P. Young. Recursive Estimation and Time-Series Analysis. Springer-Verlag, 1984.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....change to c 0 and c 1 . We use an online learning method that uses the linear mapping D cpu = c 0 c 1 pr, but continuously updates the values of c 0 and c 1 to reflect the behaviour corresponding to the current camera position. We use recursive least squares regression with exponential decay [39], a modification of the well known linear regression method [18] This gives greater weight to more recent data by decaying the weight of data exponentially over time. Our predictor uses a decay factor of 0.5, which makes it very agile, effectively remembering only the last 4 data points. It is ....

P. Young. Recursive Estimation and Time-Series Analysis. Springer, 1984.

....a way to recompute the optimal parameter values when new measurements are obtained. This allows the predictor to track changes in environmental conditions or user behaviour over time. 6. 2 Least squares regression In all the applications I studied, one basic technique least squares estimation [42, 98] proved to be of great value. Often, the output is some linear function of the input features; in other cases, we can transform the input features in some way, and then apply a linear function. The least squares method fits data to a linear model of the form y = c 0 c 1 x 1 c 2 x 2 : ....

Peter Young. Recursive Estimation and Time-Series Analysis. Springer-Verlag, Heidelberg, Germany, 1984.

....this arrangement. The effectivness is shown at an example for electric load forecast of a power distribution company. 1 INTRODUCTION The prediction of time series is an very important problem in monitoring, diagnosis, control and decision support for technical and nontechnical systems [ander] [young], andel] In addition to specific time dependent (seasonal) actuating variables for example temperature, global solar radiation, daily flow of life and so on, such signals are often subject of not or only hardly registrable actuating variables so that a prediction is combined with great ....

Young, P. C., "Recursive Estimation and Time Series Analysis ", Springer Verlag Berlin, (1984)

....arrive and depart at the same rate, the queue remains at one packet. Further assume that initially the average queue size was zero. In this case it takes 0 6j B0 ) packet arrivals (with the queue size remaining at one) until the average queue size reachs : 50 0 0 gJ [35]. For = t : 0 , this takes 1000 packet arrivals; for = t : 88 , this takes 500 packet arrivals; for = t : this takes 333 packet arrivals. In most of our simulations we use = t : 36 . 6.3 Setting , and G The optimal values for and ....

Young, P., Recursive Estimation and Time-Series Analysis, Springer-Verlag, 1984, pp. 60-65.

....problems have apparently received little attention in the literature, despite their implicit connections with useful tools in identification and signal processing. In identification problems, for instance, instrumental variable (IV) methods are often employed to guarantee consistent estimators [1, 2, 3]. The connection of these methods to oblique projections is well known and has been pointed out in [4] Likewise, in signal processing problems, oblique projections can be used in array processing and communication applications, as well as in higher order spectra (HOS) analysis [5, 6, 7] In these ....

....(z 1 ; z2 ) and ( z1 ; z2 ) The significance of this fact is the following. It often happens in applications that one is interested in solving estimation problems of either forms (3) or (4) Particular examples arise in instrumental variable methods and in higher order spectra analysis [2, 6] (though not in such an explicit form see, e.g. Sec. VIII. ahead) On the other hand, problems of the EE type will be shown here to lead, in the presence of state space structure, to what we shall call an oblique Kalman filter. By relating the solutions of the WOP and EE problems, we shall ....

P. Young, Recursive Estimation and Time-Series Analysis, Springer-Verlag, 1984.

....error is to be included. For example, if an additional query q k 1 and its observed cost c k 1 are to be included, then A k 1 needs to be computed form scratch, because it takes no advantage of previously computed values of A k . A better method, called recursive least square estimation, Lee64, You84] eliminates the duplication by using a recursive expression. It expresses the solution A k , when k n, in a recursive form: a (k) l = a (k Gamma1) l Gamma [ n X i=1 g k l;i Delta f i (q k ) n X i=1 a (k Gamma1) i Delta f i (q k ) Gamma c k ] for 1 l n (6) g (k) ....

