Inductive probability attempts to give the probability of future events based on past events. It is the basis for inductive reasoning, and gives the mathematical basis for learning and the perception of patterns. It is a source of knowledge about the world. There are three sources of knowledge: inference, communication, and deduction. Communication relays information found using other methods. Deduction establishes new facts based on existing facts. Inference establishes new facts from data. Its basis is Bayes' theorem. Information describing the world is written in a language. For example, a simple mathematical language of propositions may be chosen. Sentences may be written down in this language as strings of characters. But in the computer it is possible to encode these sentences as strings of bits (1s and 0s). Then the language may be encoded so that the most commonly used sentences are the shortest. This internal language implicitly represents probabilities of statements. Occam's razor says the "simplest theory, consistent with the data is most likely to be correct". The "simplest theory" is interpreted as the representation of the theory written in this internal language. The theory with the shortest encoding in this internal language is most likely to be correct. == History == Probability and statistics was focused on probability distributions and tests of significance. Probability was formal, well defined, but limited in scope. In particular its application was limited to situations that could be defined as an experiment or trial, with a well defined population. Bayes's theorem is named after Rev. Thomas Bayes 1701–1761. Bayesian inference broadened the application of probability to many situations where a population was not well defined. But Bayes' theorem always depended on prior probabilities, to generate new probabilities. It was unclear where these prior probabilities should come from. Ray Solomonoff developed algorithmic probability which gave an explanation for what randomness is and how patterns in the data may be represented by computer programs, that give shorter representations of the data circa 1964. Chris Wallace and D. M. Boulton developed minimum message length circa 1968. Later Jorma Rissanen developed the minimum description length circa 1978. These methods allow information theory to be related to probability, in a way that can be compared to the application of Bayes' theorem, but which give a source and explanation for the role of prior probabilities. Marcus Hutter combined decision theory with the work of Ray Solomonoff and Andrey Kolmogorov to give a theory for the Pareto optimal behavior for an Intelligent agent, circa 1998. === Minimum description/message length === The program with the shortest length that matches the data is the most likely to predict future data. This is the thesis behind the minimum message length and minimum description length methods. At first sight Bayes' theorem appears different from the minimimum message/description length principle. At closer inspection it turns out to be the same. Bayes' theorem is about conditional probabilities, and states the probability that event B happens if firstly event A happens: P ( A ∧ B ) = P ( B ) ⋅ P ( A | B ) = P ( A ) ⋅ P ( B | A ) {\displaystyle P(A\land B)=P(B)\cdot P(A|B)=P(A)\cdot P(B|A)} becomes in terms of message length L, L ( A ∧ B ) = L ( B ) + L ( A | B ) = L ( A ) + L ( B | A ) . {\displaystyle L(A\land B)=L(B)+L(A|B)=L(A)+L(B|A).} This means that if all the information is given describing an event then the length of the information may be used to give the raw probability of the event. So if the information describing the occurrence of A is given, along with the information describing B given A, then all the information describing A and B has been given. ==== Overfitting ==== Overfitting occurs when the model matches the random noise and not the pattern in the data. For example, take the situation where a curve is fitted to a set of points. If a polynomial with many terms is fitted then it can more closely represent the data. Then the fit will be better, and the information needed to describe the deviations from the fitted curve will be smaller. Smaller information length means higher probability. However, the information needed to describe the curve must also be considered. The total information for a curve with many terms may be greater than for a curve with fewer terms, that has not as good a fit, but needs less information to describe the polynomial. === Inference based on program complexity === Solomonoff's theory of inductive inference is also inductive inference. A bit string x is observed. Then consider all programs that generate strings starting with x. Cast in the form of inductive inference, the programs are theories that imply the observation of the bit string x. The method used here to give probabilities for inductive inference is based on Solomonoff's theory of inductive inference. ==== Detecting patterns in the data ==== If all the bits are 1, then people infer that there is a bias in the coin and that it is more likely also that the next bit is 1 also. This is described as learning from, or detecting a