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…
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48 results for “learning parity with noise”
Recent developments in the field of deep learning have motivated many researchers to apply these methods to problems in quantum information. Torlai and Melko first proposed a decoder for surface codes based on neural networks. Since then, many other researchers have applied neural networks to study a variety of problem…
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.
Study on list learning with noisy data, showing limits and some learnable cases.
problem Learning from noisy data in a list learning context.
method Inspired by coding theory, extends list learning model to study sparse conjunctions and parities/majors.
result Sparse conjunctions can be efficiently list learned under certain conditions, but parities and majors cannot be efficiently learned.
We learn higher-order Markov random fields from evolving data, bypassing computational barriers.
problem Learning graphical models from temporally correlated samples, especially with noisy data.
method Using the trajectory data from Glauber dynamics, we develop an algorithm to recover the graph and parameters efficiently.
result We demonstrate efficient learning of higher-order Markov random fields from trajectory data, overcoming computational hardness.
High-performance quantum codes decoded with minimal data.
problem Efficient decoding of linear-rate LDPC quantum codes.
method Tessellations of hyperbolic manifolds, Coxeter groups, and Galois fields.
result Achieved encoding rate of 13/72 with high performance.
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.
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 -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.
Parity functorsmath.GT
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.
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.
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.
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.
Parity on based matricesmath.GT
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.
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…
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.
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 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 …
New method for fair regression using optimal transport.
problem Learning fair regression models under counterfactual fairness constraints.
method Causal uncertainty view, optimal transport, post-processing method.
result High-probability fairness guarantees with decay.
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 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.
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.
SGD learns sparse parities near computational limits with discontinuous phase transitions.
problem Learning sparse parities in deep learning.
method Empirical and theoretical analysis of SGD on sparse parities.
result SGD makes progress on sparse parities via Fourier gap, not Langevin-like mechanism.
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.
Study shows computational limits for robust classification tasks, leading to cryptographic implications.
problem Computational limitations in learning robust classifiers for classification tasks.
method Extending previous work on statistical/computational tradeoffs, using average-case hard functions and one-way functions.
result Computational hardness of learning robust classifiers even when efficient non-robust classifiers exist.
New examples show non-trivial parity-biquandle bracket.
problem Constructing non-trivial parity-biquandle bracket examples.
method Slightly changed notation and constructed examples of knots and links.
result Minimality theorem: graphs appear as link invariants.
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.
Parity Calibrationcs.LG
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.
Parity Biquandlesmath.GT
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.
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.
Fairness in ML models can lead to counterintuitive predictions.
problem Enforcing fairness in machine learning models leads to unexpected outcomes.
method Introducing slack-consistency as a desirable property for fairness procedures.
result Standard fairness methods violate the property of monotonicity with respect to slack.
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.
Paper uses RNNs to design LDPC codes for binary erasure channels.
problem Designing capacity-approaching LDPC codes for binary erasure channels.
method Model Density Evolution using RNNs to determine LDPC code coefficients and structure.
result NDE improves LDPC design performance and complexity compared to differential evolution.
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 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 …
The study analyzes the conflict between group fairness and individual fairness in machine learning.
problem The conflict between group fairness (optimal statistical parity) and individual fairness in machine learning.
method Established sufficient conditions for the compatibility between optimal statistical parity and individual fairness requirements.
result Identified regions along the Pareto frontier that satisfy individual fairness requirements.
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.
Parity in Knotoidsmath.GT
The paper explores parity in knotoids and virtual knots, proving a conjecture and introducing a new polynomial.
problem Investigating parity in knotoids and its relation to virtual knots.
method Introducing a planar parity bracket polynomial and using the Nikonov/Manturov theorem.
result Minimal diagrams of knot-type knotoids have zero height.
Fairmetrics evaluates fairness in ML models for specific groups.
problem Ensuring models do not produce biased outcomes for specific groups.
method User-friendly R package for evaluating group-based fairness criteria.
result Rigorous evaluation of multiple fairness metrics.
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.
NNs can learn efficient algorithms for certain problems.
problem Learning efficient algorithms for specific problems.
method Recurrent Convolutional Neural Networks (RCNNs) that learn efficiently.
result RCNNs can learn as well as efficient algorithms described by a constant-sized program.
The paper develops methods to create fair and transferable representations without subgroup discrimination.
problem Creating fair and transferable representations without discriminating subgroups in the population.
method The approach involves modifying data representations to meet fairness constraints, leveraging task similarities via low rank matrix factorization.
result The learned fair representation transfers well to novel tasks, improving prediction performance and fairness metrics.
We relax demographic parity in regression by enforcing parity at quantile levels and score thresholds.
problem Enforcing full distributional fairness in regression can lead to substantial accuracy loss.
method Introduce (, Z)-fair predictor, derive closed-form solutions, and develop post-processing algorithm.
result The risk gap to the continuous optimum vanishes as the grid is refined, and we enable targeted fairness corrections.
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.
Following related work in law and policy, two notions of disparity have come to shape the study of fairness in algorithmic decision-making. Algorithms exhibit treatment disparity if they formally treat members of protected subgroups differently; algorithms exhibit impact disparity when outcomes differ across subgroups,…