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Record W4378673239 · doi:10.54097/hset.v49i.8586

Fundamental results in probability theory

2023· article· en· W4378673239 on OpenAlexaff
Zizhou Fang, Kaixi Tan, Ziyi Wang

Bibliographic record

VenueHighlights in Science Engineering and Technology · 2023
Typearticle
Languageen
FieldComputer Science
TopicData Mining Algorithms and Applications
Canadian institutionsUniversity of Toronto
Fundersnot available
KeywordsMathematicsCentral limit theoremRandom variableIndependent and identically distributed random variablesChebyshev's inequalityLaw of large numbersProbability theoryApplied mathematicsDiscrete mathematicsStatisticsMathematical analysis

Abstract

fetched live from OpenAlex

Probability theory is an area of mathematics that deals with the concept of likelihood. Probability theory is the mathematical foundation of statistical reasoning, and understanding how unpredictability impacts data is crucial for data scientists. Gaussian (normal) distribution is the most widely used distribution. It has two parameters which are mean and variance and easy to interpret. Also, the central limit theorem tells us that sums of independent random variables make the least number of assumptions. In addition, Poisson, Laplace, Beta, Pareto, Dirichelt, Binomial and Gamma Distributions are useful in different areas. The multivariate Gaussian is the most widely used joint probability density function. Covariance and correlation are used to measure the degree between two random variable’s X and Y. Chebyshev Inequality defines a topological space, which includes a sequence of elements, and let the sequence be called . Strong Law of Large Numbers Theorem use in large number of random variable in pairwise independent identically distributed and Renewal Theory is and example in Strong Law of Large Numbers Theorem.

Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.

How this classification was reachedexpand

Full frame distilled prediction

Teacher imitation

Not calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.

metaresearch head score (Codex)0.001
metaresearch head score (Gemma)0.000
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesnone
Consensus categoriesnone
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Theoretical or conceptual · Consensus signal: none
GenreCandidate signal: Empirical · Consensus signal: Empirical
Teacher disagreement score0.867
Threshold uncertainty score0.268

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0010.000
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0000.000
Bibliometrics0.0010.005
Science and technology studies0.0000.000
Scholarly communication0.0000.000
Open science0.0010.000
Research integrity0.0000.000
Insufficient payload (model declined to judge)0.0000.000

Machine scores (provisional)

The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.

Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.

Opus teacher head0.012
GPT teacher head0.239
Teacher spread0.227 · how far apart the two teachers sit on this one work
Validation statusscore_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it

Classification

machine, unvalidated

Machine predicted; a candidate call from one teacher head, not a consensus.

The models applied no category: nothing in the taxonomy fit this work.
Study designTheoretical or conceptual
Domainnot available
GenreEmpirical

How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".

Quick stats

Citations0
Published2023
Admission routes1
Has abstractyes

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