....k equations which has more than k variables. However, if we start the recursion by assigning a (0) i = 0, g (0) i;j = 0 for i 6= j, and g (0) i;i to some large number, then the solution computed using formulae 6 and 7 eventually converges to the one computed using formulae 5 as k increases [You84] The adaptation mechanism starts as soon as the first query is executed. During the first few queries, the cost estimation errors may be relatively large because the cost function is still in its learning stage. Our experiments show that, however, after a few queries, the estimated costs are ....

P. Young. Recursive Estimation and Time-Series Analysis. Springer-Verlag, New York, 1984.

....of A and b increase in proportion to the number of query feedbacks k, resulting in considerable overhead when fitting long series of query feedbacks. However, since the feedback arrives incrementally, we can use an iterative fitting technique know as the recursive least squares regression [29]. For this incremental approach, we only need to maintain two m Theta m matrices, as opposed to a k Theta m matrix. These matrices are updated with each feedback (for a detailed description of recursive least squares regression in the context of database query feedback, see [4] Since m (i.e, ....

P. Young. Recursive Estimation and Time-Series Analysis. Springer-Verlag, 1984.

....stack block operator required that there be a block with an empty top. Two terms were created from that subgoal. Term T6 8 Each measurement is the average of 100 experiments. The number 100 was chosen arbitrarily. Subsequent experiments, performed with the Recursive Least Squares training rule [Young, 1984] and conducted until values were known to within Sigma1 with 99 confidence, confirmed the relative utility of each representation. Use of Domain Knowledge in Constructive Induction 25 Terms T1 T12 L1 L4 Terms T1 T12 Terms L1 L4 Terms B1 B16 0.0 10.0 20.0 30.0 40.0 ....

....clearly outperformed both of the hand coded representations. A combination of two representations performed best of all. 9 Each measurement is the average of 100 experiments. The number 100 was chosen arbitrarily. Subsequent experiments, performed with the Recursive Least Squares training rule [Young, 1984] and conducted until values were known to within Sigma1 with 99 confidence, confirmed the relative utility of each representation except the B1 B16 representation. Further analysis revealed that the LMS rule would favor the B1 B16 representation if the experimental parameters were adjusted ....

Young, P. (1984). Recursive estimation and time-series analysis. New York: Springer-Verlag.

....a vector of n 1 coefficients, also known as weights. If W T Y 0, then the LTU infers that Y belongs to one class A, otherwise the LTU infers that Y belongs to the other class B. To find the set of weights that leads to an accurate classifier, we used the Recursive Least Squares (RLS) Procedure (Young 1984). RLS, invented by Gauss, is a recursive version of the Least Squares (LS) Algorithm. An LS procedure minimizes the mean squared error, P i (y i Gamma y i ) 2 of the training data, where y i is the true value and y i is the estimated value of the dependent variable, y, for feature vector i. ....

Young, P. 1984. Recursive estimation and time-series analysis. Springer-Verlag, New York.

....Thus, each node in a decision tree is either a decision or a class. Figure 6 shows a decision tree operating in a three dimensional feature space. Several methods exist for learning the weights in a linear threshold unit; this implementation uses the Recursive Least Squares (RLS) algorithm [50]. The RLS method is recommended for dual class (target vs. non target) classification, and is a recursive version of Gauss Least Squares algorithm, which minimizes the mean squared error between the estimated y i and true y i values, Sigma(y i Gamma y i ) 2 of the selected features over a ....

.... and P k = P k Gamma1 Gamma P k Gamma1 X k [1 X T k P k Gamma1 X k ] Gamma1 X T k P k Gamma1 (5) The weights are initialized randomly, and the matrix consists of 0 values everywhere except along the diagonal, which is set to a very large value: 10 6 according to Young s recommendation [50]. If at any level, the LTU results in a non negative value, the corresponding set of pixels is labeled as belonging to the object (target) otherwise, it is labeled negative (non target) Figure 7 shows the structure of a multivariate decision tree. In this tree, the non terminal nodes represent ....

P. Young, Recursive Estimation and Time-Series Analysis, New York: Springer-Verlag, 1984.

.... s correct class: fraud or non fraud) The evidence combination weights the monitor outputs and learns a threshold on the sum so that alarms may be issued with high confidence. Many training methods for evidence combining are possible. We chose a simple Linear Threshold Unit (LTU) Nilsson 1965; Young 1984) for the experiments reported below. An LTU is simple and fast, and enables a good first order judgment of the features worth. 14 FAWCETT AND PROVOST A feature selection process is used to reduce the number of monitors in the final detector. Some of the rules do not perform well when used in ....

