Correlation in the context of Kernel trick

Medical diagnosis (abbreviated Dx, D_x, or D_s) is the process of determining which disease or condition explains a person's symptoms and signs. It is most often referred to as a diagnosis with the medical context being implicit. The information required for a diagnosis is typically collected from a history and physical examination of the person seeking medical care. Often, one or more diagnostic procedures, such as medical tests, are also done during the process. Sometimes the posthumous diagnosis is considered a kind of medical diagnosis.

Diagnosis is often challenging because many signs and symptoms are nonspecific. For example, redness of the skin (erythema), by itself, is a sign of many disorders and thus does not tell the healthcare professional what is wrong. Thus differential diagnosis, in which several possible explanations are compared and contrasted, must be performed. This involves the correlation of various pieces of information followed by the recognition and differentiation of patterns. Occasionally the process is made easy by a sign or symptom (or a group of several) that is pathognomonic.

There is scientific consensus that the Earth has been consistently warming since the start of the Industrial Revolution, that the rate of recent warming is largely unprecedented, and that this warming is mainly the result of a rapid increase in atmospheric carbon dioxide (CO₂) caused by human activities. The human activities causing this warming include fossil fuel combustion, cement production, and land use changes such as deforestation, with a significant supporting role from the other greenhouse gases such as methane and nitrous oxide. This human role in climate change is considered "unequivocal" and "incontrovertible".

Nearly all actively publishing climate scientists say humans are causing climate change. Surveys of the scientific literature are another way to measure scientific consensus. A 2019 review of scientific papers found the consensus on the cause of climate change to be at 100%, and a 2021 study concluded that over 99% of scientific papers agree on the human cause of climate change. The small percentage of papers that disagreed with the consensus often contained errors or could not be replicated.

The g factor is a construct developed in psychometric investigations of cognitive abilities and human intelligence. It is a variable that summarizes positive correlations among different cognitive tasks, reflecting the assertion that an individual's performance on one type of cognitive task tends to be comparable to that person's performance on other kinds of cognitive tasks. The g factor typically accounts for 40 to 50 percent of the between-individual performance differences on a given cognitive test, and composite scores ("IQ scores") based on many tests are frequently regarded as estimates of individuals' standing on the g factor. The terms IQ, general intelligence, general cognitive ability, general mental ability, and simply intelligence are often used interchangeably to refer to this common core shared by cognitive tests. However, the g factor itself is a mathematical construct indicating the level of observed correlation between cognitive tasks. The measured value of this construct depends on the cognitive tasks that are used, and little is known about the underlying causes of the observed correlations.

The existence of the g factor was originally proposed by the English psychologist Charles Spearman in the early years of the 20th century. He observed that children's performance ratings, across seemingly unrelated school subjects, were positively correlated, and reasoned that these correlations reflected the influence of an underlying general mental ability that entered into performance on all kinds of mental tests. Spearman suggested that all mental performance could be conceptualized in terms of a single general ability factor, which he labeled g, and many narrow task-specific ability factors. Soon after Spearman proposed the existence of g, it was challenged by Godfrey Thomson, who presented evidence that such intercorrelations among test results could arise even if no g-factor existed.

Carbonate rocks are a class of sedimentary rocks composed primarily of carbonate minerals. The two major types are limestone, which is composed of calcite or aragonite (different crystal forms of CaCO₃), and dolomite rock (also known as dolostone), which is composed of dolomite (CaMg(CO₃)₂). They are usually classified on the basis of texture and grain size. Importantly, carbonate rocks can exist as metamorphic and igneous rocks, too. When recrystallized carbonate rocks are metamorphosed, marble is created. Rare igneous carbonate rocks even exist as intrusive carbonatites and, even rarer, there exists volcanic carbonate lava.

Carbonate rocks are also crucial components to understanding geologic history due to processes such as diagenesis in which carbonates undergo compositional changes based on kinetic effects. The correlation between this compositional change and temperature can be exploited to reconstruct past climate as is done in paleoclimatology. Carbonate rocks can also be used for understanding various other systems as described below.

