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Abstract Comparing a Neural-Fuzzy Scheme with a Probabilistic Neural Network for Applicatio
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3秒自动关闭窗口From Scholarpedia
Rudolf Kruse (2008), Scholarpedia, 3(11):6043.
revision #91290 []
Post-publication activityCurator:
Contributors:&
A fuzzy neural network or neuro-fuzzy system is a
that finds the parameters of a
(i.e., , ) by exploiting approximation techniques from .
Both neural networks and fuzzy systems have some things in common.
They can be used for solving a problem (e.g. pattern recognition, regression or density estimation) if there does not exist any mathematical model of the given problem.
They solely do have certain disadvantages and advantages which almost completely disappear by combining both concepts.
Neural networks can only come into play if the problem is expressed by a sufficient amount of observed examples.
These observations are used to train the black box.
On the one hand no prior knowledge about the problem needs to be given.
On the other hand, however, it is not straightforward to extract comprehensible rules from the neural network's structure.
On the contrary, a fuzzy system demands linguistic rules instead of learning examples as prior knowledge.
Furthermore the input and output variables have to be described linguistically.
If the knowledge is incomplete, wrong or contradictory, then the fuzzy system must be tuned.
Since there is not any formal approach for it, the tuning is performed in a heuristic way.
This is usually very time consuming and error-prone.
Table 1: Comparison of
Neural Networks
Fuzzy Systems
no mathematical model necessary
no mathematical model necessary
learning from scratch
apriori knowledge essential
several learning algorithms
not capable to learn
black-box behavior
simple interpretation and implementation
It is desirable for fuzzy systems to have an automatic adaption procedure which is comparable to neural networks.
As it can be seen in Table 1, combining both approaches should unite advantages and exclude disadvantages.
Compared to a common neural network, connection weights and propagation and activation functions of fuzzy neural networks differ a lot.
Although there are many different approaches to model a fuzzy neural network (Buckley and Hayashi, ; Nauck and Kruse, 1996), most of them agree on certain characteristics such as the following:
Figure 1: The architecture of a neuro-fuzzy system
A neuro-fuzzy system based on an underlying fuzzy system is trained by means of a data-driven learning method derived from neural network theory.
This heuristic only takes into account local information to cause local changes in the fundamental fuzzy system.
It can be represented as a set of fuzzy rules at any time of the learning process, i.e., before, during and after.
Thus the system might be initialized with or without prior knowledge in terms of fuzzy rules.
The learning procedure is constrained to ensure the semantic properties of the underlying fuzzy system.
A neuro-fuzzy system approximates a n-dimensional unknown function which is partly represented by training examples.
Fuzzy rules can thus be interpreted as vague prototypes of the training data.
A neuro-fuzzy system is represented as special three-layer feedforward neural network as it is shown in
The first layer corresponds to the input variables.
The second layer symbolizes the fuzzy rules.
The third layer represents the output variables.
The fuzzy sets are converted as (fuzzy) connection weights.
Some approaches also use five layers where the fuzzy sets are encoded in the units of the second and fourth layer, respectively.
However, these models can be transformed into a three-layer architecture.
One can basically distinguish between three different kinds of fuzzy neural networks, i.e., cooperative, concurrent and hybrid FNNs (Nauck et al., 1997).
Figure 2: Different cooperative fuzzy neural networks
In the case of cooperative
fuzzy systems, both artificial neural network and fuzzy system work independently from each other.
The ANN tries to learn the parameters from the fuzzy system.
This can be either performed offline or online while the fuzzy system is applied.
depicts four different kinds of cooperative fuzzy neural networks.
The upper left fuzzy neural network learns fuzzy set from given training data.
This is usually performed by fitting membership functions with a neural network.
The fuzzy sets are then determined offline.
They are then utilized to form the fuzzy system by fuzzy rules that are given (not learned) as well.
The upper right neuro-fuzzy system determines fuzzy rules from training data by a neural network.
Here as well, the neural networks learns offline before the fuzzy system is initialized.
The rule learning usually done by clustering on
(Bezdek et al., 1992; Vuorimaa, 1994).
It is also possible to apply fuzzy clustering methods to obtain rules.
In the lower left neuro-fuzzy model, the system learns all membership function parameters online, i.e., while the fuzzy system is applied.
Thus initially fuzzy rules and membership functions must be defined beforehand.
Moreover, the error has to be measured in order to improve and guide the learning step.
