The paper addresses bias amplification in prediction and decision-making using causal analysis.
problem Bias amplification in automated systems, especially after thresholding.
method Introduces margin complement and causal decomposition of prediction disparities.
result Disparity in predictor Y ^ \widehat Y Y can be decomposed into causal influences of X X X on S S S and M M M . Bubbles are essential in certain economic models with high growth and low interest rates.
problem Asset price bubbles exceeding fundamental values.
method Developed the Bubble Necessity Theorem in economic models with specific growth and interest rate conditions.
result Bubbles are inevitable in certain economic scenarios with high growth and low interest rates.
Paper proposes forecast-necessity testing for accurate causal interpretation in nonlinear time-series models.
problem Misinterpretation of causal scores from nonlinear models as regression coefficients.
method Systematic edge ablation and forecast comparison to evaluate causal necessity.
result Causal relationships with similar scores can differ in their necessity for accurate prediction.
Unified feature importance for machine learning models tackles sufficiency and necessity limitations.
problem Insufficient and incomplete explanations of machine learning models.
method Formalized sufficiency and necessity notions, proposing a unified importance measure.
result Unified importance measure detects features missed by sufficiency and necessity alone.
Paper presents a dynamic tail risk protection strategy using ML and econometrics.
problem Tail risk protection in finance with solid mathematical and statistical tools.
method Dynamic tail risk protection strategy using weak classifiers (parametric and non-parametric) to estimate exceedance probability and derive trading signals.
result Ensemble classifier improves generalization and trading performance.
Discussing rigidity in codimension 2, extending rigidity concepts.
problem Local isometric rigidity problem in codimension 2.
method Extending rigidity concepts to include genuine and honest rigidity, studying isometric immersions in semi-Euclidean spaces.
result Necessity of natural singularity in inner product for transitivity.
Study on multiple linking numbers, extending Gauss diagram formulas.
problem Extending link invariants to more complex diagrams.
method Investigate second Gauss diagram formula involving two arrows.
result Discover two types of multiple linking numbers, one Vassiliev invariant, the other sensitive to Reidemeister moves.
Study finds cryptocurrency market diversity patterns inconsistent with neutral models.
problem Cryptocurrency market diversity patterns not consistent with neutral models.
method Analysis borrowing methods from ecology, focusing on diversity patterns and community structure.
result Cryptocurrency market diversity patterns not consistent with neutral models, suggesting strong interactions between species.
We introduce an up-down coloring of a virtual-link diagram. The colorabilities give a lower bound of the minimum number of Reidemeister moves of type II which are needed between two 2-component virtual-link diagrams. By using the notion of a quandle cocycle invariant, we determine the necessity of Reidemeister moves of…
New DA method CIRM outperforms existing methods under structural causal model assumptions.
problem Improving prediction performance in domain adaptation with perturbed source and target data.
method Theoretical framework based on structural causal models to analyze and compare DA methods.
result CIRM method outperforms existing methods when covariates and label distributions are perturbed in target data.
Transformers show strengths and weaknesses in complexity analysis.
problem Understanding the strengths and limitations of attention layers in transformers.
method Analysis of representation power through complexity parameters and task-specific constructions.
result Transformers can solve sparse averaging tasks with logarithmic complexity, but triple detection tasks require linear complexity.
AdaDKRR tackles data silos by combining autonomy, privacy, and collaboration.
problem Data silos caused by privacy and interoperability constraints.
method Adaptive distributed kernel ridge regression (AdaDKRR) with autonomy, privacy, and collaboration.
result AdaDKRR performs similarly to optimal learning algorithms on the whole data under mild conditions.
Improved variational inequality algorithms using adaptive step sizes.
problem Solving monotone variational inequalities and convex-concave min-max problems efficiently.
method Adaptive step sizes that eliminate hyperparameters and global Lipschitz continuity requirements.
result Eliminated the need for the golden ratio in the algorithm and improved complexity bounds.
New algorithms improve boosting by optimizing chance-corrected measures.
problem Improving boosting algorithms to use chance-corrected measures effectively.
method Developed new algorithms (AdaBook and Multibook) that optimize chance-corrected measures.
result AdaBook and Multibook outperform standard Multiboost or AdaBoost in multiclass situations.
Using powerful posterior distributions is a popular approach to achieving better variational inference. However, recent works showed that the aggregated posterior may fail to match unit Gaussian prior, thus learning the prior becomes an alternative way to improve the lower-bound. In this paper, for the first time in th…
In 2001, Oestlund conjectured that Reidemeister moves 1 and 3 are sufficient to describe a homotopy from any generic immersion from the circle into the plane to the standard embedding of the circle. We show that this conjecture is false.