Type physicalism (also known as reductive materialism, type identity theory, mind–brain identity theory, and identity theory of mind) is a physicalist theory in the philosophy of mind. It asserts that mental events can be grouped into types, and can then be correlated with types of physical events in the brain. For example, one type of mental event, such as "mental pains" will, presumably, turn out to be describing one type of physical event (like C-fiber firings).

Type physicalism is contrasted with token identity physicalism, which argues that mental events are unlikely to have "steady" or categorical biological correlates. These positions make use of the philosophical type–token distinction (e.g., Two persons having the same "type" of car need not mean that they share a "token", a single vehicle). Type physicalism can now be understood to argue that there is an identity between types (any mental type is identical with some physical type), whereas token identity physicalism says that every token mental state/event/property is identical to some brain state/event/property.

The neural correlates of consciousness (NCC) are the minimal set of neuronal events and mechanisms sufficient for the occurrence of the mental states to which they are related. Neuroscientists use empirical approaches to discover neural correlates of subjective phenomena; that is, neural changes which necessarily and regularly correlate with a specific experience.

A syndrome is a set of medical signs and symptoms which are correlated with each other and often associated with a particular disease or disorder. The word derives from the Greek σύνδρομον, meaning "concurrence". When a syndrome is paired with a definite cause this becomes a disease. In some instances, a syndrome is so closely linked with a pathogenesis or cause that the words syndrome, disease, and disorder end up being used interchangeably for them. This substitution of terminology often confuses the reality and meaning of medical diagnoses. This is especially true of inherited syndromes. About one third of all phenotypes that are listed in OMIM are described as dysmorphic, which usually refers to the facial gestalt. For example, Down syndrome, Wolf–Hirschhorn syndrome, and Andersen–Tawil syndrome are disorders with known pathogeneses, so each is more than just a set of signs and symptoms, despite the syndrome nomenclature. In other instances, a syndrome is not specific to only one disease. For example, toxic shock syndrome can be caused by various toxins; another medical syndrome named as premotor syndrome can be caused by various brain lesions; and premenstrual syndrome is not a disease but simply a set of symptoms.

If an underlying genetic cause is suspected but not known, a condition may be referred to as a genetic association (often just "association" in context). By definition, an association indicates that the collection of signs and symptoms occurs in combination more frequently than would be likely by chance alone.

In psychology and psychometrics, the big five personality trait model or five-factor model (FFM)—sometimes called by the acronym OCEAN or CANOE—is a scientific model for measuring and describing human personality traits. The framework groups variation in personality into five separate factors, all measured on a continuous scale:

• openness (O) measures creativity, curiosity, and willingness to entertain new ideas.
• conscientiousness (C) measures self-control, diligence, and attention to detail.
• extraversion (E) measures boldness, energy, and social interactivity.
• agreeableness (A) measures kindness, helpfulness, and willingness to cooperate.
• neuroticism (N) measures depression, irritability, and moodiness.

The five-factor model was developed using empirical research into the language people used to describe themselves, which found patterns and relationships between the words people use to describe themselves. For example, because someone described as "hard-working" is more likely to be described as "prepared" and less likely to be described as "messy", all three traits are grouped under conscientiousness. Using dimensionality reduction techniques, psychologists showed that most (though not all) of the variance in human personality can be explained using only these five factors.

In statistics, a proxy or proxy variable is a variable that is not in itself directly relevant, but that serves in place of an unobservable or immeasurable variable. In order for a variable to be a good proxy, it must have a close correlation, not necessarily linear, with the variable of interest. This correlation might be either positive or negative.

Proxy variable must relate to an unobserved variable, must correlate with disturbance, and must not correlate with regressors once the disturbance is controlled for.

The Merton thesis is an argument about the nature of early experimental science proposed by Robert K. Merton. Similar to Max Weber's famous claim on the link between Protestant work ethic and the capitalist economy, Merton argued for a similar positive correlation between the rise of Protestant Pietism and early experimental science. The Merton thesis has resulted in continuous debates.