The lower right one determines rule weights for all fuzzy rules by a neural network.
This can be done online and offline.
A rule weight is interpreted as the influence of a rule (Kosko, 1992).
They are multiplied with the rule output.
In (Nauck et al., 1997) the authors argue that the semantics of rule weights are not clearly defined.
They could be replaced by modified membership functions.
However, this could destroy the interpretation of fuzzy sets.
Moreover, identical linguistic values might be represented differently in dissimilar rules.
Figure 3: A hybrid fuzzy neural network
Hybrid neuro-fuzzy systems are homogeneous and usually resemble neural networks.
Here, the fuzzy system is interpreted as special kind of neural network.
The advantage of such hybrid NFS is its architecture since both fuzzy system and neural network do not have to communicate any more with each other.
They are one fully fused entity.
These systems can learn online and offline.
shows such a hybrid FNN.
The rule base of a fuzzy system is interpreted as a neural network.
Fuzzy sets can be regarded as weights whereas the input and output variables and the rules are modeled as neurons.
Neurons can be included or deleted in the learning step.
Finally, the neurons of the network represent the fuzzy knowledge base.
Obviously, the major drawbacks of both underlying systems are thus overcome.
In order to build a fuzzy controller, membership functions which express the linguistic terms of the inference rules have to be defined.
In fuzzy set theory, there does not exist any formal approach to define these functions.
Any shape (e.g., triangular, Gaussian) can be considered as membership function with an arbitrary set of parameters.
Thus the optimization of these functions in terms of generalizing the data is very important for fuzzy systems.
Neural networks can be used to solve this problem.
By fixing a distinct shape of the membership functions, say triangular, the neural network must optimize their parameters by gradient descent (Nomura et al., 1992).
Thus, aside information about the shape of the membership functions, training data must be available as well.
Another approach (Hayashi et al., 1992) is to group the training data \(\{(\mathbf x_i, y_i)\; |\; x_i \in \mathcal X,\; y_i \in \mathcal Y,\; i = 1, 2, \ldots, l\}\) into \(M\) clusters.
Every cluster represents a rule \(R_m\) where \(m = 1, 2, \ldots, M\ .\)
Hence these rules are not defined linguistically but rather by crisp data points \(\mathbf x = (x_1, x_2, \ldots, x_n)\ .\)
Thus a neural network with \(n\) input units, hidden layers and \(M\) output units might be applied to train on the pre-defined clusters.
For testing, an arbitrary pattern \(x\) is presented to the trained neural network.
Every output unit \(m\) will return a degree to which extend \(x\) may fit to the antecedent of rule \(R_m\ .\)
To guarantee the characteristics of a fuzzy system, the learning algorithm must enforce the following mandatory constraints:
Fuzzy sets must stay normal and convex.
Fuzzy sets must not exchange their relative positions (they must not pass each other).
Fuzzy sets must always overlap.
Additionally there do exist some optional constraints like the following:
Fuzzy sets must stay symmetric.
The membership degrees must sum up to 1.
An important hybrid fuzzy neural network has been introduced in (Berenji, 1992). The ARIC (approximate reasoning-based intelligent control) is presented as a neural network where a prior defined rule base is tuned by updating the network's prediction.
Thus the advantages of fuzzy systems and neural networks are easily combined as presented in Table 1.
The ARIC is represented by two feed-forward neural networks, the action-state evaluation network (AEN) and the
network (ASN).
The ASN is a multilayer neural network representation of a fuzzy system.
It then again consists of two separate.
The first one represents the fuzzy inference and the second one computes a confidence measure based on the current and next system state.
Both parts are eventually combined to the ASN's output.
As it is shown in
Figure , the first layer represents the rule antecedents, whereas the second layer corresponds to the implemented fuzzy rules and the third layer symbolized the system action.
The network flow is at follows.
In the first layer the system variables are fuzzified.
In the next step these membership values are multiplied by the attached weights of the connections between the first and second layer.
In the latter layer, every rule's input corresponds to the minimum of its input connections.
A rule's conclusion is installed as membership function.
This function maps the inverse rule input value.
Its output values is then multiplied by the weights of the connections between second and third layer.
The final output value is eventually computed by the weighted average of all rules' conclusions.
The AEN (which is as three-layer feed-forward neural network as well) aims to forecast the system behavior.
The hidden layer obtains as input both the system state and an error signal from the underlying system.
The output of the networks shall represent the prediction of the next
which depends on the weights and the system state.