pattern in the data. Such a pattern may be represented by a computer program. A short computer program may be written that produces a series of bits which are all 1. If the length of the program K is L ( K ) {\displaystyle L(K)} bits then its prior probability is, P ( K ) = 2 − L ( K ) {\displaystyle P(K)=2^{-L(K)}} The length of the shortest program that represents the string of bits is called the Kolmogorov complexity. Kolmogorov complexity is not computable. This is related to the halting problem. When searching for the shortest program some programs may go into an infinite loop. ==== Considering all theories ==== The Greek philosopher Epicurus is quoted as saying "If more than one theory is consistent with the observations, keep all theories". As in a crime novel all theories must be considered in determining the likely murderer, so with inductive probability all programs must be considered in determining the likely future bits arising from the stream of bits. Programs that are already longer than n have no predictive power. The raw (or prior) probability that the pattern of bits is random (has no pattern) is 2 − n {\displaystyle 2^{-n}} . Each program that produces the sequence of bits, but is shorter than the n is a theory/pattern about the bits with a probability of 2 − k {\displaystyle 2^{-k}} where k is the length of the program. The probability of receiving a sequence of bits y after receiving a series of bits x is then the conditional probability of receiving y given x, which is the probability of x with y appended, divided by the probability of x. ==== Universal priors ==== The programming language affects the predictions of the next bit in the string. The language acts as a prior probability. This is particularly a problem where the programming language codes for numbers and other data types. Intuitively we think that 0 and 1 are simple numbers, and that prime numbers are somehow more complex than numbers that may be composite. Using the Kolmogorov complexity gives an unbiased estimate (a universal prior) of the prior probability of a number. As a thought experiment an intelligent agent may be fitted with a data input device giving a series of numbers, after applying some transformation function to the raw numbers. Another agent might have the same input device with a different transformation function. The agents do not see or know about these transformation functions. Then there appears no rational basis for preferring one function over another. A universal prior insures that although two agents may have different initial probability distributions for the data input, the difference will be bounded by a constant. So universal priors do not eliminate an initial bias, but they reduce and limit it. Whenever we describe an event in a language, either using a natural language or other, the language has encoded in it our prior expectations. So some reliance on prior probabilities are inevitable. A problem arises where an intelligent agent's prior expectations interact with the environment to form a self reinforcing feed back loop. This is the problem of bias or prejudice. Universal priors reduce but do not eliminate this problem. === Universal artificial intelligence === The theory of universal artificial intelligence applies decision theory to inductive probabilities. The theory shows how the best actions to optimize a reward function may be chosen. The result is a theoretical model of intelligence. It is a fundamental theory of intelligence, which optimizes the agents behavior in, Exploring the environment; performing actions to get responses that broaden the agents knowledge. Competing or co-operating with another agent; games. Balancing short and long term rewards. In general no agent will always provi
PNGOUT
PNGOUT is a freeware command line optimizer for PNG images written by Ken Silverman. The transformation is lossless, meaning that the resulting image is visually identical to the source image. According to its author, this program can often get higher compression than other optimizers by 5–10%. It is possible to compress some inflated PNGs to a size below 1% of the original file. PNGOUT was also available as a plug-in for the freeware image viewer IrfanView and can be enabled as an option when saving files. It allows editing of various PNGOUT settings via a dialog box. PNGOUT integration was removed in IrfanView version 4.58 in favour of OptiPNG. In 2006, a commercial version of PNGOUT with a graphical user interface, known as PNGOUTWin, was released by Ardfry Imaging, a small company Silverman co-founded in 2005. There is also a freeware GUI frontend to PNGOUT available, known as PNGGauntlet. == Main operation == The main function of PNGOUT is to reduce the size of image data contained in the IDAT chunk. This chunk is compressed using the deflate algorithm. Deflate algorithms can vary in speed and compression ratio, with higher compression ratios generally implying lower speed. Ken Silverman wrote a deflate compressor for PNGOUT that is slower than the ones used in most graphics software, but produces smaller files. PNGOUT also performs automatic bit depth, color, and palette reduction where appropriate.