Although scholars are still debating it, Merton's 1936 doctoral dissertation (and two years later his first monograph by the same title) Science, Technology and Society in 17th-Century England raised important issues on the connections between religion and the rise of modern science, became a significant work in the realm of the sociology of science and continues to be cited in new scholarship. Merton further developed this thesis in other publications.

In statistics, the intraclass correlation, or the intraclass correlation coefficient (ICC), is a descriptive statistic that can be used when quantitative measurements are made on units that are organized into groups. It describes how strongly units in the same group resemble each other. While it is viewed as a type of correlation, unlike most other correlation measures, it operates on data structured as groups rather than data structured as paired observations.

The intraclass correlation is commonly used to quantify the degree to which individuals with a fixed degree of relatedness (e.g. full siblings) resemble each other in terms of a quantitative trait (see heritability). Another prominent application is the assessment of consistency or reproducibility of quantitative measurements made by different observers measuring the same quantity.

In science, an empirical relationship or phenomenological relationship is a relationship or correlation that is supported by experiment or observation but not necessarily supported by theory.

Sir Francis Galton FRS FRAI (/ˈɡɔːltən/; 16 February 1822 – 17 January 1911) was an English polymath and the originator of eugenics during the Victorian era; his ideas later became the basis of behavioural genetics.

Galton produced over 340 papers and books. He also developed the statistical concept of correlation and widely promoted regression toward the mean. He was the first to apply statistical methods to the study of human differences and inheritance of intelligence, and introduced the use of questionnaires and surveys for collecting data on human communities, which he needed for genealogical and biographical works and for his anthropometric studies. He popularised the phrase "nature versus nurture". His book Hereditary Genius (1869) was the first social scientific attempt to study genius and greatness.

In physics, the terms order and disorder designate the presence or absence of some symmetry or correlation in a many-particle system.

In condensed matter physics, systems typically are ordered at low temperatures; upon heating, they undergo one or several phase transitions into less ordered states.Examples for such an order-disorder transition are:

In statistics, the Pearson correlation coefficient (PCC) is a correlation coefficient that measures linear correlation between two sets of data. It is the ratio between the covariance of two variables and the product of their standard deviations; thus, it is essentially a normalized measurement of the covariance, such that the result always has a value between −1 and 1. A key difference is that unlike covariance, this correlation coefficient does not have units, allowing comparison of the strength of the joint association between different pairs of random variables that do not necessarily have the same units. As with covariance itself, the measure can only reflect a linear correlation of variables, and ignores many other types of relationships or correlations. As a simple example, one would expect the age and height of a sample of children from a school to have a Pearson correlation coefficient significantly greater than 0, but less than 1 (as 1 would represent an unrealistically perfect correlation).

The phrase "correlation does not imply causation" refers to the inability to legitimately deduce a cause-and-effect relationship between two events or variables solely on the basis of an observed association or correlation between them. The idea that "correlation implies causation" is an example of a questionable-cause logical fallacy, in which two events occurring together are taken to have established a cause-and-effect relationship. This fallacy is also known by the Latin phrase cum hoc ergo propter hoc ("with this, therefore because of this"). This differs from the fallacy known as post hoc ergo propter hoc ("after this, therefore because of this"), in which an event following another is seen as a necessary consequence of the former event, and from conflation, the errant merging of two events, ideas, databases, etc., into one.

As with any logical fallacy, identifying that the reasoning behind an argument is flawed does not necessarily imply that the resulting conclusion is false. Statistical methods have been proposed that use correlation as the basis for hypothesis tests for causality, including the Granger causality test and convergent cross mapping. The Bradford Hill criteria, also known as Hill's criteria for causation, are a group of nine principles that can be useful in considering the epidemiologic evidence of a causal relationship. Ultimately, assumptions are always required to draw causal conclusions, and modern causal inference frameworks focus on interrogating the strength of these assumptions.