The weights are changed by a reinforcement procedure which takes into consideration the outputs of both networks ASN and AEN, respectively.
ARIC was successfully applied to the cart-pole balancing problem.
Whereas the ARIC model can be easily interpret as a set of fuzzy-if-then rules, the ASN network to adjust the weights is rather difficult to understand.
It is a working neural network architecture that utilizes aspects of fuzzy systems.
However, a semantic interpretation of some learning steps is not possible.
Berenji and Khedkar (1992) introduced an improvement of the their former approach named GARIC (generalized ARIC).
This idea does not suffer from dif-ferent interpretations of the linguistic values anymore by refraining from weighted connections in the ASN.
Instead the fuzzy sets are represented as nodes in the network.
Moreover the learning procedure changes parameters of these nodes and thus the shape of the membership functions.
GARIC is also able to use any kind of membership functions in the conclusion since a different defuzzifier and a differentiable soft-minimum function are used.
Note that the ANFIS model (Jang, 1993) also implements a Sugeno-like fuzzy system in a network structure.
Here a mixture of plain backpropagation and least mean squares procedure is used to train the system.
Both the ANFIS and the GARIC model are not so easy to interpret as, e.g., Mamdani-type fuzzy systems.
Therefore models like NEFCON (Nauck, 1994), NEFCLASS (Nauck and Kruse, 1996) and NEFPROX (Nauck and Kruse, 1997) have been developed for neuro-fuzzy control, classification and regression, respectively.
They all implement Mamdani-type fuzzy systems and thus use special learning algorithms.
Berenji, H.R. (1992). A - Based Architecture for
Con-trol. International Journal of Approximate Reasoning 6, 267--292.
Berenji, H. R. and Khedkar, P. (1992). Learning and Tuning Fuzzy Logic Controllers Through Reinforcements, IEEE Trans. Neural Networks, 3, pp. 724-740.
Bezdek, J. C., Tsao, E. C.-K. and Pal, N. R. (1992). Fuzzy Kohonen Clustering Networks, in Proc. IEEE Int. Conf. on Fuzzy Systems 1992 (San Diego), pp. .
Buckley, J. J. and Hayashi, Y. (1994). Fuzzy neural networks: A survey, Fuzzy Sets and Systems 66, pp. 1-13.
Buckley, J. J. and Hayashi, Y. (1995). Neural networks for fuzzy systems, Fuzzy Sets and Systems 71, pp. 265-276.
Hayashi, I., Nomura, H., Yamasaki, H. and Wakami, N. (1992).
Construction of Fuzzy Inference Rules by NFD and NDFL. International Journal of Approximate Reasoning, 6, pp. 241--266.
Jang, J.-S. R. (1993). ANFIS: Adaptive-Network-Based Fuzzy Inference Systems, IEEE Transaction on Systems, Man, and Cybernetics 23, pp. 665-685.
Kosko, B. (1992). Neural Networks and Fuzzy Systems. A
Approach to Machine Intelligence (Prentice-Hall, Englewood Cliffs).
Nauck, D. (1994).
A Fuzzy Perceptron as a Generic Model for Neuro-Fuzzy Approaches, in Proc. Fuzzy-Systeme 94 (Munich).
Nauck, D. and Kruse, R. (1996).
Neuro-Fuzzy Classification with NEFCLASS, in P. Kleinschmidt, A. Bachem, U. Derigs, D. Fischer, U. Leopold-Wildburger and R. Möhring (eds.), Operations Research Proceedings 1995, (Berlin), pp. 294-299.
Nauck, D. and Kruse, R. (1997).
Function Approximation by NEFPROX, in Proc. Second European Workshop on Fuzzy Decision Analysis and Neural Networks for Management, Planning, and
(EFDAN'97), (Dortmund), pp. 160-169.
Nomura, H., Hayashi, I. and Wakami, N. (1992). A Learning Method of Fuzzy Inference Rules by Descent Method, in Proc. IEEE Int. Conf. on Fuzzy Systems 1992 (San Diego), pp. 203--210.
Vuorimaa, P. (1994). Fuzzy Self-Organizing Map, Fuzzy Sets and Systems 66, pp. 223-231.
Internal references
Tony J. Prescott (2008) . , 3(2):2705.
Robert Babuska and Ebrahim Mamdani (2008) . Scholarpedia, 3(2):2103.
Milan Mares (2006) . Scholarpedia, 1(10):2031.
