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Directed Information
Directed information, I(X^n\to Y^n) , is an information theory measure that quantifies the information flow from the random process X^n = \ to the random process Y^n = \. The term ''directed information'' was coined by James Massey and is defined as :I(X^n\to Y^n) \triangleq \sum_^n I(X^i;Y_i, Y^), where I(X^;Y_i, Y^) is the conditional mutual information I(X_1,X_2,...,X_;Y_i, Y_1,Y_2,...,Y_). The Directed information has many applications in problems where causality plays an important role such as channel capacity, capacity of channel with Feedback capacity, feedback, capacity of discrete memoryless networks with feedback, gambling with causal side information, Data compression, compression with causal side information, and in real-time control communication settings, statistical physics. Marko's theory of bidirectional communication Massey's directed information was motivated by Marko's work on developing a theory of bidirectional communication Estimation and optimization ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Information Theory
Information theory is the scientific study of the quantification (science), quantification, computer data storage, storage, and telecommunication, communication of information. The field was originally established by the works of Harry Nyquist and Ralph Hartley, in the 1920s, and Claude Shannon in the 1940s. The field is at the intersection of probability theory, statistics, computer science, statistical mechanics, information engineering (field), information engineering, and electrical engineering. A key measure in information theory is information entropy, entropy. Entropy quantifies the amount of uncertainty involved in the value of a random variable or the outcome of a random process. For example, identifying the outcome of a fair coin flip (with two equally likely outcomes) provides less information (lower entropy) than specifying the outcome from a roll of a dice, die (with six equally likely outcomes). Some other important measures in information theory are mutual informat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Context Tree Weighting
The context tree weighting method (CTW) is a lossless compression and prediction algorithm by . The CTW algorithm is among the very few such algorithms that offer both theoretical guarantees and good practical performance (see, e.g. ). The CTW algorithm is an “ ensemble method”, mixing the predictions of many underlying variable order Markov model In probability theory, a Markov model is a stochastic model used to model pseudo-randomly changing systems. It is assumed that future states depend only on the current state, not on the events that occurred before it (that is, it assumes the Mark ...s, where each such model is constructed using zero-order conditional probability ''estimators''. References * * * External links Relevant CTW papers and implementationsCTW Official Homepage Lossless compression algorithms {{comp-sci-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gradient Descent
In mathematics, gradient descent (also often called steepest descent) is a first-order iterative optimization algorithm for finding a local minimum of a differentiable function. The idea is to take repeated steps in the opposite direction of the gradient (or approximate gradient) of the function at the current point, because this is the direction of steepest descent. Conversely, stepping in the direction of the gradient will lead to a local maximum of that function; the procedure is then known as gradient ascent. Gradient descent is generally attributed to Augustin-Louis Cauchy, who first suggested it in 1847. Jacques Hadamard independently proposed a similar method in 1907. Its convergence properties for non-linear optimization problems were first studied by Haskell Curry in 1944, with the method becoming increasingly well-studied and used in the following decades. Description Gradient descent is based on the observation that if the multi-variable function F(\mathbf) is def ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Graphical Methods (the Q-graphs)
A chart (sometimes known as a graph) is a graphical representation for data visualization, in which "the data is represented by symbols, such as bars in a bar chart, lines in a line chart, or slices in a pie chart". A chart can represent tabular numeric data, functions or some kinds of quality structure and provides different info. The term "chart" as a graphical representation of data has multiple meanings: * A data chart is a type of diagram or graph, that organizes and represents a set of numerical or qualitative data. * Maps that are adorned with extra information (map surround) for a specific purpose are often known as charts, such as a nautical chart or aeronautical chart, typically spread over several map sheets. * Other domain-specific constructs are sometimes called charts, such as the chord chart in music notation or a record chart for album popularity. Charts are often used to ease understanding of large quantities of data and the relationships between parts of th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Reinforcement Learning
Reinforcement learning (RL) is an area of machine learning concerned with how intelligent agents ought to take actions in an environment in order to maximize the notion of cumulative reward. Reinforcement learning is one of three basic machine learning paradigms, alongside supervised learning and unsupervised learning. Reinforcement learning differs from supervised learning in not needing labelled input/output pairs to be presented, and in not needing sub-optimal actions to be explicitly corrected. Instead the focus is on finding a balance between exploration (of uncharted territory) and exploitation (of current knowledge). The environment is typically stated in the form of a Markov decision process (MDP), because many reinforcement learning algorithms for this context use dynamic programming techniques. The main difference between the classical dynamic programming methods and reinforcement learning algorithms is that the latter do not assume knowledge of an exact mathematica ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Recurrent Neural Network