20Q
20Q is a computerized game of twenty questions that began as a test in artificial intelligence (AI). It was invented by Robin Burgener in 1988. The game was made handheld by Radica in 2003, but was discontinued in 2011 because Techno Source took the license for 20Q handheld devices. The game 20Q is based on the spoken parlor game known as twenty questions, and is both a website and a handheld device. 20Q asks the player to think of something and will then try to guess what they are thinking of with twenty yes-or-no questions. If it fails to guess in 20 questions, it will ask an additional 5 questions. If it fails to guess even with 25 (or 30) questions, the player is declared the winner. Sometimes the first guess of the object can be asked at question 14. == Principle and history == The principle is that the player thinks of something and the 20Q artificial intelligence asks a series of questions before guessing what the player is thinking. This artificial intelligence learns on its own with the information relayed back to the players who interact with it, and is not programmed. The player can answer these questions with: Yes, No, Unknown, and Sometimes. The experiment is based on the classic word game of Twenty Questions, and on the computer game "Animals," popular in the early 1970s, which used a somewhat simpler method to guess an animal. The 20Q AI uses an artificial neural network to pick the questions and to guess. After the player has answered the twenty questions posed (sometimes fewer), 20Q makes a guess. If it is incorrect, it asks more questions, then guesses again. It makes guesses based on what it has learned; it is not programmed with information or what the inventor thinks. Answers to any question are based on players’ interpretations of the questions asked. Newer editions were made for different categories, such as music 20Q which has the player think of a song, and Harry Potter 20Q, which has the player think of something from the world of the Harry Potter series. The 20Q AI can draw its own conclusions on how to interpret the information. It can be described as more of a folk taxonomy than a taxonomy. Its knowledge develops with every game played. In this regard, the online version of the 20Q AI can be inaccurate because it gathers its answers from what people think rather than from what people know. Limitations of taxonomy are often overcome by the AI itself because it can learn and adapt. For example, if the player was thinking of a "Horse" and answered "No" to the question "Is it an animal?," the AI will, nevertheless, guess correctly, despite being told that a horse is not an animal. Patent applications in the US and Europe were submitted in 2005. In August 2014, 20Q.net Inc., with Brashworks Studios, developed and released an iOS iPad version available at the Apple iTunes store. == Game show == On June 13, 2009, GSN began a TV version of the game, hosted by Cat Deeley, with Hal Sparks as the voice of Mr. Q.
Feigenbaum test
A Feigenbaum test is a variation of the Turing test where a computer system attempts to replicate an expert in a given field such as chemistry or marketing. It is also known, as a subject matter expert Turing test and was proposed by Edward Feigenbaum in a 2003 paper. The concept is also described by Ray Kurzweil in his 2005 book The Singularity is Near. Kurzweil argues that machines who pass this test are an inevitable consequence of Moore's Law.
