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wiki_9_chunk_16 | Algorithms for calculating variance | population_variance = S / w_sum
# Bessel's correction for weighted samples
# Frequency weights
sample_frequency_variance = S / (w_sum - 1)
# Reliability weights
sample_reliability_variance = S / (w_sum - w_sum2 / w_sum) Parallel algorithm
Chan et al. note that Welford's online algorithm detailed abo... | wikipedia |
wiki_9_chunk_17 | Algorithms for calculating variance | Chan's method for estimating the mean is numerically unstable when and both are large, because the numerical error in is not scaled down in the way that it is in the case. In such cases, prefer .
def parallel_variance(n_a, avg_a, M2_a, n_b, avg_b, M2_b):
n = n_a + n_b
delta = avg_b - avg_a
M2 = M2_a + M2... | wikipedia |
wiki_9_chunk_18 | Algorithms for calculating variance | Example
Assume that all floating point operations use standard IEEE 754 double-precision arithmetic. Consider the sample (4, 7, 13, 16) from an infinite population. Based on this sample, the estimated population mean is 10, and the unbiased estimate of population variance is 30. Both the naïve algorithm and two-pass a... | wikipedia |
wiki_9_chunk_19 | Algorithms for calculating variance | While this loss of precision may be tolerable and viewed as a minor flaw of the naïve algorithm, further increasing the offset makes the error catastrophic. Consider the sample (, , , ). Again the estimated population variance of 30 is computed correctly by the two-pass algorithm, but the naïve algorithm now computes... | wikipedia |
wiki_9_chunk_20 | Algorithms for calculating variance | Higher-order statistics
Terriberry extends Chan's formulae to calculating the third and fourth central moments, needed for example when estimating skewness and kurtosis: Here the are again the sums of powers of differences from the mean , giving For the incremental case (i.e., ), this simplifies to: By preserving the ... | wikipedia |
wiki_9_chunk_21 | Algorithms for calculating variance | An example of the online algorithm for kurtosis implemented as described is:
def online_kurtosis(data):
n = mean = M2 = M3 = M4 = 0 | wikipedia |
wiki_9_chunk_22 | Algorithms for calculating variance | for x in data:
n1 = n
n = n + 1
delta = x - mean
delta_n = delta / n
delta_n2 = delta_n * delta_n
term1 = delta * delta_n * n1
mean = mean + delta_n
M4 = M4 + term1 * delta_n2 * (n*n - 3*n + 3) + 6 * delta_n2 * M2 - 4 * delta_n * M3
M3 = M3 + term1... | wikipedia |
wiki_9_chunk_23 | Algorithms for calculating variance | # Note, you may also calculate variance using M2, and skewness using M3
# Caution: If all the inputs are the same, M2 will be 0, resulting in a division by 0.
kurtosis = (n * M4) / (M2 * M2) - 3
return kurtosis Pébaÿ
further extends these results to arbitrary-order central moments, for the incremental and t... | wikipedia |
wiki_9_chunk_24 | Algorithms for calculating variance | Choi and Sweetman
offer two alternative methods to compute the skewness and kurtosis, each of which can save substantial computer memory requirements and CPU time in certain applications. The first approach is to compute the statistical moments by separating the data into bins and then computing the moments from the ge... | wikipedia |
wiki_9_chunk_25 | Algorithms for calculating variance | where and represent the frequency and the relative frequency at bin and is the total area of the histogram. After this normalization, the raw moments and central moments of can be calculated from the relative histogram: where the superscript indicates the moments are calculated from the histogram. For constant b... | wikipedia |
wiki_9_chunk_26 | Algorithms for calculating variance | The second approach from Choi and Sweetman is an analytical methodology to combine statistical moments from individual segments of a time-history such that the resulting overall moments are those of the complete time-history. This methodology could be used for parallel computation of statistical moments with subsequent... | wikipedia |
wiki_9_chunk_27 | Algorithms for calculating variance | The benefit of expressing the statistical moments in terms of is that the sets can be combined by addition, and there is no upper limit on the value of . where the subscript represents the concatenated time-history or combined . These combined values of can then be inversely transformed into raw moments representin... | wikipedia |