A recurrent neural network (RNN) is a class of artificial neural networks where connections between nodes can create a cycle, allowing output from some nodes to affect subsequent input to the same nodes. This allows it to exhibit temporal dynamic behavior. Derived from feedforward neural networks, RNNs can use their internal state (memory) to process variable length sequences of inputs. This makes them applicable to tasks such as unsegmented, connected handwriting recognition or speech recognition. Recurrent neural networks are theoretically Turing complete and can run arbitrary programs to process arbitrary sequences of inputs. The term "recurrent neural network" is used to refer to the class of networks with an infinite impulse response, whereas "convolutional neural network" refers to the class of finite impulse response. Both classes of networks exhibit temporal dynamic behavior. A finite impulse recurrent network is a directed acyclic graph that can be unrolled and replace ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Blahut–Arimoto Algorithm
The term Blahut–Arimoto algorithm is often used to refer to a class of algorithms for computing numerically either the information theoretic capacity of a channel, the rate-distortion function of a source or a source encoding (i.e. compression to remove the redundancy). They are iterative algorithms that eventually converge to one of the maxima of the optimization problem that is associated with these information theoretic concepts. History and application For the case of channel capacity, the algorithm was independently invented by Suguru Arimoto and Richard Blahut. In addition, Blahut's treatment gives algorithms for computing rate distortion and generalized capacity with input contraints (i.e. the capacity-cost function, analogous to rate-distortion). These algorithms are most applicable to the case of arbitrary finite alphabet sources. Much work has been done to extend it to more general problem instances. Recently, a version of the algorithm that accounts for continu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Long Short-term Memory
Long short-term memory (LSTM) is an artificial neural network used in the fields of artificial intelligence and deep learning. Unlike standard feedforward neural networks, LSTM has feedback connections. Such a recurrent neural network (RNN) can process not only single data points (such as images), but also entire sequences of data (such as speech or video). For example, LSTM is applicable to tasks such as unsegmented, connected handwriting recognition, speech recognition, machine translation, robot control, video games, and healthcare. The name of LSTM refers to the analogy that a standard RNN has both "long-term memory" and "short-term memory". The connection weights and biases in the network change once per episode of training, analogous to how physiological changes in synaptic strengths store long-term memories; the activation patterns in the network change once per time-step, analogous to how the moment-to-moment change in electric firing patterns in the brain store short- ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Real-time Control
Real-time computing (RTC) is the computer science term for hardware and software systems subject to a "real-time constraint", for example from event to system response. Real-time programs must guarantee response within specified time constraints, often referred to as "deadlines". Ben-Ari, Mordechai; "Principles of Concurrent and Distributed Programming", ch. 16, Prentice Hall, 1990, , page 164 Real-time responses are often understood to be in the order of milliseconds, and sometimes microseconds. A system not specified as operating in real time cannot usually ''guarantee'' a response within any timeframe, although ''typical'' or ''expected'' response times may be given. Real-time processing ''fails'' if not completed within a specified deadline relative to an event; deadlines must always be met, regardless of system load. A real-time system has been described as one which "controls an environment by receiving data, processing them, and returning the results sufficiently quic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Information
Information is an abstract concept that refers to that which has the power to inform. At the most fundamental level information pertains to the interpretation of that which may be sensed. Any natural process that is not completely random, and any observable pattern in any medium can be said to convey some amount of information. Whereas digital signals and other data use discrete signs to convey information, other phenomena and artifacts such as analog signals, poems, pictures, music or other sounds, and currents convey information in a more continuous form. Information is not knowledge itself, but the meaning that may be derived from a representation through interpretation. Information is often processed iteratively: Data available at one step are processed into information to be interpreted and processed at the next step. For example, in written text each symbol or letter conveys information relevant to the word it is part of, each word conveys information rele ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Data Compression
In information theory, data compression, source coding, or bit-rate reduction is the process of encoding information using fewer bits than the original representation. Any particular compression is either lossy or lossless. Lossless compression reduces bits by identifying and eliminating statistical redundancy. No information is lost in lossless compression. Lossy compression reduces bits by removing unnecessary or less important information. Typically, a device that performs data compression is referred to as an encoder, and one that performs the reversal of the process (decompression) as a decoder. The process of reducing the size of a data file is often referred to as data compression. In the context of data transmission, it is called source coding; encoding done at the source of the data before it is stored or transmitted. Source coding should not be confused with channel coding, for error detection and correction or line coding, the means for mapping data onto a signal. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
