This paper tackles fair Bayes-optimal classifiers under predictive parity, proving their limitations and proposing a new algorithm.
problem Ensuring fair Bayes-optimal classifiers under predictive parity, especially when group performance levels vary widely.
method Proving the limitations of fair Bayes-optimal classifiers under predictive parity and proposing a new adaptive thresholding algorithm, FairBayes-DPP.
result Fair Bayes-optimal classifiers under predictive parity may not hold if group performance levels vary widely, leading to within-group unfairness.
Parity functors assign labels to knot diagrams based on crossing parity.
problem Assigning consistent labels to knot diagrams.
method Define parity functors for knot diagrams and surfaces.
result Universal oriented parity functors for free knots and fixed surface knots.
Algorithm ensures demographic parity in regression without sensitive attribute data.
problem Performing regression with demographic parity constraints.
method Post-processing algorithm using accurate estimates and sensitive attribute predictor.
result Generates predictions meeting demographic parity constraint.
Parity defined for based matrices, a new example of virtual knot parity.
problem Defining parity for a new algebraic structure.
method Introduced parity for based matrices, defined reduced stable parity.
result New example of parity for virtual knots.
New method controls bias in training data for fair outcomes.
problem Ensuring equal treatment between different groups in machine learning.
method Contrastive information estimation to control mutual information between representations and protected attributes.
result Our method provides strong theoretical guarantees on the parity of any downstream algorithm.
We introduce the 2-colour parity. It is a theory of parity for a large class of virtual links, defined using the interaction between orientations of the link components and a certain type of colouring. The 2-colour parity is an extension of the Gaussian parity, to which it reduces on virtual knots. We show that the 2-c…
In the present paper, we develop the parity theory invented in \cite{ManSb}; we construct new parities for two-component (virtual and free) links. New parities significantly depend on geometrical properties of diagrams; in particular, they are mutation-sensitive. New parities can be used practically in all problems, wh…
Transformers solve parity problems efficiently with step-by-step reasoning.
problem Training transformers to solve complex, recursive problems like parity.
method Training a one-layer transformer to solve k-parity, incorporating intermediate parities into the loss function, and using teacher forcing or augmented data. result Transformers can learn parity in one gradient update with intermediate supervision or self-consistency checks.
In \cite {FrKn,Sbornik} it was shown that in some knot theories the crucial role is played by {\em parity}, i.e.\ a function on crossings valued in {0,1} and behaving nicely with respect to Reidemeister moves. Any parity allows one to construct functorial mappings from knots to knots, to refine many invariants and …
We identify conditional parity as a general notion of non-discrimination in machine learning. In fact, several recently proposed notions of non-discrimination, including a few counterfactual notions, are instances of conditional parity. We show that conditional parity is amenable to statistical analysis by studying ran…
Proposes a framework to create fair IDRs by enforcing demographic parity constraints.
problem Discrimination in IDRs trained on biased data.
method Incorporates DP and CDP constraints into IDR estimation.
result Theoretically optimal IDRs can be efficiently obtained through perturbations.
Universal Gaussian parity proven for 2D knots.
problem Proving universal Gaussian parity for 2D knots.
method Analyzing Gaussian parity on free 2D knots.
result Gaussian parity is universal for 2D knots.
New parities defined on virtual knots linked to crossing indices.
problem Defining parities on virtual knots.
method Connecting parities to invariant cycles on arcs and quasi-indices on crossings.
result New series of parities on virtual knots defined.
We mathematically compare four competing definitions of group-level nondiscrimination: demographic parity, equalized odds, predictive parity, and calibration. Using the theoretical framework of Friedler et al., we study the properties of each definition under various worldviews, which are assumptions about how, if at a…
Meta-theorems validate fair regression algorithms under demographic parity constraints.
problem Regression under demographic parity constraints.
method Meta-theorems and post-processing methods.
result Fair minimax optimal regression can be achieved through post-processing.
Parity calibration aims to predict increase-decrease events, not values.
problem Forecasting future increase-decrease events rather than exact values.
method Online binary calibration method to achieve parity calibration.
result Online binary calibration achieves parity calibration effectively.