Young, P. (1984). Recursive estimation and time-series analysis. New York: Springer-Verlag.

....for , k = 1 k k X i=1 i 0 i # Gamma1 1 k k X i=1 i i # : 4.14) Lemma (4.1) gives a set of conditions under which we can expect k as defined by Equation (4.14) to converge in probability to . Appendix C. 1 gives a proof based on one provided by Young [104]. Lemma 4.1 If the correlation matrix Cor( is nonsingular and finite, and the output observation noise j i is uncorrelated with the input observations i , then k as defined by Equation (4.14) converges in probability to . Equation (4.12) models the situation where observation ....

....only on the output. In the more general case, however, the input observations are also noisy. Instead of being able to observe k directly, we can only observe k = k i k , where i k 54 is the input observation noise vector at time k. This is known as an errors in variables situation [104]. Equation (4.15) models the errors in variables situation. k = Psi( k ) j k = Psi( k Gamma i k ) j k = 0 k Gamma i 0 k j k : 4.15) The problem with errors in variables is that we cannot use k instead of k in Equation (4.14) without violating the ....

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Young, P. Recursive estimation and time-series analysis. Springer--Verlag, 1984.

....Thus, each node in a decision tree is either a decision or a class. Figure 5 shows a decision tree operating in a three dimensional feature space. Several methods exist for learning the weights in a linear threshold unit; this implementation uses the Recursive Least Squares (RLS) algorithm [44]. The RLS method is recommended for dual class (target vs. non target) classification, and is a recursive version of Gauss Least Squares algorithm, which minimizes the mean squared error between the estimated y i and true y i values, Sigma(y i Gamma y i ) 2 of the selected features over a ....

.... and P k = P k Gamma1 Gamma P k Gamma1 X k [1 X T k P k Gamma1 X k ] Gamma1 X T k P k Gamma1 (5) The weights are initialized randomly, and the matrix consists of 0 values everywhere except along the diagonal, which is set to a very large value: 10 6 according to Young s recommendation [44]. If at any level, the LTU results in a non negative value, the corresponding set of pixels is labeled as belonging to the object (target) otherwise, it is labeled negative (non target) Figure 6 shows the structure of a multivariate decision tree. In this tree, the non terminal nodes represent ....

P. Young, Recursive Estimation and Time-Series Analysis, New York: Springer-Verlag, 1984.

....and depart at the same rate, the queue remains at one packet. Further assume that initially the average queue size was zero. In this case it takes Gamma1=ln(1 Gamma w q ) packet arrivals (with the queue size remaining at one) until the average queue size avg reachs 0:63 = 1 Gamma 1=e [35]. For w q = 0:001, this takes 1000 packet arrivals; for w q = 0:002, this takes 500 packet arrivals; for w q = 0:003, this takes 333 packet arrivals. In most of our simulations we use w q = 0:002. 6.3 Setting min th and max th The optimal values for min th and max th depend on the ....

Young, P., Recursive Estimation and Time-Series Analysis, Springer-Verlag, 1984, pp. 60-65.

.... rule I t = p(x t j Z t ; U t Gamma1 ) 1 c(z t ) p(z t j x t ) Z Omega x t Gamma1 p(x t j x t Gamma1 ; u t Gamma1 ) I t Gamma1 dx t Gamma1 = Psi (I t Gamma1 ; u t Gamma1 ; z t ) 8) where c(z t ) is a normalizing constant that depends on the most recent sensation (see, e.g. Young, 1984). CHAPTER 3. APPROACH TO THE SOLUTION 44 3.1.3 Optimal Policy and Value Function The optimal policy is a function of the feedback type that maps the agent s state to the best action the agent can execute at that state u t = I t ) 9) where I t is the agent s state at stage t. The ....