Moral Machine
Moral Machine is an online platform, developed by Iyad Rahwan's Scalable Cooperation group at the Massachusetts Institute of Technology, that generates moral dilemmas and collects information on the decisions that people make between two destructive outcomes. The platform is the idea of Iyad Rahwan and social psychologists Azim Shariff and Jean-François Bonnefon, who conceived of the idea ahead of the publication of their article about the ethics of self-driving cars. The key contributors to building the platform were MIT Media Lab graduate students Edmond Awad and Sohan Dsouza. The presented scenarios are often variations of the trolley problem, and the information collected would be used for further research regarding the decisions that machine intelligence must make in the future. For example, as artificial intelligence plays an increasingly significant role in autonomous driving technology, research projects like Moral Machine help to find solutions for challenging life-and-death decisions that will face self-driving vehicles. Moral Machine was active from January 2016 to July 2020. The Moral Machine continues to be available on their website for people to experience. == The experiment == The Moral Machine was an ambitious project; it was the first attempt at using such an experimental design to test a large number of humans in over 200 countries worldwide. The study was approved by the Institute Review Board (IRB) at Massachusetts Institute of Technology (MIT). The setup of the experiment asks the viewer to make a decision on a single scenario in which a self-driving car is about to hit pedestrians. The user can decide to have the car either swerve to avoid hitting the pedestrians or keep going straight to preserve the lives it is transporting. Participants can complete as many scenarios as they want to, however the scenarios themselves are generated in groups of thirteen. Within this thirteen, a single scenario is entirely random while the other twelve are generated from a space in a database of 26 million different possibilities. They are chosen with two dilemmas focused on each of six dimensions of moral preferences: character gender, character age, character physical fitness, character social status, character species, and character number. The experiment setup remains the same throughout multiple scenarios but each scenario tests a different set of factors. Most notably, the characters involved in the scenario are different in each one. Characters may include ones such as: Stroller, girl, boy, pregnant, Male Doctor, Female Doctor, Female Athlete, Executive Female, Male Athlete, Executive Male, Large Woman, Large Man, homeless, old man, old woman, dog, criminal, and a cat. Through these different characters researchers were able to understand how a wide variety of people will judge scenarios based on those involved. == Analysis == The Moral Machine collected 40 million moral decisions from 4 million participants in 233 countries, analysis of which revealed trends within individual countries and humanity as a whole. It tested for nine factors: preference for sparing humans versus pets, passengers versus pedestrians, men versus women, young versus elderly, fit versus overweight, higher versus lower social status, jaywalkers versus law abiders, larger versus smaller groups, and inaction (i.e. staying on course) versus swerving. Globally, participants favored human lives over lives of animals like dogs and cats. They preferred to spare more lives if possible, and younger lives as opposed to older. Babies were most often spared with cats being the least spared. In terms of gender variations, people tended to spare men over women for doctors and the elderly. All countries generally shared the preference to spare pedestrians over passengers and law-abiders over criminals. Participants from less wealthy countries showed a higher tendency of sparing pedestrians who crossed illegally compared to those from more wealthy and developed countries. This is most likely due to their experience living in a society where individuals are more likely to deviate from rules due to less stringent enforcement of laws. Countries of higher economic inequality overwhelmingly prefer to save wealthier individuals over poorer ones. === Cultural differences === Researchers subdivided 130 countries with similar results into three ‘cultural clusters’. North America and European countries with significant Christian populations had a higher preference for inaction on the part of the driver and thus had less of a preference for sparing pedestrians as compared to other clusters. East Asian and Islamic countries, together constituting the second cluster, did not have as much preference to spare younger humans compared to the other two clusters and had a higher preference for sparing law-abiding humans. Latin America and Francophone countries had a higher preference for sparing women, the young, the fit, and those of higher status, but a lower preference for sparing humans over pets or other animals. Individualistic cultures tended to spare larger groups, and collectivist cultures had a stronger preference for sparing the lives of older people. For instance, China ranked far below the world average for preference to spare the younger over elderly, while the average respondent from the US exhibited a much higher tendency to save younger lives and larger groups. == Applications of the data == The findings from the moral machine can help decision makers when designing self-driving automotive systems. Designers must make sure that these vehicles are able to solve problems on the road that aligns with the moral values of humans around it. This is a challenge because of the complex nature of humans who may all make different decisions based on their personal values. However, by collecting a large amount of decisions from humans all over the world, researchers can begin to understand patterns in the context of a particular culture, community, and people. == Other features == The Moral Machine was deployed in June 2016. In October 2016, a feature was added that offered users the option to fill a survey about their demographics, political views, and religious beliefs. Between November 2016 and March 2017, the website was progressively translated into nine languages in addition to English (Arabic, Chinese, French, German, Japanese, Korean, Portuguese, Russian, and Spanish). Overall, the Moral Machine offers four different modes, with the focus being on the data-gathering feature of the website, called the Judge mode. This means that the Moral Machine, in addition to providing their own scenarios for users to judge, also invites users to create their own scenarios to be submitted and approved so that other people may also judge those scenarios. Data is also open sourced for anyone to explore via an interactive map that is featured on the Moral Machine website. == In the literature == Studies and research on the Moral Machine have taken a wide variety of approaches. However, theological examinations of the topic are still scarce where two bodies of work that examine such perspective currently exist in this regard: One is Buddhist while the other is Christian.