Teuvo Kohonen and Timo Honkela (2007) . Scholarpedia, 2(1):1568.
Rodolfo Llinas (2008) . Scholarpedia, 3(8):1490.
Klawonn, F. Nauck D. and Kruse, R. (1997). Foundations of Neuro-Fuzzy Systems (Wiley, Chichester, United Kingdom).
Klawonn, F., Kruse R., Nauck, D. and Borgelt, C. (2003). Neuro-Fuzzy-Systeme (Vieweg, Wiesbaden).
Focal areasFrom Wikipedia, the free encyclopedia
(Redirected from )
"Neural network" redirects here. For networks of living neurons, see . For the journal, see . For the evolutionary concept, see .
An artificial neural network is an interconnected group of nodes, akin to the vast network of
in a . Here, each circular node represents an artificial neuron and an arrow represents a connection from the output of one neuron to the input of another.
and , artificial neural networks (ANNs) are a family of statistical learning algorithms inspired by
of animals, in particular the ) and are used to estimate or
that can depend on a large number of
and are generally unknown. Artificial neural networks are generally presented as systems of interconnected "" which can compute values from inputs, and are capable of
as well as
thanks to their adaptive nature.
For example, a neural network for
is defined by a set of input neurons which may be activated by the pixels of an input image. After being weighted and transformed by a
(determined by the network's designer), the activations of these neurons are then passed on to other neurons. This process is repeated until finally, an output neuron is activated. This determines which character was read.
Like other machine learning methods - systems that learn from data - neural networks have been used to solve a wide variety of tasks that are hard to solve using ordinary , including
Examinations of the human's
inspired the concept of neural networks. In an Artificial Neural Network, simple artificial , known as "", "neurodes", "processing elements" or "units", are connected together to form a network which mimics a biological neural network.
There is no single formal definition of what an artificial neural network is. However, a class of statistical models may commonly be called "Neural" if they possess the following characteristics:
consist of sets of
weights, i.e. numerical parameters that are tuned by a learning , and
are capable of
non-linear functions of their inputs.
The adaptive weights are conceptually connection strengths between neurons, which are activated during training and prediction.
Neural networks are similar to biological neural networks in performing functions collectively and in parallel by the units, rather than there being a clear delineation of subtasks to which various units are assigned. The term "neural network" usually refers to models employed in ,
and . Neural network models which emulate the central nervous system are part of
of artificial neural networks, the approach inspired by biology has been largely abandoned for a more practical approach based on statistics and signal processing. In some of these systems, neural networks or parts of neural networks (like artificial neurons) form components in larger systems that combine both adaptive and non-adaptive elements. While the more general approach of such systems is more suitable for real-world problem solving, it has little to do with the traditional artificial intelligence connectionist models. What they do have in common, however, is the principle of non-linear, distributed, parallel and local processing and adaptation. Historically, the use of neural networks models marked a paradigm shift in the late eighties from high-level (symbolic) , characterized by
with knowledge embodied in if-then rules, to low-level (sub-symbolic) , characterized by knowledge embodied in the parameters of a .
(1943) created a computational model for neural networks based on
and algorithms. They called this model . The model paved the way for neural network research to split into two distinct approaches. One approach focused on biological processes in the brain and the other focused on the application of neural networks to artificial intelligence.
In the late 1940s psychologist
created a hypothesis of learning based on the mechanism of neural plasticity that is now known as . Hebbian learning is considered to be a 'typical'
rule and its later variants were early models for . These ideas started being applied to computational models in 1948 with .
Farley and
(1954) first used computational machines, then called calculators, to simulate a Hebbian network at MIT. Other neural network computational machines were created by Rochester, Holland, Habit, and Duda (1956).
(1958) created the , an algorithm for pattern recognition based on a two-layer learning computer network using simple addition and subtraction. With mathematical notation, Rosenblatt also described circuitry not in the basic perceptron, such as the
circuit, a circuit whose mathematical computation could not be processed until after the
algorithm was created by
Neural network research stagnated after the publication of machine learning research by
(1969). They discovered two key issues with the computational machines that processed neural networks. The first issue was that single-layer neural networks were incapable of processing the exclusive-or circuit. The second significant issue was that computers were not sophisticated enough to effectively handle the long run time required by large neural networks. Neural network research slowed until computers achieved greater processing power. Also key later advances was the
algorithm which effectively solved the exclusive-or problem (Werbos 1975).
of the mid-1980s became popular under the name . The text by
(1986) provided a full exposition on the use of connectionism in computers to simulate neural processes.
