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PAQ
PAQ is a series of lossless data compression archivers that have gone through collaborative development to top rankings on several benchmarks measuring compression ratio (although at the expense of speed and memory usage). Specialized versions of PAQ have won the Hutter Prize and the Calgary Challenge. PAQ is free software distributed under the GNU General Public License. Algorithm PAQ uses a context mixing algorithm. Context mixing is related to prediction by partial matching (PPM) in that the compressor is divided into a predictor and an arithmetic coder, but differs in that the next-symbol prediction is computed using a weighted combination of probability estimates from a large number of models conditioned on different contexts. Unlike PPM, a context doesn't need to be contiguous. Most PAQ versions collect next-symbol statistics for the following contexts: * ''n''-grams; the context is the last bytes before the predicted symbol (as in PPM); * whole-word ''n''-grams, i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hutter Prize
The Hutter Prize is a cash prize funded by Marcus Hutter which rewards data compression improvements on a specific 1 Gigabyte, GB English text file, with the goal of encouraging research in artificial intelligence (AI). Launched in 2006, the prize awards 5000 euros for each one percent improvement (with 500,000 euros total funding) in the compressed size of the file ''enwik9'', which is the larger of two files used in the Large Text Compression Benchmark; enwik9 consists of the first 1,000,000,000 characters of a specific version of English Wikipedia. The ongoing competition is organized by Hutter, Matt Mahoney, and Jim Bowery. Goals The goal of the Hutter Prize is to encourage research in artificial intelligence (AI). The organizers believe that text compression and AI are equivalent problems. Hutter proved that the optimal behavior of a goal-seeking agent in an unknown but computable environment is to guess at each step that the environment is probably controlled by one of the s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hutter Prize
The Hutter Prize is a cash prize funded by Marcus Hutter which rewards data compression improvements on a specific 1 Gigabyte, GB English text file, with the goal of encouraging research in artificial intelligence (AI). Launched in 2006, the prize awards 5000 euros for each one percent improvement (with 500,000 euros total funding) in the compressed size of the file ''enwik9'', which is the larger of two files used in the Large Text Compression Benchmark; enwik9 consists of the first 1,000,000,000 characters of a specific version of English Wikipedia. The ongoing competition is organized by Hutter, Matt Mahoney, and Jim Bowery. Goals The goal of the Hutter Prize is to encourage research in artificial intelligence (AI). The organizers believe that text compression and AI are equivalent problems. Hutter proved that the optimal behavior of a goal-seeking agent in an unknown but computable environment is to guess at each step that the environment is probably controlled by one of the s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Context Mixing
Context mixing is a type of data compression algorithm in which the next-symbol predictions of two or more statistical models are combined to yield a prediction that is often more accurate than any of the individual predictions. For example, one simple method (not necessarily the best) is to average the probabilities assigned by each model. The random forest is another method: it outputs the prediction that is the mode of the predictions output by individual models. Combining models is an active area of research in machine learning. The PAQ series of data compression programs use context mixing to assign probabilities to individual bits of the input. Application to Data Compression Suppose that we are given two conditional probabilities, P(X, A) and P(X, B), and we wish to estimate P(X, A,B), the probability of event X given both conditions A and B. There is insufficient information for probability theory to give a result. In fact, it is possible to construct scenarios in which ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Prediction By Partial Matching
Prediction by partial matching (PPM) is an adaptive statistical data compression technique based on context modeling and prediction. PPM models use a set of previous symbols in the uncompressed symbol stream to predict the next symbol in the stream. PPM algorithms can also be used to cluster data into predicted groupings in cluster analysis. Theory Predictions are usually reduced to symbol rankings. Each symbol (a letter, bit or any other amount of data) is ranked before it is compressed, and the ranking system determines the corresponding codeword (and therefore the compression rate). In many compression algorithms, the ranking is equivalent to probability mass function estimation. Given the previous letters (or given a context), each symbol is assigned with a probability. For instance, in arithmetic coding the symbols are ranked by their probabilities to appear after previous symbols, and the whole sequence is compressed into a single fraction that is computed according ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Prediction By Partial Matching
Prediction by partial matching (PPM) is an adaptive statistical data compression technique based on context modeling and prediction. PPM models use a set of previous symbols in the uncompressed symbol stream to predict the next symbol in the stream. PPM algorithms can also be used to cluster data into predicted groupings in cluster analysis. Theory Predictions are usually reduced to symbol rankings. Each symbol (a letter, bit or any other amount of data) is ranked before it is compressed, and the ranking system determines the corresponding codeword (and therefore the compression rate). In many compression algorithms, the ranking is equivalent to probability mass function estimation. Given the previous letters (or given a context), each symbol is assigned with a probability. For instance, in arithmetic coding the symbols are ranked by their probabilities to appear after previous symbols, and the whole sequence is compressed into a single fraction that is computed according ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Backpropagation