wiki_9_chunk_28 | Algorithms for calculating variance | Covariance
Very similar algorithms can be used to compute the covariance. Naïve algorithm
The naïve algorithm is For the algorithm above, one could use the following Python code:
def naive_covariance(data1, data2):
n = len(data1)
sum12 = 0
sum1 = sum(data1)
sum2 = sum(data2) for i1, i2 in zip(data1, dat... | wikipedia |
wiki_9_chunk_29 | Algorithms for calculating variance | With estimate of the mean
As for the variance, the covariance of two random variables is also shift-invariant, so given any two constant values and it can be written: and again choosing a value inside the range of values will stabilize the formula against catastrophic cancellation as well as make it more robust again... | wikipedia |
wiki_9_chunk_30 | Algorithms for calculating variance | def shifted_data_covariance(data_x, data_y):
n = len(data_x)
if n < 2:
return 0
kx = data_x[0]
ky = data_y[0]
Ex = Ey = Exy = 0
for ix, iy in zip(data_x, data_y):
Ex += ix - kx
Ey += iy - ky
Exy += (ix - kx) * (iy - ky)
return (Exy - Ex * Ey / n) / n | wikipedia |
wiki_9_chunk_31 | Algorithms for calculating variance | Two-pass
The two-pass algorithm first computes the sample means, and then the covariance: The two-pass algorithm may be written as:
def two_pass_covariance(data1, data2):
n = len(data1) mean1 = sum(data1) / n
mean2 = sum(data2) / n covariance = 0 for i1, i2 in zip(data1, data2):
a = i1 - mean1
b... | wikipedia |
wiki_9_chunk_32 | Algorithms for calculating variance | A slightly more accurate compensated version performs the full naive algorithm on the residuals. The final sums and should be zero, but the second pass compensates for any small error. Online A stable one-pass algorithm exists, similar to the online algorithm for computing the variance, that computes co-moment : The... | wikipedia |
wiki_9_chunk_33 | Algorithms for calculating variance | def online_covariance(data1, data2):
meanx = meany = C = n = 0
for x, y in zip(data1, data2):
n += 1
dx = x - meanx
meanx += dx / n
meany += (y - meany) / n
C += dx * (y - meany) population_covar = C / n
# Bessel's correction for sample variance
sample_covar = C /... | wikipedia |
wiki_9_chunk_34 | Algorithms for calculating variance | def online_weighted_covariance(data1, data2, data3):
meanx = meany = 0
wsum = wsum2 = 0
C = 0
for x, y, w in zip(data1, data2, data3):
wsum += w
wsum2 += w * w
dx = x - meanx
meanx += (w / wsum) * dx
meany += (w / wsum) * (y - meany)
C += w * dx * (y - mea... | wikipedia |
wiki_9_chunk_35 | Algorithms for calculating variance | population_covar = C / wsum
# Bessel's correction for sample variance
# Frequency weights
sample_frequency_covar = C / (wsum - 1)
# Reliability weights
sample_reliability_covar = C / (wsum - wsum2 / wsum) Likewise, there is a formula for combining the covariances of two sets that can be used to para... | wikipedia |
wiki_9_chunk_36 | Algorithms for calculating variance | See also
Kahan summation algorithm
Squared deviations from the mean
Yamartino method References External links Statistical algorithms
Statistical deviation and dispersion
Articles with example pseudocode
Articles with example Python (programming language) code | wikipedia |
wiki_10_chunk_0 | Algebraic number | An algebraic number is a number that is a root of a non-zero polynomial in one variable with integer (or, equivalently, rational) coefficients. For example, the golden ratio, , is an algebraic number, because it is a root of the polynomial . That is, it is a value for x for which the polynomial evaluates to zero. As ... | wikipedia |
wiki_10_chunk_1 | Algebraic number | The set of algebraic numbers is countably infinite and has measure zero in the Lebesgue measure as a subset of the uncountable complex numbers. In that sense, almost all complex numbers are transcendental. | wikipedia |
wiki_10_chunk_2 | Algebraic number | Examples
All rational numbers are algebraic. Any rational number, expressed as the quotient of an integer and a (non-zero) natural number , satisfies the above definition, because is the root of a non-zero polynomial, namely .
