We prove that a topological manifold (possibly with boundary) admitting a continuous cancellative binary operation is orientable. This implies that the Möbius band admits no cancellative continuous binary operation. This answers a question posed by the second author in 2010.
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A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
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48 results for “binary questions”
Minimal triangulations of circle bundles linked to circular permutations.
problem Which circle bundles can be triangulated over a given base triangulation?
method Minimal triangulations encoded by local systems of circular permutations of vertices.
result Classical Huntington transitivity axiom for cyclic orders expressed as a binary Chern cocycle.
Optimizes clustering from noisy binary feedback in crowdsourcing.
problem Clustering items from binary user feedback with noisy answers.
method Develops algorithms for clustering items using adaptive selection of questions and items.
result Adaptive algorithm achieves performance close to information-theoretical limits.
Crowdsourcing with prospect theory handles spammers in binary classification.
problem Binary classification with spammers and reject option.
method Prospect theory for worker behavior, weighted majority voting for decision fusion.
result Asymptotic system performance and correct classification probability derived.
Optimal ability estimation in adaptive testing with binary responses.
problem Estimating a continuous ability parameter from sequential binary responses.
method Adaptive selection of questions to maximize Fisher information, updating estimate using method-of-moments, and deciding accuracy with a test statistic.
result Fisher-tracking strategy achieves optimal performance in fixed-confidence and fixed-budget regimes.
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.
Bayesian learning rule trains binary neural networks effectively.
problem Training binary neural networks is challenging due to discrete optimization.
method Proposes the Bayesian learning rule to estimate Bernoulli weights.
result Obtains state-of-the-art performance and enables uncertainty estimation.
This paper optimizes how many samples are needed to estimate a population's binary responses.
problem Estimating a distribution from incomplete or corrupted samples.
method The approach involves computing the empirical mean of a certain function, pre-solving a linear program, and using complex-analytic methods.
result Optimal sample complexity for population recovery is determined, showing phase transitions and sensitivity to dimension.
Paper tackles training binary classifiers from unlabeled data with minimal supervision.
problem Training arbitrary binary classifiers from only unlabeled data is impossible without supervision.
method Proposes an ERM-based learning method from two sets of unlabeled data with different class priors.
result The proposed method is consistent and outperforms state-of-the-art methods.
The paper analyzes binary option markets with exogenous information and price sensitivity.
problem Analyzing binary option markets with exogenous information and price sensitivity.
method Derive and analyze a continuous model of binary option markets with exogenous information, using Filippov surfaces and general assumptions on purchasing rules.
result Price always converges when exogenous information is constant, and price sensitivity affects price lag vs. information.
Composite Binary Lossesstat.ML
We study losses for binary classification and class probability estimation and extend the understanding of them from margin losses to general composite losses which are the composition of a proper loss with a link function. We characterise when margin losses can be proper composite losses, explicitly show how to determ…
New methods predict links in hypergraphs with multiple entities.
problem Link prediction in knowledge hypergraphs with non-binary relations.
method Introduce HSimplE and HypE embedding-based methods for hypergraphs.
result Proposed methods outperform baselines in hypergraph prediction.
The paper explores how to select data points for optimal learning performance.
problem Optimizing data selection for empirical risk minimizers.
method Fixing a learning rule and focusing on optimizing the training data selection.
result Achieving performance comparable to training on the entire population with a small subset of data points.
Elicit performance metrics from classifier comparisons.
problem Discover the performance metric a practitioner prefers for binary classification.
method Formalize and exploit geometric properties of confusion matrices for efficient metric elicitation.
result Provably efficient algorithms for eliciting linear and linear-fractional metrics from pairwise feedback.
Robo-advisors estimate clients' risk aversion using interactive questionnaires.
problem Estimating risk aversion of non-expert clients using adaptive questionnaires.
method Model risk aversion with cost functions and spectral risk measures. Use inverse reinforcement learning to design questions maximizing distinguishing power.
result Designing questions by maximizing distinguishing power achieves satisfactory accuracy in learning risk aversion with fewer than 50 questions.
New binary classification techniques help multiclass classification by aggregating proper learners.
problem Multiclass classification faces a properness barrier that prevents optimal learning by proper learners.
method Aggregations of proper binary learners, generalized to multiclass settings, achieve optimal sample complexity.
result Optimal binary learners can achieve sample complexity $O\left(\frac{d_G + \ln(1 / δ)}ε
ight)$ for classes with finite Graph dimension .