The great success of deep learning poses urgent challenges for understanding its working mechanism and rationality. The depth, structure, and massive size of the data are recognized to be three key ingredients for deep learning. Most of the recent theoretical studies for deep learning focus on the necessity and advanta…
Paper proposes methods to learn accurate models from incomplete data without imputation.
problem Learning accurate models from datasets with missing values.
method Unified approach for checking data imputation necessity and efficient algorithms.
result Significant reduction in time and effort needed for data imputation.
Optimal machine learning requires interpolating training data in high-dimensional linear regression.
problem Achieving optimal predictive risk in overparameterized linear regression models.
method Analyzing proportional asymptotics of random design and label noise variance.
result Optimal performance in linear regression requires fitting training data to higher accuracy than inherent noise.
Using Jeff Holman's comments in Quantitative Finance to illustrate 4 critical errors students should learn to avoid: 1) Mistaking tails (4th moment) for volatility (2nd moment), 2) Missing Jensen's Inequality, 3) Analyzing the hedging wihout the underlying, 4) The necessity of a numeraire in finance.
We discuss general notions of metrics and of Finsler structures which we call weak metrics and weak Finsler structures. Any convex domain carries a canonical weak Finsler structure, which we call its tautological weak Finsler structure. We compute distances in the tautological weak Finsler structure of a domain and we …
DOODLER detects out-of-distribution inputs by reconstructing in-distribution data.
problem Detecting real-world out-of-distribution inputs for deep learning models.
method DOODLER uses a Variational Auto-Encoder to reconstruct in-distribution data and identifies failures as out-of-distribution.
result DOODLER outperforms other OOD detection methods under similar constraints.
Tensoring p p p -weak differentiable structures preserves their properties.
problem Tensorization of p p p -weak differentiable structures. method Proving the product of p p p -weak charts is a p p p -weak chart, and showing isometric embeddings. result Tensorization of p p p -weak differentiable structures is possible under certain conditions. New structures defined for studying contact foliations and their geometry.
problem Understanding dynamics of contact foliations and their applications.
method Define and study weak nearly S- and weak nearly C-structures.
result Characterize weak nearly S- and weak nearly C- submanifolds in weak nearly Kähler manifolds.
The study examines conditions for weak nearly cosymplectic manifolds to split into products.
problem Understanding the curvature and topology of weak nearly cosymplectic manifolds.
method Analyzes the conditions for splitting and characterizes specific manifolds.
result Conditions for weak nearly cosymplectic manifolds to become Riemannian products are identified.
Subset selection improves weak supervision performance.
problem Optimizing the use of weakly-labeled data.
method Combining pretrained data representations with the cut statistic for subset selection.
result Subset selection improves weak supervision performance by up to 19%.
Defines weak geodesics on specific subsets of manifolds.
problem Characterizing geodesics on prox-regular subsets of Riemannian manifolds.
method Defining weak geodesics as continuous curves with weak regularities, and characterizing them as viscosity critical points of the energy functional.
result Characterizes weak geodesics on prox-regular subsets of Riemannian manifolds.
Study weak conjugacy in surface homeomorphisms.
problem Understanding weak conjugacy in homeomorphisms of surfaces.
method Exploring the group of homeomorphisms isotopic to the identity.
result New insights into weak conjugacy relations.
New model shows weak teachers can help strong students learn even with imperfect labels.
problem Improving strong student's performance with weak teacher's imperfect pseudolabels.
method Stylized overparameterized spiked covariance model with Gaussian covariates, proving two phases of generalization.
result Provable successful and random guessing phases of strong student's generalization.
Introduces weak ( p , k ) (p,k) ( p , k ) -Dirac structures in geometric settings.
problem Defining and analyzing new geometric structures.
method Introducing and studying weak ( p , k ) (p,k) ( p , k ) -Dirac structures in T M ⊕ Λ p T ∗ M TM \oplus \Lambda^pT^*M T M ⊕ Λ p T ∗ M . result Weak ( p , k ) (p,k) ( p , k ) -Dirac structures contain more information than ( p , k ) (p,k) ( p , k ) -Lagrangian structures. RAVEN improves weak-to-strong generalization under distribution shifts.
problem Weak models fail to supervise strong models effectively under distribution shifts.
method RAVEN dynamically learns optimal combinations of weak models and strong model parameters.
result RAVEN outperforms existing methods by over 30% on out-of-distribution tasks.
Study weak f f f -K-contact manifolds, finding Einstein-type metrics and solitons.
problem Characterize and study geometric properties of weak f f f -K-contact manifolds. method Analyzing weak metric f f f -structures, using Killing vector fields, and Jacobi operators. result Einstein weak f f f -K-contact manifolds are Ricci flat. Study the geometry of weak para-f-structures and subclasses.
problem Understand the geometry of weak para-f-structures and their subclasses.
method Express covariant derivative of f, prove Killing characteristic vector fields, show foliations, and demonstrate rigidity.
result Prove that characteristic vector fields are Killing and ker f defines a totally geodesic foliation.