Neural networks, as used in artificial intelligence, have traditionally been viewed as simplified models of
in the brain, even though the relation between this model and brain biological architecture is debated, as it is not clear to what degree artificial neural networks mirror brain function.
Neural networks were gradually overtaken in popularity in machine learning by
and other, much simpler methods such as . Renewed interest in neural nets was sparked in the late 2000s by the advent of .
Computational devices have been created in , for both biophysical simulation and . More recent efforts show promise for creating
for very large scale
analyses and . If successful, these efforts could usher in a new era of
that is a step beyond digital computing, because it depends on
rather than
and because it is fundamentally
rather than
even though the first instantiations may in fact be with CMOS digital devices.
Between 2009 and 2012, the
and deep feedforward neural networks developed in the research group of
have won eight international competitions in
and . For example, the bi-directional and
(LSTM) of Alex Graves et al. won three competitions in connected handwriting recognition at the 2009 International Conference on Document Analysis and Recognition (ICDAR), without any prior knowledge about the three different languages to be learned.
Fast -based implementations of this approach by Dan Ciresan and colleagues at
have won several pattern recognition contests, including the IJCNN 2011 Traffic Sign Recognition Competition, the ISBI 2012 Segmentation of Neuronal Structures in Electron Microscopy Stacks challenge, and others. Their neural networks also were the first artificial pattern recognizers to achieve human-competitive or even superhuman performance on important benchmarks such as traffic sign recognition (IJCNN 2012), or the
Deep, highly nonlinear neural architectures similar to the 1980
and the "standard architecture of vision", inspired by the simple and complex cells identified by
in the primary , can also be pre-trained by unsupervised methods of 's lab at . A team from this lab won a 2012 contest sponsored by
to design software to help find molecules that might lead to new drugs.
Neural network models in artificial intelligence are usually referred to as artificial neural networks (ANNs); these are essentially simple mathematical models defining a function
or a distribution over
and , but sometimes models are also intimately associated with a particular learning algorithm or learning rule. A common use of the phrase ANN model really means the definition of a class of such functions (where members of the class are obtained by varying parameters, connection weights, or specifics of the architecture such as the number of neurons or their connectivity).
The word network in the term 'artificial neural network' refers to the inter–connections between the neurons in the different layers of each system. An example system has three layers. The first layer has input neurons which send data via synapses to the second layer of neurons, and then via more synapses to the third layer of output neurons. More complex systems will have more layers of neurons with some having increased layers of input neurons and output neurons. The synapses store parameters called "weights" that manipulate the data in the calculations.
An ANN is typically defined by three types of parameters:
The interconnection pattern between the different layers of neurons
The learning process for updating the weights of the interconnections
The activation function that converts a neuron's weighted input to its output activation.
Mathematically, a neuron's network function
is defined as a composition of other functions , which can further be defined as a composition of other functions. This can be conveniently represented as a network structure, with arrows depicting the dependencies between variables. A widely used type of composition is the nonlinear weighted sum, where , where
(commonly referred to as the ) is some predefined function, such as the . It will be convenient for the following to refer to a collection of functions
as simply a vector .
ANN dependency graph
This figure depicts such a decomposition of , with dependencies between variables indicated by arrows. These can be interpreted in two ways.
The first view is the functional view: the input
is transformed into a 3-dimensional vector , which is then transformed into a 2-dimensional vector , which is finally transformed into . This view is most commonly encountered in the context of .
The second view is the probabilistic view: the
depends upon the random variable , which depends upon , which depends upon the random variable . This view is most commonly encountered in the context of .
The two views are largely equivalent. In either case, for this particular network architecture, the components of individual layers are independent of each other (e.g., the components of
are independent of each other given their input ). This naturally enables a degree of parallelism in the implementation.
Two separate depictions of the recurrent ANN dependency graph
Networks such as the previous one are commonly called , because their graph is a . Networks with
are commonly called . Such networks are commonly depicted in the manner shown at the top of the figure, where
is shown as being dependent upon itself. However, an implied temporal dependence is not shown.
What has attracted the most interest in neural networks is the possibility of learning. Given a specific task to solve, and a class of functions , learning means using a set of observations to find
which solves the task in some optimal sense.
This entails defining a cost function
such that, for the optimal solution ,
– i.e., no solution has a cost less than the cost of the optimal solution (see ).