Quadratic irrational numbers, irrational solutions of a quadratic polynomial with intege... | wikipedia |
wiki_10_chunk_3 | Algebraic number | Properties | wikipedia |
wiki_10_chunk_4 | Algebraic number | If a polynomial with rational coefficients is multiplied through by the least common denominator, the resulting polynomial with integer coefficients has the same roots. This shows that an algebraic number can be equivalently defined as a root of a polynomial with either integer or rational coefficients.
Given an algeb... | wikipedia |
wiki_10_chunk_5 | Algebraic number | Field The sum, difference, product and quotient (if the denominator is nonzero) of two algebraic numbers is again algebraic, as can be demonstrated by using the resultant, and algebraic numbers thus form a field (sometimes denoted by , but that usually denotes the adele ring). Every root of a polynomial equation whose... | wikipedia |
wiki_10_chunk_6 | Algebraic number | The set of real algebraic numbers itself forms a field. Related fields Numbers defined by radicals
Any number that can be obtained from the integers using a finite number of additions, subtractions, multiplications, divisions, and taking (possibly complex) th roots where is a positive integer are algebraic. The conver... | wikipedia |
wiki_10_chunk_7 | Algebraic number | has a unique real root that cannot be expressed in terms of only radicals and arithmetic operations. Closed-form number | wikipedia |
wiki_10_chunk_8 | Algebraic number | Algebraic numbers are all numbers that can be defined explicitly or implicitly in terms of polynomials, starting from the rational numbers. One may generalize this to "closed-form numbers", which may be defined in various ways. Most broadly, all numbers that can be defined explicitly or implicitly in terms of polynomia... | wikipedia |
wiki_10_chunk_9 | Algebraic number | Algebraic integers An algebraic integer is an algebraic number that is a root of a polynomial with integer coefficients with leading coefficient 1 (a monic polynomial). Examples of algebraic integers are and Therefore, the algebraic integers constitute a proper superset of the integers, as the latter are the roots ... | wikipedia |
wiki_10_chunk_10 | Algebraic number | The sum, difference and product of algebraic integers are again algebraic integers, which means that the algebraic integers form a ring. The name algebraic integer comes from the fact that the only rational numbers that are algebraic integers are the integers, and because the algebraic integers in any number field are ... | wikipedia |
wiki_10_chunk_11 | Algebraic number | Special classes
Algebraic solution
Gaussian integer
Eisenstein integer
Quadratic irrational number
Fundamental unit
Root of unity
Gaussian period
Pisot–Vijayaraghavan number
Salem number Notes References Hardy, G. H. and Wright, E. M. 1978, 2000 (with general index) An Introduction to the Theory of Numbers: 5th Edition... | wikipedia |
wiki_10_chunk_12 | Algebraic number | Niven, Ivan 1956. Irrational Numbers, Carus Mathematical Monograph no. 11, Mathematical Association of America.
Ore, Øystein 1948, 1988, Number Theory and Its History, Dover Publications, Inc. New York, (pbk.) | wikipedia |
wiki_11_chunk_0 | Artificial intelligence | Artificial intelligence (AI) is intelligence demonstrated by machines, as opposed to natural intelligence displayed by animals including humans. Leading AI textbooks define the field as the study of "intelligent agents": any system that perceives its environment and takes actions that maximize its chance of achieving i... | wikipedia |
wiki_11_chunk_1 | Artificial intelligence | AI applications include advanced web search engines (e.g., Google), recommendation systems (used by YouTube, Amazon and Netflix), understanding human speech (such as Siri and Alexa), self-driving cars (e.g., Tesla), automated decision-making and competing at the highest level in strategic game systems (such as chess an... | wikipedia |
wiki_11_chunk_2 | Artificial intelligence | Artificial intelligence was founded as an academic discipline in 1956, and in the years since has experienced several waves of optimism, followed by disappointment and the loss of funding (known as an "AI winter"), followed by new approaches, success and renewed funding. AI research has tried and discarded many differe... | wikipedia |
wiki_11_chunk_3 | Artificial intelligence | The various sub-fields of AI research are centered around particular goals and the use of particular tools. The traditional goals of AI research include reasoning, knowledge representation, planning, learning, natural language processing, perception, and the ability to move and manipulate objects. General intelligence ... | wikipedia |
wiki_11_chunk_4 | Artificial intelligence | The field was founded on the assumption that human intelligence "can be so precisely described that a machine can be made to simulate it".