Coded Federated Learning speeds up model convergence by preemptively computing on parity data.
problem Federated learning's convergence is slow on heterogeneous platforms due to stragglers.
method Develops CFL scheme where clients generate parity data and share it once, allowing the server to compute redundantly.
result CFL allows global model to converge nearly four times faster than uncoded federated learning.
We use crossing parity to construct a generalization of biquandles for virtual knots which we call Parity Biquandles. These structures include all biquandles as a standard example referred to as the even parity biquandle. Additionally, we find all Parity Biquandles arising from the Alexander Biquandle and Quaternionic …
Diversified risk parity strategies outperform equally-weighted portfolios in various asset universes.
problem Finding optimal portfolio allocations that balance risk and reward.
method Integrates various reward-risk measures and generic allocation rules into diversified risk parity.
result Diversified reward-risk parity strategies exhibit higher average returns, Sharpe ratios, and Calmar ratios compared to equally-weighted risk portfolios.
This paper shows neural networks can learn non-linear sparse parities.
problem The challenge of learning non-linear models with neural networks.
method Gradient descent on depth-two neural networks.
result Sparse parities are learnable by neural networks but not by linear methods.
Functorial maps and weak parities are equivalent descriptions of rules of substitution virtual crossings for classical in diagrams of a knot in a way compatible with Reidemeister moves. We introduce the notion of maximal weak parity and describe it for knots in a given closed oriented surface. This weak parity defines …
Introduce a two-variable parity polynomial for virtual knotoids
problem Define a polynomial invariant for virtual knotoids
method Based on the parity of classical crossings
result Can distinguish pairs not distinguished by odd writhe and affine index polynomial
Paper solves k-sparse parity problem with sign SGD, matching SQ lower bound.
problem Solving k-sparse parity problems efficiently.
method Sign stochastic gradient descent on neural networks.
result Matches Statistical Query lower bound for solving k-sparse parity problems.
Neural networks struggle with learning fixed parities.
problem Difficulty of learning fixed parities with neural networks.
method Using perturbed gradient descent on one-hidden-layer ReLU networks.
result Training neural networks on fixed parities fails to produce meaningful results.
Integrates differential privacy and demographic parity in multi-class classification.
problem Ensuring fairness and privacy in sensitive applications.
method Designs DP2DP algorithm that enforces both demographic parity and differential privacy.
result DP2DP converges towards demographic parity at nearly the same rate as non-private methods, achieving state-of-the-art trade-offs.
Curriculum learning helps neural networks learn parities more efficiently.
problem Improving learning efficiency for neural networks on parity targets.
method Using a curriculum learning approach with a mixture of sparse and dense inputs.
result A 2-layer ReLU neural network can learn parities more efficiently than a fully connected network.
In [3] we constructed the parity-biquandle bracket valued in {\em pictures} (linear combinations of 4-valent graphs). We gave no example of classical links such that the parity-biquandle bracket of which is not trivial. In the present paper we slightly change the notation of the parity-biquandle bracket and give exam…
Paper creates fair synthetic data ensuring equal predictions across sensitive attributes.
problem Ensuring fair predictions across sensitive attributes in synthetic data.
method Equalizing target probability distributions across sensitive attributes in synthetic data generation.
result Synthetic data provides strong fair predictions, equal across all thresholds.
Study shows physical drift affects put-call parity enforcement, not just option payoffs.
problem Inconsistency between quoted put-call parity and actual market behavior.
method Examined SPX and RUT index options, used drift-preserving GBM term to improve fit.
result Physical drift enters the enforcement of risk-neutral parity, not just option payoffs.
Parity mappings from the chords of a Gauss diagram to the integers is defined. The parity of the chords is used to construct families of invariants of Gauss diagrams and virtual knots. One family consists of degree n Vassiliev invariants.
We define counting and cocycle enhancement invariants of virtual knots using parity biquandles. These invariants are determined by pairs consisting of a biquandle 2-cocycle φ^0 and a map φ^1 with certain compatibility conditions leading to one-variable or two-variable polynomial invariants of virtual knots. We provide …
Proposes a risk parity portfolio optimization method that accounts for uncertainty in asset returns.
problem Risk parity portfolio optimization under uncertainty.
method Distributionally robust optimization with ambiguity set for worst-case scenario analysis.
result Distributionally robust risk parity portfolios can yield higher risk-adjusted returns.