The cost function
is an important concept in learning, as it is a measure of how far away a particular solution is from an optimal solution to the problem to be solved. Learning algorithms search through the solution space to find a function that has the smallest possible cost.
For applications where the solution is dependent on some data, the cost must necessarily be a function of the observations, otherwise we would not be modelling anything related to the data. It is frequently defined as a
to which only approximations can be made. As a simple example, consider the problem of finding the model , which minimizes , for data pairs
drawn from some distribution . In practical situations we would only have
samples from
and thus, for the above example, we would only minimize . Thus, the cost is minimized over a sample of the data rather than the entire data set.
some form of
must be used, where the cost is partially minimized as each new example is seen. While online machine learning is often used when
is fixed, it is most useful in the case where the distribution changes slowly over time. In neural network methods, some form of online machine learning is frequently used for finite datasets.
See also: ,
While it is possible to define some arbitrary
cost function, frequently a particular cost will be used, either because it has desirable properties (such as ) or because it arises naturally from a particular formulation of the problem (e.g., in a probabilistic formulation the posterior probability of the model can be used as an inverse cost). Ultimately, the cost function will depend on the desired task. An overview of the three main categories of learning tasks is provided below:
There are three major learning paradigms, each corresponding to a particular abstract learning task. These are ,
In , we are given a set of example pairs
and the aim is to find a function
in the allowed class of functions that matches the examples. In other words, we wish to infer the mapping the cost function is related to the mismatch between our mapping and the data and it implicitly contains prior knowledge about the problem domain.
A commonly used cost is the , which tries to minimize the average squared error between the network's output, , and the target value
over all the example pairs. When one tries to minimize this cost using
for the class of neural networks called , one obtains the common and well-known
for training neural networks.
Tasks that fall within the paradigm of supervised learning are
(also known as classification) and
(also known as function approximation). The supervised learning paradigm is also applicable to sequential data (e.g., for speech and gesture recognition). This can be thought of as learning with a "teacher", in the form of a function that provides continuous feedback on the quality of solutions obtained thus far.
In , some data
is given and the cost function to be minimized, that can be any function of the data
and the network's output, .
The cost function is dependent on the task (what we are trying to model) and our a priori assumptions (the implicit properties of our model, its parameters and the observed variables).
As a trivial example, consider the model
is a constant and the cost . Minimizing this cost will give us a value of
that is equal to the mean of the data. The cost function can be much more complicated. Its form depends on the application: for example, in compression it could be related to the
and , whereas in statistical modeling, it could be related to the
of the model given the data (note that in both of those examples those quantities would be maximized rather than minimized).
Tasks that fall within the paradigm of unsupervised learning are
the applications include , the estimation of ,
are usually not given, but generated by an agent's interactions with the environment. At each point in time , the agent performs an action
and the environment generates an observation
and an instantaneous cost , according to some (usually unknown) dynamics. The aim is to discover a policy for selecting actions that minimizes some measure of a long- i.e., the expected cumulative cost. The environment's dynamics and the long-term cost for each policy are usually unknown, but can be estimated.
More formally the environment is modelled as a
(MDP) with states
and actions
with the following probability distributions: the instantaneous cost distribution , the observation distribution
and the transition , while a policy is defined as conditional distribution over actions given the observations. Taken together, the two then define a
(MC). The aim is to discover the policy tha i.e., the MC for which the cost is minimal.
ANNs are frequently used in reinforcement learning as part of the overall algorithm.
has been coupled with ANNs (Neuro dynamic programming) by
and Tsitsiklis and applied to multi-dimensional nonlinear problems such as those involved in ,
because of the ability of ANNs to mitigate losses of accuracy even when reducing the discretization grid density for numerically approximating the solution of the original control problems.
Tasks that fall within the paradigm of reinforcement learning are control problems,
Training a neural network model essentially means selecting one model from the set of allowed models (or, in a
framework, determining a distribution over the set of allowed models) that minimizes the cost criterion. There are numerous algorithms available for training n most of them can be viewed as a straightforward application of
theory and .
Most of the algorithms used in training artificial neural networks employ some form of , using backpropagation to compute the actual gradients. This is done by simply taking the derivative of the cost function with respect to the network parameters and then changing those parameters in a
direction.
are some commonly used methods for training neural networks.
Perhaps the greatest advantage of ANNs is their ability to be used as an arbitrary function approximation mechanism that 'learns' from observed data. However, using them is not so straightforward, and a relatively good understanding of the underlying theory is essential.