Paper shows similarity learning can lead to strong binary classification performance.
problem How similarity learning can lead to good classification performance.
method Product-type formulation of similarity learning is connected to binary classification through an excess risk bound.
result Similarity learning can directly elicit a decision boundary for binary classification.
New research shows that binary classification can be done with noisy data, but only if there are clean samples available.
problem Learning binary classification with instance and label dependent label noise.
method Theoretical analysis and empirical risk minimization.
result Empirical risk minimization achieves the optimal excess risk bound without additional assumptions.
The paper examines the stability of binary choice models using Gini index and scoring indicators.
problem Stability and discriminatory power of binary choice models.
method Derives the real Gini index and incorporates PSI and KS statistics into the model.
result The real Gini index should be less than the calculated Gini index when the population distribution changes.
New metric reduces arbitrariness in fair binary classification predictions.
problem Variance in predictions leads to arbitrary decisions in fair classification.
method Developed a self-consistency metric and an abstention algorithm.
result Fair binary classification is often close to fair due to variance, not interventions.
New binary loss functions improve density ratio estimation accuracy.
problem Improving accuracy of density ratio estimators using binary classifiers.
method Characterized loss functions based on prescribed error measures in Bregman divergences.
result Novel loss functions prioritize accurate estimation of large density ratio values.
Reduces bounded loss learning to binary classification.
problem Universal consistency of non-i.i.d. processes with bounded loss.
method Constructive reduction to binary classification.
result Any bounded loss output setting can be reduced to binary classification.
This work proves DP learnability implies online learnability for general classification tasks.
problem Link between differential privacy and online learning for general classification tasks.
method Establishes Ramsey-type theorems for trees to prove DP learnability implies online learnability.
result DP learnability implies online learnability for general classification tasks.
MLBench: How Good Are Machine Learning Clouds for Binary Classification Tasks on Structured Data?cs.DC
Study compares cloud ML services for binary classification tasks.
problem Evaluate performance of major cloud ML services on binary classification.
method Constructed benchmark using Kaggle datasets; compared Azure and Amazon services.
result Identifies strengths and weaknesses of current cloud ML services.
Contradiction graphs reveal VC dimension threshold.
problem Determining VC dimension of concept classes.
method Study contradiction graphs of binary concept classes.
result Single contradiction graph determines VC dimension.
Adversarial Regularization for Visual Question Answering: Strengths, Shortcomings, and Side Effectscs.LG
AdvReg improves VQA models but introduces instability and bias issues.
problem VQA models over-rely on linguistic biases, ignoring visual context.
method Adversarial regularization to encourage bias-free question representations.
result AdvReg yields side-effects like unstable gradients and reduced performance on in-domain examples.
We develop a new model and algorithms for machine learning-based learning analytics, which estimate a learner's knowledge of the concepts underlying a domain, and content analytics, which estimate the relationships among a collection of questions and those concepts. Our model represents the probability that a learner p…
Machine learning offers novel ways and means to design personalized learning systems wherein each student's educational experience is customized in real time depending on their background, learning goals, and performance to date. SPARse Factor Analysis (SPARFA) is a novel framework for machine learning-based learning a…
New algorithm for faster feature enumeration over finite fields.
problem Learning k-juntas over finite fields for multi-labeled data.
method Exploits Fourier detection techniques to develop an O(n^0.8k)-time algorithm.
result First non-trivial algorithm for k-juntas over F_q, answering Mossel et al.'s question.
This work refines Cover's theory for binary classification on low-dimensional data.
problem The challenge of analyzing how low-dimensional data structures affect classification models.
method Refines Cover's function-counting theory to account for low-dimensional data structure.
result Derives dichotomy counts and analyzes the impact of data structure on classification models.
Simplified EEG analysis improves Parkinson's disease detection.
problem Improving accuracy in EEG-based Parkinson's disease diagnosis.
method Binary electrode grouping, Tsallis Entropy, and dual ec/eo EEG states.
result Binary grouping retains enough information for HC vs PD discrimination.
Combines cost-sensitive and Neyman-Pearson paradigms for better binary classification.
problem Asymmetric binary classification problems with unequal error severities.
method Develops TUBE-CS algorithm to bridge cost-sensitive and Neyman-Pearson paradigms.
result High-probability control of population type I error.