This raises philosophical arguments about the mind and the ethics of creating artificial beings endowed with human-like intelligence. These issues have been explored by myth, fictio... | wikipedia |
wiki_11_chunk_5 | Artificial intelligence | Artificial beings with intelligence appeared as storytelling devices in antiquity,
and have been common in fiction, as in Mary Shelley's Frankenstein or Karel Čapek's R.U.R. These characters and their fates raised many of the same issues now discussed in the ethics of artificial intelligence. | wikipedia |
wiki_11_chunk_6 | Artificial intelligence | The study of mechanical or "formal" reasoning began with philosophers and mathematicians in antiquity. The study of mathematical logic led directly to Alan Turing's theory of computation, which suggested that a machine, by shuffling symbols as simple as "0" and "1", could simulate any conceivable act of mathematical de... | wikipedia |
wiki_11_chunk_7 | Artificial intelligence | The Church-Turing thesis, along with concurrent discoveries in neurobiology, information theory and cybernetics, led researchers to consider the possibility of building an electronic brain.
The first work that is now generally recognized as AI was McCullouch and Pitts' 1943 formal design for Turing-complete "artificial... | wikipedia |
wiki_11_chunk_8 | Artificial intelligence | The field of AI research was born at a workshop at Dartmouth College in 1956.
The attendees became the founders and leaders of AI research.
They and their students produced programs that the press described as "astonishing":
computers were learning checkers strategies, solving word problems in algebra, proving logical ... | wikipedia |
wiki_11_chunk_9 | Artificial intelligence | Researchers in the 1960s and the 1970s were convinced that symbolic approaches would eventually succeed in creating a machine with artificial general intelligence and considered this the goal of their field.
Herbert Simon predicted, "machines will be capable, within twenty years, of doing any work a man can do".
Marvin... | wikipedia |
wiki_11_chunk_10 | Artificial intelligence | They failed to recognize the difficulty of some of the remaining tasks. Progress slowed and in 1974, in response to the criticism of Sir James Lighthill
and ongoing pressure from the US Congress to fund more productive projects, both the U.S. and British governments cut off exploratory research in AI. The next few year... | wikipedia |
wiki_11_chunk_11 | Artificial intelligence | In the early 1980s, AI research was revived by the commercial success of expert systems,
a form of AI program that simulated the knowledge and analytical skills of human experts. By 1985, the market for AI had reached over a billion dollars. At the same time, Japan's fifth generation computer project inspired the U.S a... | wikipedia |
wiki_11_chunk_12 | Artificial intelligence | Many researchers began to doubt that the symbolic approach would be able to imitate all the processes of human cognition, especially perception, robotics, learning and pattern recognition. A number of researchers began to look into "sub-symbolic" approaches to specific AI problems. Robotics researchers, such as Rodney ... | wikipedia |
wiki_11_chunk_13 | Artificial intelligence | AI gradually restored its reputation in the late 1990s and early 21st century by finding specific solutions to specific problems. The narrow focus allowed researchers to produce verifiable results, exploit more mathematical methods, and collaborate with other fields (such as statistics, economics and mathematics).
By ... | wikipedia |
wiki_11_chunk_14 | Artificial intelligence | Faster computers, algorithmic improvements, and access to large amounts of data enabled advances in machine learning and perception; data-hungry deep learning methods started to dominate accuracy benchmarks around 2012.