Choice of model: This will depend on the data representation and the application. Overly complex models tend to lead to problems with learning.
Learning algorithm: There are numerous trade-offs between learning algorithms. Almost any algorithm will work well with the correct
for training on a particular fixed data set. However, selecting and tuning an algorithm for training on unseen data requires a significant amount of experimentation.
Robustness: If the model, cost function and learning algorithm are selected appropriately the resulting ANN can be extremely robust.
With the correct implementation, ANNs can be used naturally in
and large data set applications. Their simple implementation and the existence of mostly local dependencies exhibited in the structure allows for fast, parallel implementations in hardware.
The utility of artificial neural network models lies in the fact that they can be used to infer a function from observations. This is particularly useful in applications where the complexity of the data or task makes the design of such a function by hand impractical.
The tasks artificial neural networks are applied to tend to fall within the following broad categories:
, or , including ,
and modeling.
, including
and sequence recognition,
and sequential decision making.
, including filtering, clustering,
and compression.
, including directing manipulators, .
, including .
Application areas include the system identification and control (vehicle control, process control,
management), quantum chemistry, game-playing and decision making (backgammon, chess, ), pattern recognition (radar systems, face identification, object recognition and more), sequence recognition (gesture, speech, handwritten text recognition), medical diagnosis, financial applications (e.g. ),
(or knowledge discovery in databases, "KDD"), visualization and
filtering.
Artificial neural networks have also been used to diagnose several cancers. An ANN based hybrid lung cancer detection system named HLND improves the accuracy of diagnosis and the speed of lung cancer radiology. These networks have also been used to diagnose prostate cancer. The diagnoses can be used to make specific models taken from a large group of patients compared to information of one given patient. The models do not depend on assumptions about correlations of different variables. Colorectal cancer has also been predicted using the neural networks. Neural networks could predict the outcome for a patient with colorectal cancer with more accuracy than the current clinical methods. After training, the networks could predict multiple patient outcomes from unrelated institutions.
Theoretical and
is the field concerned with the theoretical analysis and the computational modeling of biological neural systems. Since neural systems are intimately related to cognitive processes and behavior, the field is closely related to cognitive and behavioral modeling.
The aim of the field is to create models of biological neural systems in order to understand how biological systems work. To gain this understanding, neuroscientists strive to make a link between observed biological processes (data), biologically plausible mechanisms for neural processing and learning ( models) and theory (statistical learning theory and ).
Many models are used in the field, defined at different levels of abstraction and modeling different aspects of neural systems. They range from models of the short-term behavior of , models of how the dynamics of neural circuitry arise from interactions between individual neurons and finally to models of how behavior can arise from abstract neural modules that represent complete subsystems. These include models of the long-term, and short-term plasticity, of neural systems and their relations to learning and memory from the individual neuron to the system level.
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Neural network software is used to , , develop and apply artificial neural networks,
and, in some cases, a wider array of .
Main article:
Artificial neural network types vary from those with only one or two layers of single direction logic, to complicated multi–input many directional feedback loops and layers. On the whole, these systems use algorithms in their programming to determine control and organization of their functions. Most systems use "weights" to change the parameters of the throughput and the varying connections to the neurons. Artificial neural networks can be autonomous and learn by input from outside "teachers" or even self-teaching from written-in rules.
(MLP) is a universal function approximator, as proven by the . However, the proof is not constructive regarding the number of neurons required or the settings of the weights.
has provided a proof that a specific recurrent architecture with rational valued weights (as opposed to full precision -valued weights) has the full power of a
using a finite number of neurons and standard linear connections. Further, it has been shown that the use of irrational values for weights results in a machine with
Artificial neural network models have a property called 'capacity', which roughly corresponds to their ability to model any given function. It is related to the amount of information that can be stored in the network and to the notion of complexity.
Nothing can be said in general about convergence since it depends on a number of factors. Firstly, there may exist many local minima. This depends on the cost function and the model. Secondly, the optimization method used might not be guaranteed to converge when far away from a local minimum. Thirdly, for a very large amount of data or parameters, some methods become impractical. In general, it has been found that theoretical guarantees regarding convergence are an unreliable guide to practical application.[]
In applications where the goal is to create a system that generalizes well in unseen examples, the problem of over-training has emerged. This arises in convoluted or over-specified systems when the capacity of the network significantly exceeds the needed free parameters. There are two schools of thought for avoiding this problem: The first is to use
and similar techniques to check for the presence of overtraining and optimally select hyperparameters such as to minimize the generalization error. The second is to use some form of . This is a concept that emerges naturally in a probabilistic (Bayesian) framework, where the regularization can be performed by selecting a larger prior probability but also in statistical learning theory, where the goal is to minimize over two quantities: the 'empirical risk' and the 'structural risk', which roughly corresponds to the error over the training set and the predicted error in unseen data due to overfitting.