Time series
In mathematics, a time series is a sequence of data points indexed, listed, or graphed in chronological order. Most commonly, a time series consists of observations recorded at successive equally spaced points in time. Thus, it represents a form of discrete-time data. A time series may describe measurements collected over seconds, days, years, or even centuries. Common examples include heights of ocean tides, counts of sunspots, daily temperature readings, and the closing values of stock market indices such as the Dow Jones Industrial Average. A time series is often visualized using a run chart (a type of temporal line chart), which helps identify patterns such as trends, seasonal effects, and irregular fluctuations. Time series are widely used in statistics, actuarial science, signal processing, pattern recognition, econometrics, mathematical finance, weather forecasting, earthquake prediction, electroencephalography, control engineering, astronomy, communications engineering, and many other areas of applied science and engineering that involve temporal measurements. Time series analysis comprises methods for analyzing time series data in order to extract meaningful statistics and other characteristics of the data. Time series forecasting is the use of a model to predict future values based on previously observed values. Generally, time series data is modeled as a stochastic process. While regression analysis is often employed in such a way as to test relationships between one or more different time series, this type of analysis is not usually called "time series analysis", which refers in particular to relationships between different points in time within a single series. Time series data have a natural temporal ordering. This makes time series analysis distinct from cross-sectional studies, in which there is no natural ordering of the observations (e.g. explaining people's wages by reference to their respective education levels, where the individuals' data could be entered in any order). Time series analysis is also distinct from spatial data analysis where the observations typically relate to geographical locations (e.g. accounting for house prices by the location as well as the intrinsic characteristics of the houses). A stochastic model for a time series will generally reflect the fact that observations close together in time will be more closely related than observations further apart. In addition, time series models will often make use of the natural one-way ordering of time so that values for a given period will be expressed as deriving in some way from past values, rather than from future values (see time reversibility). Time series analysis can be applied to real-valued, continuous data, discrete numeric data, or discrete symbolic data (i.e. sequences of characters, such as letters and words in the English language). == Methods for analysis == Methods for time series analysis may be divided into two classes: frequency-domain methods and time-domain methods. The former include spectral analysis and wavelet analysis; the latter include auto-correlation and cross-correlation analysis. In the time domain, correlation and analysis can be made in a filter-like manner using scaled correlation, thereby mitigating the need to operate in the frequency domain. Additionally, time series analysis techniques may be divided into parametric and non-parametric methods. The parametric approaches assume that the underlying stationary stochastic process has a certain structure which can be described using a small number of parameters (for example, using an autoregressive or moving-average model). In these approaches, the task is to estimate the parameters of the model that describes the stochastic process. By contrast, non-parametric approaches explicitly estimate the covariance or the spectrum of the process without assuming that the process has any particular structure. Methods of time series analysis may also be divided into linear and non-linear, and univariate and multivariate. == Panel data == A time series is one type of panel data. Panel data is the general class, a multidimensional data set, whereas a time series data set is a one-dimensional panel (as is a cross-sectional dataset). A data set may exhibit characteristics of both panel data and time series data. One way to tell is to ask what makes one data record unique from the other records. If the answer is the time data field, then this is a time series data set candidate. If determining a unique record requires a time data field and an additional identifier which is unrelated to time (e.g. student ID, stock symbol, country code), then it is panel data candidate. If the differentiation lies on the non-time identifier, then the data set is a cross-sectional data set candidate. == Analysis == There are several types of motivation and data analysis available for time series which are appropriate for different purposes. === Motivation === In the context of statistics, econometrics, quantitative