According to Bloomberg's Jack Clark, 2015 was a landmark year for artificial intelligence, with the ... | wikipedia |
wiki_11_chunk_15 | Artificial intelligence | Numerous academic researchers became concerned that AI was no longer pursuing the original goal of creating versatile, fully intelligent machines. Much of current research involves statistical AI, which is overwhelmingly used to solve specific problems, even highly successful techniques such as deep learning. This conc... | wikipedia |
wiki_11_chunk_16 | Artificial intelligence | Reasoning, problem solving Early researchers developed algorithms that imitated step-by-step reasoning that humans use when they solve puzzles or make logical deductions.
By the late 1980s and 1990s, AI research had developed methods for dealing with uncertain or incomplete information, employing concepts from probabil... | wikipedia |
wiki_11_chunk_17 | Artificial intelligence | Knowledge representation and knowledge engineering
allow AI programs to answer questions intelligently and make deductions about real world facts. | wikipedia |
wiki_11_chunk_18 | Artificial intelligence | A representation of "what exists" is an ontology: the set of objects, relations, concepts, and properties formally described so that software agents can interpret them.
The most general ontologies are called upper ontologies, which attempt to provide a foundation for all other knowledge and act as mediators between dom... | wikipedia |
wiki_11_chunk_19 | Artificial intelligence | AI research has developed tools to represent specific domains, such as: objects, properties, categories and relations between objects;
situations, events, states and time;
causes and effects;
knowledge about knowledge (what we know about what other people know);.
default reasoning (things that humans assume are true un... | wikipedia |
wiki_11_chunk_20 | Artificial intelligence | as well as other domains. Among the most difficult problems in AI are: the breadth of commonsense knowledge (the number of atomic facts that the average person knows is enormous);
and the sub-symbolic form of most commonsense knowledge (much of what people know is not represented as "facts" or "statements" that they co... | wikipedia |
wiki_11_chunk_21 | Artificial intelligence | An intelligent agent that can plan makes a representation of the state of the world, makes predictions about how their actions will change it and makes choices that maximize the utility (or "value") of the available choices.
In classical planning problems, the agent can assume that it is the only system acting in the w... | wikipedia |
wiki_11_chunk_22 | Artificial intelligence | Learning Machine learning (ML), a fundamental concept of AI research since the field's inception,
is the study of computer algorithms that improve automatically through experience. | wikipedia |
wiki_11_chunk_23 | Artificial intelligence | Unsupervised learning finds patterns in a stream of input. Supervised learning requires a human to label the input data first, and comes in two main varieties: classification and numerical regression. Classification is used to determine what category something belongs in—the program sees a number of examples of things ... | wikipedia |
wiki_11_chunk_24 | Artificial intelligence | Computational learning theory can assess learners by computational complexity, by sample complexity (how much data is required), or by other notions of optimization. Natural language processing Natural language processing (NLP)
allows machines to read and understand human language. A sufficiently powerful natural langu... | wikipedia |
wiki_11_chunk_25 | Artificial intelligence | Symbolic AI used formal syntax to translate the deep structure of sentences into logic. This failed to produce useful applications, due to the intractability of logic and the breadth of commonsense knowledge. Modern statistical techniques include co-occurrence frequencies (how often one word appears near another), "Key... | wikipedia |
wiki_11_chunk_26 | Artificial intelligence | Machine perception
is the ability to use input from sensors (such as cameras, microphones, wireless signals, and active lidar, sonar, radar, and tactile sensors) to deduce aspects of the world. Applications include speech recognition,
facial recognition, and object recognition.
Computer vision is the ability to analyze... | wikipedia |
wiki_11_chunk_27 | Artificial intelligence | AI is heavily used in robotics.
Localization is how a robot knows its location and maps its environment. When given a small, static, and visible environment, this is easy; however, dynamic environments, such as (in endoscopy) the interior of a patient's breathing body, pose a greater challenge.
