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Naïve Bayes
In statistics, naive (sometimes simple or idiot's) Bayes classifiers are a family of "probabilistic classifiers" which assumes that the features are conditionally independent, given the target class. In other words, a naive Bayes model assumes the information about the class provided by each variable is unrelated to the information from the others, with no information shared between the predictors. The highly unrealistic nature of this assumption, called the naive independence assumption, is what gives the classifier its name. These classifiers are some of the simplest Bayesian network models. Naive Bayes classifiers generally perform worse than more advanced models like logistic regressions, especially at quantifying uncertainty (with naive Bayes models often producing wildly overconfident probabilities). However, they are highly scalable, requiring only one parameter for each feature or predictor in a learning problem. Maximum-likelihood training can be done by evaluating a clo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Naive Corral
Naivety (also spelled naïvety), naiveness, or naïveté is the state of being naive. It refers to an apparent or actual lack of experience and sophistication, often describing a neglect of pragmatism in favor of moral idealism. A ''naïve'' may be called a ''naïf''. Etymology In its early use, the word ''naïve'' meant "natural or innocent", and did not connote ineptitude. As a French adjective, it is spelled ''naïve'', for feminine nouns, and ''naïf'', for masculine nouns. As a French noun, it is spelled ''naïveté''. It is sometimes spelled "naïve" with a diaeresis, but as an unitalicized English word, "naive" is now the more usual spelling. "naïf" often represents the French masculine, but has a secondary meaning as an artistic style. "Naïve" is pronounced as two syllables, in the French manner, and with the stress on the second one. Culture The naïf appears as a cultural type in two main forms. On the one hand, there is 'the satirical naïf, such as Candide'. Nor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Maximum Likelihood
In statistics, maximum likelihood estimation (MLE) is a method of estimating the parameters of an assumed probability distribution, given some observed data. This is achieved by maximizing a likelihood function so that, under the assumed statistical model, the observed data is most probable. The point in the parameter space that maximizes the likelihood function is called the maximum likelihood estimate. The logic of maximum likelihood is both intuitive and flexible, and as such the method has become a dominant means of statistical inference. If the likelihood function is differentiable, the derivative test for finding maxima can be applied. In some cases, the first-order conditions of the likelihood function can be solved analytically; for instance, the ordinary least squares estimator for a linear regression model maximizes the likelihood when the random errors are assumed to have normal distributions with the same variance. From the perspective of Bayesian inference, ML ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Arithmetic Underflow
The term arithmetic underflow (also floating-point underflow, or just underflow) is a condition in a computer program where the result of a calculation is a number of more precise absolute value than the computer can actually represent in memory on its central processing unit (CPU). Arithmetic underflow can occur when the true result of a floating-point operation is smaller in magnitude (that is, closer to zero) than the smallest value representable as a normal floating-point number in the target datatype. Underflow can in part be regarded as negative overflow of the exponent of the floating-point value. For example, if the exponent part can represent values from −128 to 127, then a result with a value less than −128 may cause underflow. Underflow gap The interval between −''fminN'' and ''fminN'', where ''fminN'' is the smallest positive normal floating-point value, is called the underflow gap. This is because the size of this interval is many orders of magnitude ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nat (unit)
The natural unit of information (symbol: nat), sometimes also nit or nepit, is a unit of information or information entropy, based on natural logarithms and powers of e (mathematical constant), ''e'', rather than the powers of 2 and binary logarithm, base 2 logarithms, which define the shannon (unit), shannon. This unit is also known by its unit symbol, the nat. One nat is the information content of an event when the probability of that event occurring is 1/e (mathematical constant), ''e''. One nat is equal to shannon (unit), shannons ≈ 1.44 Sh or, equivalently, hartley (unit), hartleys ≈ 0.434 Hart. History Boulton and Chris Wallace (computer scientist), Wallace used the term ''nit'' in conjunction with minimum message length, which was subsequently changed by the minimum description length community to ''nat'' to avoid confusion with the nit (unit), nit used as a unit of luminance. Alan Turing used the ''natural ban (unit), ban''. Entropy Shan ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Discriminative Model
Discriminative models, also referred to as conditional models, are a class of models frequently used for classification. They are typically used to solve binary classification problems, i.e. assign labels, such as pass/fail, win/lose, alive/dead or healthy/sick, to existing datapoints. Types of discriminative models include logistic regression (LR), conditional random fields (CRFs), decision trees among many others. Generative model approaches which uses a joint probability distribution instead, include naive Bayes classifiers, Gaussian mixture models, variational autoencoders, generative adversarial networks and others. Definition Unlike generative modelling, which studies the joint probability P(x,y), discriminative modeling studies the P(y, x) or maps the given unobserved variable (target) x to a class label y dependent on the observed variables (training samples). For example, in object recognition, x is likely to be a vector of raw pixels (or features extracted from the ra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Proportionality (mathematics)
In mathematics, two sequences of numbers, often experimental data, are proportional or directly proportional if their corresponding elements have a constant ratio. The ratio is called ''coefficient of proportionality'' (or ''proportionality constant'') and its reciprocal is known as ''constant of normalization'' (or ''normalizing constant''). Two sequences are inversely proportional if corresponding elements have a constant product. Two functions f(x) and g(x) are ''proportional'' if their ratio \frac is a constant function. If several pairs of variables share the same direct proportionality constant, the equation expressing the equality of these ratios is called a proportion, e.g., (for details see Ratio). Proportionality is closely related to ''linearity''. Direct proportionality Given an independent variable ''x'' and a dependent variable ''y'', ''y'' is directly proportional to ''x'' if there is a positive constant ''k'' such that: : y = kx The relation is oft ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mutually Independent
Independence is a fundamental notion in probability theory, as in statistics and the theory of stochastic processes. Two events are independent, statistically independent, or stochastically independent if, informally speaking, the occurrence of one does not affect the probability of occurrence of the other or, equivalently, does not affect the odds. Similarly, two random variables are independent if the realization of one does not affect the probability distribution of the other. When dealing with collections of more than two events, two notions of independence need to be distinguished. The events are called pairwise independent if any two events in the collection are independent of each other, while mutual independence (or collective independence) of events means, informally speaking, that each event is independent of any combination of other events in the collection. A similar notion exists for collections of random variables. Mutual independence implies pairwise independence, b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Conditional Independence
In probability theory, conditional independence describes situations wherein an observation is irrelevant or redundant when evaluating the certainty of a hypothesis. Conditional independence is usually formulated in terms of conditional probability, as a special case where the probability of the hypothesis given the uninformative observation is equal to the probability without. If A is the hypothesis, and B and C are observations, conditional independence can be stated as an equality: :P(A\mid B,C) = P(A \mid C) where P(A \mid B, C) is the probability of A given both B and C. Since the probability of A given C is the same as the probability of A given both B and C, this equality expresses that B contributes nothing to the certainty of A. In this case, A and B are said to be conditionally independent given C, written symbolically as: (A \perp\!\!\!\perp B \mid C). The concept of conditional independence is essential to graph-based theories of statistical inference, as it estab ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