....but not the value of the external parameter 2 It is assumed independent additive Gaussian noise with zero mean and constant covariance matrix. 3 Kalman filters are commonly used in control systems to estimate the state of the dynamic system when the incoming sensations are noisy (Ogata, 1990; Young, 1984; Stengel, 1994; Bertsekas, 1995a) CHAPTER 6. INCOMPLETE KNOWLEDGE 156 vector. Additionally, the sensations are contaminated with additive Gaussian noise with zero mean and constant covariance matrix R. 4 z t = H(x t ) x t ffl t ffl t i:i:d: 5 N(0; R) 66) The internal state of the ....

Young, P. (1984). Recursive Estimation and Time-Series Analysis. Springer-Verlag, New York, NY.

....many cells. So, an eventual recomputation of the affected models is advisable. The updating of the model can be achieved by using techniques similar to those described in [4] to update polynomial models for selectivity estimation. The techniques use a method called recursive least square error [28] to avoid a lot of expensive recomputation. 2.7 Query processing Once the Quasi Cube is constructed, we can use it to answer queries. Any query will request a chunk of the matrix entries which spans one or more of our regions. For each cell in the query, we use the index to decide if the entry ....

P. Young. Recursive estimation and time-series analysis. Springer-Verlag, New York, 1984.

.... Delta Delta ; S t Gamma1 ; K e ) 20) Equations (14) 15) and (20) provide a self correcting mechanism as the model updates the prediction of C t and the likelihood of K e at each stage (t) to the observed data. In time series analysis, equations (14) and (15) are called a Kalman filter model (Young, 1984). In this paper, the model is used to estimate the phosphorus accretion rate in a sequence of divided regions along the flow path of the wetland, instead of a time series. One of the many advantages of using this type of model is that the effects of the initial uncertainty in the phosphorus ....

Young, P.C., 1984. Recursive Estimation and Time-series Analysis, Springer-Verlag, Berlin.

....to divide feature space are represented as linear threshold units (LTUs) Nilsson 1965, Duda and Hart 1973] Several methods exist for learning the weights in a linear threshold unit. Brodley and Utgoff [Brodley and Utgoff] discuss four such methods: the Recursive Least Squares (RLS) algorithm [Young 1984], the Pocket al..gorithm [Gallant 1986] Thermal Training [Frean 1990] and CART s coefficient learning method [Breiman, et al. 1984] Because we are concerned only with two class classification in this domain, the RLS training method is used in this paper (see [Young 1984] for a description of ....

.... Squares (RLS) algorithm [Young 1984] the Pocket al..gorithm [Gallant 1986] Thermal Training [Frean 1990] and CART s coefficient learning method [Breiman, et al. 1984] Because we are concerned only with two class classification in this domain, the RLS training method is used in this paper (see [Young 1984] for a description of training LTUs for two class classification, and [Draper, et al. 1994] for a description of multi class classification using Frean s thermal training rule [Frean 1990] Like other non parametric learning techniques, decision trees are susceptible to overtraining. In order to ....

Young, P., Recursive Estimation and Time-Series Analysis, New York: Springer-Verlag, 1984.

....) A(z 1 ) u(k d ) 4) where g(k) is a time variable model scaling factor introduced to allow for the variable SSG, while d is the artificial time delay. The adaptive gain g(k) is recursively estimated in real time using a stochastic time variable parameter (TVP) estimation algorithm (e.g. Young, 1984). This on line estimation technique, which has a similar algorithmic form to Kalman filtering, results in an adaptive gain parameter which effectively estimates the changing gain or scale factor associated with the river system dynamics. The adaptive gain approach enables these fairly slow changes ....

Young, P.C. (1984) Recursive Estimation and Time Series Analysis. Springer-Verlag: Berlin.

....test based on n Gamma 1 features is more general than one based on n features. 3 Learning the coefficients of a linear combination test In this section we describe four different methods for learning the coefficients of a linear combination test. The first method, Recursive Least Squares (RLS) (Young, 1984), minimizes the mean squared error over the training data. The second method, the Pocket al..gorithm (Gallant, 1986) maximizes the number of correct classifications on the training data. The third method, Thermal Training (Frean, 1990) converges to a set of coefficients by paying decreasing ....

