimal treatment rules with censored survival data.
problem Estimating optimal treatment rules for censored survival data.
method Developed two robust criteria and a sampling-based difference-of-convex algorithm for learning optimal treatment rules.
result Proposed methods show improved performance compared to existing methods in simulations and real data.
Stop-loss rules are often studied in the financial literature, but the stop-loss levels are seldom constructed systematically. In many papers, and indeed in practice as well, the level of the stops is too often set arbitrarily. Guided by the overarching goal in finance to maximize expected returns given available infor…
DNF-Net tackles tabular data challenges with neural architecture.
problem Handling tabular data efficiently using neural networks.
method DNF-Net uses a neural architecture with inductive bias corresponding to logical Boolean formulas in disjunctive normal form over affine soft-threshold decision terms.
result DNF-Net significantly outperforms fully connected networks on tabular data.
New method controls false discoveries in real-time data streams.
problem Online testing of hypotheses with strict error constraints and no future data.
method Structure-adaptive sequential testing (SAST) with alpha-investment algorithm.
result Substantial power gain over existing online testing rules.
Distribution grids are currently challenged by frequent voltage excursions induced by intermittent solar generation. Smart inverters have been advocated as a fast-responding means to regulate voltage and minimize ohmic losses. Since optimal inverter coordination may be computationally challenging and preset local contr…
A new framework for consistent segmentation evaluation reduces operating losses.
problem Inconsistent thresholding-based segmentation methods lead to suboptimal solutions.
method Developed a consistent ranking-based framework (RankDice/RankIoU) using Bayes rules and Dice-/IoU-calibration.
result The proposed framework is Dice-/IoU-calibrated and provides excess risk bounds and convergence rates.
"Sparse" neural networks, in which relatively few neurons or connections are active, are common in both machine learning and neuroscience. Whereas in machine learning, "sparsity" is related to a penalty term that leads to some connecting weights becoming small or zero, in biological brains, sparsity is often created wh…
Recently, a novel family of biologically plausible online algorithms for reducing the dimensionality of streaming data has been derived from the similarity matching principle. In these algorithms, the number of output dimensions can be determined adaptively by thresholding the singular values of the input data matrix. …
A new bias score method optimizes fairness in classification.
problem Ensuring fairness in binary classification under group constraints.
method Introducing bias scores and developing a post-hoc approach to adapt to fairness constraints.
result The method maintains high accuracy while ensuring fairness constraints.
New method improves classification accuracy in imbalanced high-dimensional data.
problem Imbalanced classification in high-dimensional data.
method Data splitting and hard-thresholding rules for LDA.
result Proposed method reduces misclassification rates in minority class.
The paper studies early stopping methods in linear contextual bandits.
problem Minimizing in-experiment regret and conducting robust post-experiment inferences in contextual bandits.
method The study proposes early stopping rules based on the Opportunity Cost and Threshold Method, using variances of estimators to quantify upper regret bounds.
result The proposed method provides a systematic approach to minimize in-experiment regret and conduct robust post-experiment inferences.
Optimal Volt/VAR control rules designed using deep learning.
problem Designing optimal Volt/VAR control rules for DERs to regulate voltage fluctuations.
method Formulated as a deep learning problem, where a DNN emulates Volt/VAR dynamics and optimizes rule parameters.
result DNN-based optimization outperforms MINLP in efficiency and accuracy.
A privacy-preserving algorithm for high-dimensional bandits.
problem High-dimensional stochastic contextual linear bandits with sparse parameters under privacy constraints.
method PrivateLASSO algorithm based on sparse hard-thresholding and episodic thresholding.
result Minimax private lower bounds and utility guarantees for PrivateLASSO.
A new method learns to stop with minimal data, outperforming traditional approaches.
problem Optimal stopping problems with unknown distributions.
method Explore-then-exploit approach with logarithmic exploration phase.
result Performance comparable to full information DP solution with minimal exploration.
The aim of this paper is to investigate the mean curvature flow soliton solutions on the Heisenberg group H when the initial data is a ruled surface by straight lines. We give a family of those solutions which are generated by Iso0(H) (the isometries of H for which the …
The study examines when to trust confidence thresholding in pseudo-labelling regression.
problem Calibrated probabilities from classifiers used for pseudo-labelling need careful handling to avoid bias in downstream regression.
method Developed a diagnostic apparatus to predict and bound the bias induced by confidence thresholding, derived a closed-form expression for the attenuation bias.
result The bias can be predicted from the residual score variance V∗, motivating a structural separation between classifier features and downstream controls. The paper tackles fair classification with multiple sensitive features.
problem Existing fair classification methods often consider a single sensitive feature, but in practice, individuals are defined by multiple sensitive features.
method Characterizes Bayes-optimal fair classifiers for multiple sensitive features under various fairness measures, proposing in-processing and post-processing algorithms.
result Bayes-optimal fair classifiers for multiple sensitive features are instance-dependent thresholding rules that rely on a weighted sum of group membership probabilities.
We study Lagrangian points on smooth holomorphic curves in TP1 equipped with a natural neutral Kähler structure, and prove that they must form real curves. By virtue of the identification of TP1 with the space L(E3) of oriented affine lines in Euclidean 3-space ${\mathbb…
Spiking neuronal networks are usually simulated with three main simulation schemes: the classical time-driven and event-driven schemes, and the more recent hybrid scheme. All three schemes evolve the state of a neuron through a series of checkpoints: equally spaced in the first scheme and determined neuron-wise by spik…
Deep learning uses layers of transformations to predict structured data with uncertainty.
problem Predicting structured high-dimensional data efficiently and with uncertainty.
method Applying layers of semi-affine input transformations to find features for probabilistic statistical methods.
result Achieves scalable prediction rules with uncertainty quantification and feature selection.