finance, seismology, meteorology, and geophysics the primary goal of time series analysis is forecasting. In the context of signal processing, control engineering and communication engineering it is used for signal detection. Other applications are in data mining, pattern recognition and machine learning, where time series analysis can be used for clustering, classification, query by content, anomaly detection as well as forecasting. === Exploratory analysis === A simple way to examine a regular time series is manually with a line chart. The datagraphic shows tuberculosis deaths in the United States, along with the yearly change and the percentage change from year to year. The total number of deaths declined in every year until the mid-1980s, after which there were occasional increases, often proportionately - but not absolutely - quite large. A study of corporate data analysts found two challenges to exploratory time series analysis: discovering the shape of interesting patterns, and finding an explanation for these patterns. Visual tools that represent time series data as heat map matrices can help overcome these challenges. === Estimation, filtering, and smoothing === This approach may be based on harmonic analysis and filtering of signals in the frequency domain using the Fourier transform, and spectral density estimation. Its development was significantly accelerated during World War II by mathematician Norbert Wiener, electrical engineers Rudolf E. Kálmán, Dennis Gabor and others for filtering signals from noise and predicting signal values at a certain point in time. An equivalent effect may be achieved in the time domain, as in a Kalman filter; see filtering and smoothing for more techniques. Other related techniques include: Autocorrelation analysis to examine serial dependence Spectral analysis to examine cyclic behavior which need not be related to seasonality. For example, sunspot activity varies over 11 year cycles. Other common examples include celestial phenomena, weather patterns, neural activity, commodity prices, and economic activity. Separation into components representing trend, seasonality, slow and fast variation, and cyclical irregularity: see trend estimation and decomposition of time series === Curve fitting === Curve fitting is the process of constructing a curve, or mathematical function, that has the best fit to a series of data points, possibly subject to constraints. Curve fitting can involve either interpolation, where an exact fit to the data is required, or smoothing, in which a "smooth" function is constructed that approximately fits the data. A related topic is regression analysis, which focuses more on questions of statistical inference such as how much uncertainty is present in a curve that is fit to data observed with random errors. Fitted curves can be used as an aid for data visualization, to infer values of a function where no data are available, and to summarize the relationships among two or more variables. Extrapolation refers to the use of a fitted curve beyond the range of the observed data, and is subject to a degree of uncertainty since it may reflect the method used to construct the curve as much as it reflects the observed data. For processes that are expected to generally grow in magnitude one of the curves in the graphic (and many others) can be fitted by estimating their parameters. The construction of economic time series involves the estimation of some components for some dates by interpolation between values ("benchmarks") for earlier and later dates. Interpolation is estimation of an unknown quantity between two known quantities (historical data), or drawing conclusions about missing information from the available information ("reading between the lines"). Interpolation is useful where the data surrounding the missing data is available and its trend, seasonality, and longer-term cycles are known. This is often done by using a relat
Computer Science Ontology
The Computer Science Ontology (CSO) is an automatically generated taxonomy of research topics in the field of Computer Science. It was produced by the Open University in collaboration with Springer Nature by running an information extraction system over a large corpus of scientific articles. Several branches were manually improved by domain experts. The current version (CSO 3.2) includes about 14K research topics and 160K semantic relationships. CSO is available in OWL, Turtle, and N-Triples. It is aligned with several other knowledge graphs, including DBpedia, Wikidata, YAGO, Freebase, and Cyc. New versions of CSO are regularly released on the CSO Portal. CSO is mostly used to characterise scientific papers and other documents according to their research areas, in order to enable different kinds of analytics. The CSO Classifier is an open-source python tool for automatically annotating documents with CSO. == Applications == Recommender Systems. Computing the semantic similarity of documents. Extracting metadata from video lecture subtitles. Performing bibliometrics analysis.