....error covariance matrix. If little is known about the true W and W 0 is set to zero, then the initial values of P should reflect this uncertainty: the diagonal elements should be set to large values to indicate a high initial error variance and little confidence in the initial estimate of W 0 . Young (1984) suggests setting the diagonal elements to 10 6 . The off diagonal elements should be set to zero showing when there is no a priori information about the covariance properties of W. In this case, the best estimate is that they are zero. When there is no noise in the data and the number of ....

[Article contains additional citation context not shown here]

Young, P. (1984). Recursive estimation and time-series analysis. New York: SpringerVerlag.

.... metric (Quinlan, 1986) Linear Discriminant Functions: For two class tasks the system uses a linear threshold unit, and for multiclass tasks it uses a linear machine (Nilsson, 1965) To find the weights of a linear discriminant function the system uses the Recursive Least Squares procedure (Young, 1984) for two class tasks and the Thermal Training rule (Frean, 1990; Brodley Utgoff, 1992) for multiclass tasks. To select the terms to use with a linear discriminant function, one of four search procedures is used: sequential backward elimination (SBE) Kittler, 1986) a variation of SBE that uses ....

Young, P. (1984). Recursive estimation and time-series analysis. New York: Springer-Verlag.

....into arbitrary (multi dimensional) polygons (see [25, 9] for more detailed descriptions) 3.4 Learning Weights in the Linear Threshold Units. Several methods exist for learning tests in a linear threshold unit. Brodley and Utgoff [5] discuss four such methods: the Recursive Least Squares (RLS) [29], the Pocket al..gorithm [15] Thermal Training [14] and CART s coefficient learning method ( 4] The RLS method is recommended for dual class classification. The RLS algorithm is a recursive version of Gauss Least Squares algorithm, which minimizes the mean squared error between the estimated ....

....initial weights be set (to 0 if little is known about the weights) The covariance matrix should reflect the uncertainty in the weights. If the weights are initialized to 0, the matrix should consist of 0 values everywhere except along the diagonal, which should be set to a very large value. Young [29] recommends that the diagonal be initialized to 10 6 . 3.5 Building the Tree The optimal discriminant function can be determined by training over a set of known instances. If a set of instances is linearly separable, a single test is sufficient for separation. Typically, however, a large set ....

Young, P., Recursive Estimation and Time-Series Analysis, New York: Springer-Verlag.

....and that, as packets arrive and depart at the same rate, the queue remains at one packet. Further assume that initially the average queue size was zero. In this case it takes 1 ln(1 w q ) packet arrivals (with the queue size remaining at one) until the average queue size avg reachs 0. 63 = 1 1 e [35]. For w q = 0.001, this takes 1000 packet arrivals; for w q = 0.002, this takes 500 packet arrivals; for w q = 0.003, this takes 333 packet arrivals. In most of our simulations we use w q = 0.002. 6.3 Setting min th and max th The optimal values for min th and max th depend on the desired average ....

Young, P., Recursive Estimation and Time-Series Analysis, Springer-Verlag, 1984, pp. 60-65.

....the relevant model(s) need to be updated to reflect the effect of this data. The updating of the model can be achieved by using techniques similar to those described in [CR94] to update polynomial models for selectivity estimation. The techniques use a method called recursive least square error [You84] to avoid a lot of expensive recomputation. 5 Log Linear Models Log linear modeling is a methodology for approximating discrete multidimensional probability distributions. The multi way table of joint probabilities is approximated by a product of lower order tables. For example, suppose the four ....

P. Young. Recursive estimation and time-series analysis. Springer-Verlag, New York, 1984.

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P. Young. Recursive Estimation and Time-Series Analysis. Springer-Verlag, 1984.

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P. Young. Recursive Estimation and Time-Series Analysis. Springer-Verlag, 1984.

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P. Young. Recursive Estimation and Time-Series Analysis. Springer, 1984.

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P. Young. Recursive Estimation and Time-Series Analysis. Springer-Verlag, 1984.

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Young, P., Recursive Estimation and Time-Series Analysis, New York: Springer-Verlag, 1984.

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Young, P., Recursive Estimation and TimeSeries Analysis, Springer-Verlag, 1984, pp. 6065.

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Young, P.C. (1984). Recursive Estimation and Time-series Analysis, Springer-Verlag, Berlin.

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P. Young, Recursive Estimation and Time-Series Analysis, Springer-Verlag, 1984, pp. 60-65.

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