Motion planning is the p... | wikipedia |
wiki_11_chunk_28 | Artificial intelligence | Affective computing is an interdisciplinary umbrella that comprises systems which recognize, interpret, process, or simulate human feeling, emotion and mood.
For example, some virtual assistants are programmed to speak conversationally or even to banter humorously; it makes them appear more sensitive to the emotional ... | wikipedia |
wiki_11_chunk_29 | Artificial intelligence | General intelligence A machine with general intelligence can solve a wide variety of problems with a breadth and versatility similar to human intelligence. There are several competing ideas about how to develop artificial general intelligence. Hans Moravec and Marvin Minsky argue that work in different individual domai... | wikipedia |
wiki_11_chunk_30 | Artificial intelligence | Search and optimization Many problems in AI can be solved theoretically by intelligently searching through many possible solutions:
Reasoning can be reduced to performing a search. For example, logical proof can be viewed as searching for a path that leads from premises to conclusions, where each step is the applicatio... | wikipedia |
wiki_11_chunk_31 | Artificial intelligence | Simple exhaustive searches
are rarely sufficient for most real-world problems: the search space (the number of places to search) quickly grows to astronomical numbers. The result is a search that is too slow or never completes. The solution, for many problems, is to use "heuristics" or "rules of thumb" that prioritize ... | wikipedia |
wiki_11_chunk_32 | Artificial intelligence | A very different kind of search came to prominence in the 1990s, based on the mathematical theory of optimization. For many problems, it is possible to begin the search with some form of a guess and then refine the guess incrementally until no more refinements can be made. These algorithms can be visualized as blind hi... | wikipedia |
wiki_11_chunk_33 | Artificial intelligence | Logic Logic
is used for knowledge representation and problem solving, but it can be applied to other problems as well. For example, the satplan algorithm uses logic for planning
and inductive logic programming is a method for learning. | wikipedia |
wiki_11_chunk_34 | Artificial intelligence | Several different forms of logic are used in AI research. Propositional logic involves truth functions such as "or" and "not". First-order logic
adds quantifiers and predicates, and can express facts about objects, their properties, and their relations with each other. Fuzzy logic assigns a "degree of truth" (between 0... | wikipedia |
wiki_11_chunk_35 | Artificial intelligence | Probabilistic methods for uncertain reasoning | wikipedia |
wiki_11_chunk_36 | Artificial intelligence | Many problems in AI (in reasoning, planning, learning, perception, and robotics) require the agent to operate with incomplete or uncertain information. AI researchers have devised a number of powerful tools to solve these problems using methods from probability theory and economics.
Bayesian networks
are a very general... | wikipedia |
wiki_11_chunk_37 | Artificial intelligence | A key concept from the science of economics is "utility": a measure of how valuable something is to an intelligent agent. Precise mathematical tools have been developed that analyze how an agent can make choices and plan, using decision theory, decision analysis,
and information value theory. These tools include models... | wikipedia |
wiki_11_chunk_38 | Artificial intelligence | The simplest AI applications can be divided into two types: classifiers ("if shiny then diamond") and controllers ("if diamond then pick up"). Controllers do, however, also classify conditions before inferring actions, and therefore classification forms a central part of many AI systems. Classifiers are functions that ... | wikipedia |
wiki_11_chunk_39 | Artificial intelligence | A classifier can be trained in various ways; there are many statistical and machine learning approaches.
The decision tree is the simplest and most widely used symbolic machine learning algorithm.
K-nearest neighbor algorithm was the most widely used analogical AI until the mid-1990s.