We prove that every Kaehler solvmanifold has a finite covering whose holomorphic reduction is a principal bundle. An example is given that illustrates the necessity, in general, of passing to a proper covering. We also answer a stronger version of a question posed by Akhiezer for homogeneous spaces of nonsolvable algeb…
Weak labels can significantly speed up learning for strong tasks.
problem Learning with limited strong labels.
method Using weak labels to accelerate learning of strong tasks.
result Weak labels can accelerate learning to O ( i c e f r a c 1 n ) \mathcal{O}(
icefrac{1}{n}) O ( i ce f r a c 1 n ) rate. The study explores new metric structures on manifolds, linking them to Einstein metrics.
problem Characterizing and understanding weak K-contact manifolds and their properties.
method Analyzing weak K-contact manifolds and their properties, including the parallel Ricci tensor and generalized Ricci soliton structures.
result Sufficient conditions for weak K-contact manifolds with specific properties to be Einstein manifolds.
Study on Ricci solitons and Einstein metrics in weak β-Kenmotsu manifolds.
problem Characterizing Einstein metrics in weak β-Kenmotsu manifolds.
method Adapted ∗ \ast ∗ -Ricci tensor to weak almost contact manifolds and studied its interaction with weak β-Kenmotsu structures. result New characteristics of Einstein metrics obtained.
This paper studies properties of weak reducing pairs in critical Heegaard splittings.
problem Characterize weak reducing pairs in critical Heegaard splittings.
method Analyze the properties of weak reducing pairs in critical Heegaard splittings.
result Provide a necessary condition for a Heegaard surface to be critical.
We study weakened f f f -structures on manifolds, generalizing classical results.
problem Classical f f f -structures and their properties on manifolds. method Introduced and studied weakened f f f -structures, subclasses, and their properties. result Generalized known results on globally framed f f f -manifolds. In this work we wish characterize the Einstein manifolds ( M , g ) (M,g) ( M , g ) , however without the necessity of hypothesis of compactness over M M M and unitary volume of g g g , which are well known in many works. Our result says that if all eingenvalues λ λ λ of r g r_{g} r g , with respect to g g g , satisfy λ ≥ 1 n s g λ\geq \frac{1}{n}s_{g} λ ≥ n 1 s g , then $(M,g)…
New causal analysis reconciles predictive and statistical fairness.
problem Mutual exclusivity of predictive and statistical fairness notions.
method Derive a new causal decomposition formula for fairness measures.
result Predictive and statistical fairness are complementary, not mutually exclusive.
Equivalent bicategories constructed from action Lie groupoids.
problem Equivalence of bicategories constructed from action Lie groupoids.
method Localizing at equivariant weak equivalences, surjective submersive equivariant weak equivalences, and all weak equivalences.
result Weak equivalences between action Lie groupoids are isomorphic to compositions of nice forms of equivariant weak equivalences.
We deal with a notion of weak binormal and weak principal normal for non-smooth curves of the Euclidean space with finite total curvature and total absolute torsion. By means of piecewise linear methods, we first introduce the analogous notation for polygonal curves, where the polarity property is exploited, and then m…
Classifies compact spaces by shape, finite spaces by weak homotopy.
problem Classifying compact Hausdorff spaces and finite topological spaces.
method Constructs a category that classifies spaces by shape and weak homotopy.
result Classifies compact spaces by shape, finite spaces by weak homotopy.
Simplicial spheres have a weak Lefschetz property in characteristic 2.
problem Proving the weak Lefschetz property for simplicial spheres.
method Using bistellar moves to show the property is preserved.
result The weak Lefschetz property is preserved by bistellar moves for PL-spheres.
Optimal algorithm converts weak to strong learner with less data.
problem Constructing a strong learner from a weak learner with minimal data.
method New algorithm that uses less training data than AdaBoost.
result Optimal sample complexity for converting weak to strong learner.
Formalizes weak and strong verification for LLMs, controlling errors without assumptions.
problem Balancing cost and reliability in reasoning with LLMs.
method Formalizes weak-strong verification policies, introduces metrics, develops online algorithm.
result Optimal policies admit a two-threshold structure, and calibration and sharpness govern value of weak verifiers.
In this paper we discuss the possibility of using multilevel Monte Carlo (MLMC) methods for weak approximation schemes. It turns out that by means of a simple coupling between consecutive time discretisation levels, one can achieve the same complexity gain as under the presence of a strong convergence. We exemplify thi…