Proves homology of mapping class groups for infinite-type surfaces.
problem Homology of mapping class groups for infinite-type surfaces.
method Modification of Mather's argument and homological stability result.
result Homology of mapping class groups determined for binary tree surfaces.
This paper optimizes retraining models using their own predictions and noisy labels.
problem Improving model performance through optimal retraining of noisy labels.
method Developed a principled framework based on approximate message passing (AMP) to analyze iterative retraining procedures.
result Derivation of the Bayes optimal aggregator function to minimize prediction error.
ML4C uses binary classification to infer causal structures from latent vicinity.
problem Learning causal relations from observational data without ground truth.
method Two-phase paradigm with binary classifier and novel featurization.
result ML4C outperforms state-of-the-art algorithms in causal learning.
Gravitational waves are predicted by the general theory of relativity. In [6] D. Christodoulou showed that gravitational waves have a nonlinear memory. We proved in [3] that the electromagnetic field contributes at highest order to the nonlinear memory effect of gravitational waves. In the present paper, we study this …
New method turns optimization algorithms into uniformly stable learning algorithms for non-Euclidean norms.
problem Non-Euclidean norms in binary classification problems.
method Black-box reduction method using uniformly convex regularizers.
result Achieves optimal statistical risk bounds on excess risk for non-Euclidean norms.
The recently proposed SPARse Factor Analysis (SPARFA) framework for personalized learning performs factor analysis on ordinal or binary-valued (e.g., correct/incorrect) graded learner responses to questions. The underlying factors are termed "concepts" (or knowledge components) and are used for learning analytics (LA),…
Quantum oracles help identify counterfactuals better than classical ones.
problem Identifying unknown causal parameters in causal models.
method Using quantum oracles to query and identify all causal parameters and counterfactuals.
result Quantum oracles enable identification of all two-way joint counterfactuals and tighter bounds on higher-order counterfactuals.
This tutorial introduces causal modeling methods for researchers.
problem Understanding causal relationships in research studies.
method Integrates potential outcomes and graphical methods for causal modeling.
result Clear notation and practical examples for applied researchers.
We propose SPARFA-Trace, a new machine learning-based framework for time-varying learning and content analytics for education applications. We develop a novel message passing-based, blind, approximate Kalman filter for sparse factor analysis (SPARFA), that jointly (i) traces learner concept knowledge over time, (ii) an…
We investigate whether the bid/ask queue imbalance in a limit order book (LOB) provides significant predictive power for the direction of the next mid-price movement. We consider this question both in the context of a simple binary classifier, which seeks to predict the direction of the next mid-price movement, and a p…
Characterizes uncertainty in low-rank matrix completion with noisy data.
problem Uncertainty quantification in low-rank matrix completion with heterogeneous sub-exponential noise.
method Characterizes the distribution of estimated matrix entries under low-rank estimators with heterogeneous sub-exponential noise.
result Explicit formulas for the distribution of estimated matrix entries under Poisson and Binary noise.
Paper proposes using blockchain for trustable machine learning with streaming layer and synthetic data.
problem Machine learning results are not fully trusted due to mutable data and difficulty in automation.
method Blockchain technology for immutable data storage and smart contracts for automation. Server, streaming, and smart contract implementations.
result A compact binary model format for streaming layer and synthetic data generation for limited training data.
Paper proves SCNNs and BNNs have universal approximation property and similar energy consumption.
problem Accuracy and applicability of SCNNs and BNNs in hardware implementations.
method Proof of universal approximation property using strong law of large numbers and SCNNs as a bridge.
result SCNNs and BNNs have the same asymptotic energy consumption.
In various situations one is given only the predictions of multiple classifiers over a large unlabeled test data. This scenario raises the following questions: Without any labeled data and without any a-priori knowledge about the reliability of these different classifiers, is it possible to consistently and computation…
The paper explores how machine learning models can be learnable despite label shifts.
problem Learnability of binary classification models in the presence of label shifts.
method Developed a performative empirical risk function that is an unbiased estimate of the true risk on the shifted distribution.
result PAC-learnable hypothesis spaces remain PAC-learnable for performative scenarios.
Modern machine learning methods are critical to the development of large-scale personalized learning systems that cater directly to the needs of individual learners. The recently developed SPARse Factor Analysis (SPARFA) framework provides a new statistical model and algorithms for machine learning-based learning analy…