Confidence analysis of a neural network
Supervised neural networks that use a
(MSE) cost function can use formal statistical methods to determine the confidence of the trained model. The MSE on a validation set can be used as an estimate for variance. This value can then be used to calculate the
of the output of the network, assuming a . A confidence analysis made this way is statistically valid as long as the output
stays the same and the network is not modified.
By assigning a , a generalization of the , on the output layer of the neural network (or a softmax component in a component-based neural network) for categorical target variables, the outputs can be interpreted as posterior probabilities. This is very useful in classification as it gives a certainty measure on classifications.
The softmax activation function is:
A common criticism of neural networks, particularly in robotics, is that they require a large diversity of training for real-world operation[]. This is not surprising, since any learning machine needs sufficient representative examples in order to capture the underlying structure that allows it to generalize to new cases. Dean Pomerleau, in his research presented in the paper "Knowledge-based Training of Artificial Neural Networks for Autonomous Robot Driving," uses a neural network to train a robotic vehicle to drive on multiple types of roads (single lane, multi-lane, dirt, etc.). A large amount of his research is devoted to (1) extrapolating multiple training scenarios from a single training experience, and (2) preserving past training diversity so that the system does not become overtrained (if, for example, it is presented with a series of right turns – it should not learn to always turn right). These issues are common in neural networks that must decide from amongst a wide variety of responses, but can be dealt with in several ways, for example by randomly shuffling the training examples, by using a numerical optimization algorithm that does not take too large steps when changing the network connections following an example, or by grouping examples in so-called mini-batches.
, a former
columnist, wrote in 1997, "Although neural nets do solve a few toy problems, their powers of computation are so limited that I am surprised anyone takes them seriously as a general problem-solving tool." (Dewdney, p. 82)
To implement large and effective software neural networks, considerable processing and storage resources need to be committed[]. While the brain has hardware tailored to the task of processing signals through a
of neurons, simulating even a most simplified form on
technology may compel a neural network designer to fill many millions of
rows for its connections – which can consume vast amounts of computer
space. Furthermore, the designer of neural network systems will often need to simulate the transmission of signals through many of these connections and their associated neurons – which must often be matched with incredible amounts of
processing power and time. While neural networks often yield effective programs, they too often do so at the cost of efficiency (they tend to consume considerable amounts of time and money).
Computing power continues to grow roughly according to , which may provide sufficient resources to accomplish new tasks.
addresses the hardware difficulty directly, by constructing non-Von-Neumann chips with circuits designed to implement neural nets from the ground up.
Arguments against Dewdney's position are that neural networks have been successfully used to solve many complex and diverse tasks, ranging from autonomously flying aircraft to detecting credit card fraud .[]
Technology writer
commented on Dewdney's statements about neural nets:
Neural networks, for instance, are in the dock not only because they have been hyped to high heaven, (what hasn't?) but also because you could create a successful net without understanding how it worked: the bunch of numbers that captures its behaviour would in all probability be "an opaque, unreadable table...valueless as a scientific resource".
In spite of his emphatic declaration that science is not technology, Dewdney seems here to pillory neural nets as bad science when most of those devising them are just trying to be good engineers. An unreadable table that a useful machine could read would still be well worth having.
Although it is true that analyzing what has been learned by an artificial neural network is difficult, it is much easier to do so than to analyze what has been learned by a biological neural network. Furthermore, researchers involved in exploring learning algorithms for neural networks are gradually uncovering generic principles which allow a learning machine to be successful. For example, Bengio and LeCun (2007) wrote an article regarding local vs non-local learning, as well as shallow vs deep architecture.
Some other criticisms came from believers of hybrid models (combining neural networks and symbolic approaches). They advocate the intermix of these two approaches and believe that hybrid models can better capture the mechanisms of the human mind.
A single-layer feedforward artificial neural network. Arrows originating from
are omitted for clarity. There are p inputs to this network and q outputs. In this system, the value of the qth output,
would be calculated as
A two-layer feedforward artificial neural network.
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