Kernel methods such as the support... | wikipedia |
wiki_11_chunk_40 | Artificial intelligence | Classifier performance depends greatly on the characteristics of the data to be classified, such as the dataset size, distribution of samples across classes, the dimensionality, and the level of noise. Model-based classifiers perform well if the assumed model is an extremely good fit for the actual data. Otherwise, if ... | wikipedia |
wiki_11_chunk_41 | Artificial intelligence | Neural networks
were inspired by the architecture of neurons in the human brain. A simple "neuron" N accepts input from other neurons, each of which, when activated (or "fired"), casts a weighted "vote" for or against whether neuron N should itself activate. Learning requires an algorithm to adjust these weights based ... | wikipedia |
wiki_11_chunk_42 | Artificial intelligence | Modern neural networks model complex relationships between inputs and outputs or and find patterns in data. They can learn continuous functions and even digital logical operations. Neural networks can be viewed a type of mathematical optimization — they perform a gradient descent on a multi-dimensional topology that wa... | wikipedia |
wiki_11_chunk_43 | Artificial intelligence | The main categories of networks are acyclic or feedforward neural networks (where the signal passes in only one direction) and recurrent neural networks (which allow feedback and short-term memories of previous input events). Among the most popular feedforward networks are perceptrons, multi-layer perceptrons and radia... | wikipedia |
wiki_11_chunk_44 | Artificial intelligence | Deep learning
Deep learning
uses several layers of neurons between the network's inputs and outputs. The multiple layers can progressively extract higher-level features from the raw input. For example, in image processing, lower layers may identify edges, while higher layers may identify the concepts relevant to a h... | wikipedia |
wiki_11_chunk_45 | Artificial intelligence | Deep learning often uses convolutional neural networks for many or all of its layers. In a convolutional layer, each neuron receives input from only a restricted area of the previous layer called the neuron's receptive field. This can substantially reduce the number of weighted connections between neurons, and creates ... | wikipedia |
wiki_11_chunk_46 | Artificial intelligence | In a recurrent neural network the signal will propagate through a layer more than once;
thus, an RNN is an example of deep learning.
RNNs can be trained by gradient descent,
however long-term gradients which are back-propagated can "vanish" (that is, they can tend to zero) or "explode" (that is, they can tend to infin... | wikipedia |
wiki_11_chunk_47 | Artificial intelligence | Specialized languages for artificial intelligence have been developed, such as Lisp, Prolog, TensorFlow and many others. Hardware developed for AI includes AI accelerators and neuromorphic computing. Applications AI is relevant to any intellectual task.
Modern artificial intelligence techniques are pervasive and are to... | wikipedia |
wiki_11_chunk_48 | Artificial intelligence | In the 2010s, AI applications were at the heart of the most commercially successful areas of computing, and have become a ubiquitous feature of daily life. AI is used in search engines (such as Google Search),
targeting online advertisements,
recommendation systems (offered by Netflix, YouTube or Amazon),
driving inter... | wikipedia |
wiki_11_chunk_49 | Artificial intelligence | There are also thousands of successful AI applications used to solve problems for specific industries or institutions. A few examples are:
energy storage,
deepfakes,
medical diagnosis,
military logistics, or
supply chain management. | wikipedia |
wiki_11_chunk_50 | Artificial intelligence | Game playing has been a test of AI's strength since the 1950s. Deep Blue became the first computer chess-playing system to beat a reigning world chess champion, Garry Kasparov, on 11 May 1997.
In 2011, in a Jeopardy! quiz show exhibition match, IBM's question answering system, Watson, defeated the two greatest Jeopard... | wikipedia |
wiki_11_chunk_51 | Artificial intelligence | By 2020, Natural Language Processing systems such as the enormous GPT-3 (then by far the largest artificial neural network) were matching human performance on pre-existing benchmarks, albeit without the system attaining commonsense understanding of the contents of the benchmarks.
DeepMind's AlphaFold 2 (2020) demonstra... | wikipedia |
wiki_11_chunk_52 | Artificial intelligence | Alan Turing wrote in 1950 "I propose to consider the question 'can machines think'?"
He advised changing the question from whether a machine "thinks", to "whether or not it is possible for machinery to show intelligent behaviour".