Counterfactual fairness not equivalent to demographic parity, finds study.
problem Equivalence between causal and probabilistic concepts in fairness metrics.
method Close examination of recent claim about counterfactual fairness.
result Counterfactual fairness is not equivalent to demographic parity.
The adoption of automated, data-driven decision making in an ever expanding range of applications has raised concerns about its potential unfairness towards certain social groups. In this context, a number of recent studies have focused on defining, detecting, and removing unfairness from data-driven decision systems. …
2-dimensional knots and links are studied in the article. The notion of parity is introduced via techniques similar to the ones used by the second named author in 1-dimensional case. By using parity new invariants are constructed and known invariants are refined.
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.
Extends Demographic Parity for fairer wage predictions with expert knowledge.
problem Inadequate fairness metrics limit user domain knowledge and ignore intersectional fairness.
method Develops a parametric method to incorporate expert knowledge in fair predictions.
result Offers a robust solution for real-life applications with limited data and spending constraints.
The article develops a model for skewness risk in risk parity portfolios.
problem Managing skewness risk in asset allocation models.
method Modeling asset returns with skewness and jumps, deriving analytical formulas for risk contributions.
result Skewness-based risk parity portfolios outperform volatility-based portfolios in managing jump risks.
This paper optimizes portfolios using HRP and CLA algorithms on NIFTY 50 stocks.
problem Designing an optimal stock portfolio with accurate forecasting of future returns and risks.
method Uses hierarchical risk parity and critical line algorithms on NIFTY 50 stocks.
result Hierarchical risk parity algorithm outperformed the critical line algorithm on test data.
The paper tackles fair set-valued classification under demographic parity constraints.
problem Set-valued classification can amplify discriminatory bias, especially in multiclass settings.
method Proposes two strategies: an oracle-based method and a proxy method, both aiming to satisfy demographic parity and expected size constraints.
result Established distribution-free convergence rates and excess-risk bounds for both methods.
New welfare-based fairness notions align with existing error rate balance and predictive parity.
problem Aligning fairness notions with welfare-based criteria.
method Discussing and establishing conditions for envy freeness and prejudice freeness.
result Envy freeness and prejudice freeness are equivalent to error rate balance and predictive parity.
We consider knot theories possessing a {\em parity}: each crossing is decreed {\em odd} or {\em even} according to some universal rule. If this rule satisfies some simple axioms concerning the behaviour under Reidemeister moves, this leads to a possibility of constructing new invariants and proving minimality and non-t…
We investigate an application of crossing parity for the bracket expansion of the Jones polynomial for virtual knots. In addition we consider an application of parity for the arrow polynomial as well as for the categorifications of both polynomials. We present a number of examples found through our calculations. We pro…
This paper is an introduction to virtual knot theory and an exposition of new ideas and constructions, including the parity bracket polynomial, the arrow polynomial, the parity arrow polynomial and categorifications of the arrow polynomial. The paper is relatively self-contained and it describes virtual knot theory bot…
Incorrect parity-based descriptions of realizable Gauss diagrams found, but bipartite graphs provide a valid approach.
problem Incorrect descriptions of realizable Gauss diagrams using parity conditions.
method Used bipartite graphs to describe realizable Gauss diagrams.
result Realizable Gauss diagrams can be accurately described using bipartite graphs.
Solves a model for sudden problem-solving ability in deep learning.
problem Emergence of new problem-solving abilities in deep learning models.
method Solves a simple multi-linear model in a skill-basis, finding analytic expressions for emergence and scaling laws.
result Simple model captures sigmoidal emergence of multiple new skills in neural networks.
New framework tackles fairness in link prediction beyond demographic parity.
problem Systemic biases in link prediction can exacerbate societal inequalities.
method Formalizes limitations of existing fairness evaluations and proposes a new framework.
result Proposes a lightweight post-processing method combined with decoupled link predictors.
Valuation and parity formulas for both European-style and American-style exchange options are presented in a general financial model allowing for jumps, possibility of default and "bubbles" in asset prices. The formulas are given via expectations of auxiliary probabilities using the change-of-numeraire technique. Exten…