In machine learning, backpropagation (backprop, BP) is a widely used algorithm for training feedforward neural network, feedforward artificial neural networks. Generalizations of backpropagation exist for other artificial neural networks (ANNs), and for functions generally. These classes of algorithms are all referred to generically as "backpropagation". In Artificial neural network#Learning, fitting a neural network, backpropagation computes the gradient of the loss function with respect to the Glossary of graph theory terms#weight, weights of the network for a single input–output example, and does so Algorithmic efficiency, efficiently, unlike a naive direct computation of the gradient with respect to each weight individually. This efficiency makes it feasible to use gradient methods for training multilayer networks, updating weights to minimize loss; gradient descent, or variants such as stochastic gradient descent, are commonly used. The backpropagation algorithm works by ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Root Mean Square
In mathematics and its applications, the root mean square of a set of numbers x_i (abbreviated as RMS, or rms and denoted in formulas as either x_\mathrm or \mathrm_x) is defined as the square root of the mean square (the arithmetic mean of the squares) of the set. The RMS is also known as the quadratic mean (denoted M_2) and is a particular case of the generalized mean. The RMS of a continuously varying function (denoted f_\mathrm) can be defined in terms of an integral of the squares of the instantaneous values during a cycle. For alternating electric current, RMS is equal to the value of the constant direct current that would produce the same power dissipation in a resistive load. In estimation theory, the root-mean-square deviation of an estimator is a measure of the imperfection of the fit of the estimator to the data. Definition The RMS value of a set of values (or a continuous-time waveform) is the square root of the arithmetic mean of the squares of the values, or th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nonlinear
In mathematics and science, a nonlinear system is a system in which the change of the output is not proportional to the change of the input. Nonlinear problems are of interest to engineers, biologists, physicists, mathematicians, and many other scientists because most systems are inherently nonlinear in nature. Nonlinear dynamical systems, describing changes in variables over time, may appear chaotic, unpredictable, or counterintuitive, contrasting with much simpler linear systems. Typically, the behavior of a nonlinear system is described in mathematics by a nonlinear system of equations, which is a set of simultaneous equations in which the unknowns (or the unknown functions in the case of differential equations) appear as variables of a polynomial of degree higher than one or in the argument of a function which is not a polynomial of degree one. In other words, in a nonlinear system of equations, the equation(s) to be solved cannot be written as a linear combination of the un ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hash Table
In computing, a hash table, also known as hash map, is a data structure that implements an associative array or dictionary. It is an abstract data type that maps keys to values. A hash table uses a hash function to compute an ''index'', also called a ''hash code'', into an array of ''buckets'' or ''slots'', from which the desired value can be found. During lookup, the key is hashed and the resulting hash indicates where the corresponding value is stored. Ideally, the hash function will assign each key to a unique bucket, but most hash table designs employ an imperfect hash function, which might cause hash ''collisions'' where the hash function generates the same index for more than one key. Such collisions are typically accommodated in some way. In a well-dimensioned hash table, the average time complexity for each lookup is independent of the number of elements stored in the table. Many hash table designs also allow arbitrary insertions and deletions of key–value pairs, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
English Wikipedia
The English Wikipedia is, along with the Simple English Wikipedia, one of two English-language editions of Wikipedia, an online encyclopedia. It was founded on January 15, 2001, as Wikipedia's first edition, and, as of , has the most articles of any edition, at . As of , of articles in all Wikipedias belong to the English-language edition; this share was more than 50% in 2003. The edition's one-billionth edit was made on January 13, 2021. Articles The English Wikipedia has pioneered some ideas as conventions, policies or features which were later adopted by Wikipedia editions in some of the other languages. These ideas include "featured articles", the neutral-point-of-view policy, navigation templates, the sorting of short "stub" articles into sub-categories, dispute resolution mechanisms such as mediation and arbitration, and weekly collaborations. It surpassed six million articles on 23 January 2020. In November 2022, the total volume of the compressed texts of it ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lookup Table
In computer science, a lookup table (LUT) is an array that replaces runtime computation with a simpler array indexing operation. The process is termed as "direct addressing" and LUTs differ from hash tables in a way that, to retrieve a value v with key k, a hash table would store the value v in the slot h(k) where h is a hash function i.e. k is used to compute the slot, while in the case of LUT, the value v is stored in slot k, thus directly addressable. The savings in processing time can be significant, because retrieving a value from memory is often faster than carrying out an "expensive" computation or input/output operation. The tables may be precalculated and stored in static program storage, calculated (or "pre-fetched") as part of a program's initialization phase ( memoization), or even stored in hardware in application-specific platforms. Lookup tables are also used extensively to validate input values by matching against a list of valid (or invalid) items in an array and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