The only thing visible is the behavior of the machine, so it does not matter if the mach... | wikipedia |
wiki_11_chunk_53 | Artificial intelligence | Acting humanly vs. acting intelligently: intelligent agents AI founder John McCarthy said: "Artificial intelligence is not, by definition, simulation of human intelligence". Russell and Norvig agree and criticize the Turing test. They wrote: "Aeronautical engineering texts do not define the goal of their field as 'maki... | wikipedia |
wiki_11_chunk_54 | Artificial intelligence | The intelligent agent paradigm
defines intelligent behavior in general, without reference to human beings. An intelligent agent is a system that perceives its environment and takes actions that maximize its chances of success. Any system that has goal-directed behavior can be analyzed as an intelligent agent: something... | wikipedia |
wiki_11_chunk_55 | Artificial intelligence | The paradigm has other advantages for AI. It provides a reliable and scientific way to test programs; researchers can directly compare or even combine different approaches to isolated problems, by asking which agent is best at maximizing a given "goal function". It also gives them a common language to communicate with... | wikipedia |
wiki_11_chunk_56 | Artificial intelligence | Evaluating approaches to AI
No established unifying theory or paradigm has guided AI research for most of its history. The unprecedented success of statistical machine learning in the 2010s eclipsed all other approaches (so much so that some sources, especially in the business world, use the term "artificial intellige... | wikipedia |
wiki_11_chunk_57 | Artificial intelligence | Symbolic AI (or "GOFAI") simulated the high-level conscious reasoning that people use when they solve puzzles, express legal reasoning and do mathematics. They were highly successful at "intelligent" tasks such as algebra or IQ tests. In the 1960s, Newell and Simon proposed the physical symbol systems hypothesis: "A ph... | wikipedia |
wiki_11_chunk_58 | Artificial intelligence | However, the symbolic approach failed dismally on many tasks that humans solve easily, such as learning, recognizing an object or commonsense reasoning. Moravec's paradox is the discovery that high-level "intelligent" tasks were easy for AI, but low level "instinctive" tasks were extremely difficult.
Philosopher Hubert... | wikipedia |
wiki_11_chunk_59 | Artificial intelligence | The issue is not resolved: sub-symbolic reasoning can make many of the same inscrutable mistakes that human intuition does, such as algorithmic bias. Critics such Noam Chomsky argue continuing research into symbolic AI will still be necessary to attain general intelligence, in part because sub-symbolic AI is a move awa... | wikipedia |
wiki_11_chunk_60 | Artificial intelligence | "Neats" hope that intelligent behavior be described using simple, elegant principles (such as logic, optimization, or neural networks). "Scruffies" expect that it necessarily requires solving a large number of unrelated problems. This issue was actively discussed in the 70s and 80s,
but in the 1990s mathematical method... | wikipedia |
wiki_11_chunk_61 | Artificial intelligence | Finding a provably correct or optimal solution is intractable for many important problems. Soft computing is a set of techniques, including genetic algorithms, fuzzy logic and neural networks, that are tolerant of imprecision, uncertainty, partial truth and approximation. Soft computing was introduced in the late 80s a... | wikipedia |
wiki_11_chunk_62 | Artificial intelligence | AI researchers are divided as to whether to pursue the goals of artificial general intelligence and superintelligence (general AI) directly, or to solve as many specific problems as possible (narrow AI) in hopes these solutions will lead indirectly to the field's long-term goals
General intelligence is difficult to def... | wikipedia |
wiki_11_chunk_63 | Artificial intelligence | The philosophy of mind does not know whether a machine can have a mind, consciousness and mental states, in the same sense that human beings do. This issue considers the internal experiences of the machine, rather than its external behavior. Mainstream AI research considers this issue irrelevant, because it does not ef... | wikipedia |
wiki_11_chunk_64 | Artificial intelligence | Consciousness David Chalmers identified two problems in understanding the mind, which he named the "hard" and "easy" problems of consciousness. The easy problem is understanding how the brain processes signals, makes plans and controls behavior. The hard problem is explaining how this feels or why it should feel like a... | wikipedia |
wiki_11_chunk_65 | Artificial intelligence | Computationalism and functionalism Computationalism is the position in the philosophy of mind that the human mind is an information processing system and that thinking is a form of computing. Computationalism argues that the relationship between mind and body is similar or identical to the relationship between software... | wikipedia |
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