Above are papers related to the following paper: [Paper_ID] Paper #1132505. 	[Title] TO IMPROVE FORECASTING [Abstract] Working Paper IS-97-007, Leonard N. Stern School of Business, New York University. In: Journal of Computational Intelligence in Finance 6 (1998) 14-23. (Special Issue on "Improving Generalization of Nonlinear Financial Forecasting Models".) http://www.stern.nyu.edu/~aweigend/Research/Papers/InteractionLayer Abstract. Predictive models for financial data are often based on a large number of plausible inputs that are potentially nonlinearly combined to yield the conditional expectation of a target, such as a daily return of an asset. This paper introduces a new architecture for this task: On the output side, we predict dynamical variables such as first derivatives and curvatures on different time spans. These are subsequently combined in an interaction output layer to form several estimates of the variable of interest. Those estimates are then averaged to yield the final prediction. Independently from this idea, on the input side, we propose a new internal preprocessing layer connected with a diagonal matrix of positive weights to a layer of squashing functions. These weights adapt for each input individually and learn to squash outliers in the input. We apply these two ideas to the real world example of the daily predictions of the German stock index DAX (Deutscher Aktien Index), and compare the results to a network with a single output. The new six layer architecture is more stable in training due to two facts: (1) More information is flowing back from the outputs to the input in the backward pass; (2) The constraint of predicting first and second derivatives focuses the learning on the relevant variables for the dynamics. The architectures are compared from both the training perspective (squared errors, robust errors), and from the trading perspective (annualized returns, percent correct, Sharpe ratio). Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #675649. 	[Title] Modeling Volatility using State Space Models [Abstract] In time series problems, noise can be divided into two categories: dynamic noise which drives the process, and observational noise which is added in the measurement process, but does not influence future values of the system. In this framework, empirical volatilities (the squared relative returns of prices) exhibit a significant amount of observational noise. To model and predict their time evolution adequately, we estimate state space models that explicitly include observational noise. We obtain relaxation times for shocks in the logarithm of volatility ranging from three weeks (for foreign exchange) to three to five months (for stock indices). In most cases, a two-dimensional hidden state is required to yield residuals that are consistent with white noise. We compare these results with ordinary autoregressive models (without a hidden state) and find that autoregressive models underestimate the relaxation times by about two orders of magnitude due to their ignoring the distinction between observational and dynamic noise. This new interpretation of the dynamics of volatility in terms of relaxators in a state space model carries over to stochastic volatility models and to GARCH models, and is useful for several problems in finance, including risk management and the pricing of derivative securities. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #240321. 	[Title] Nonlinear gated experts for time series: discovering regimes and avoiding overfitting [Abstract] In: International Journal of Neural Systems 6 (1995) p. 373 - 399. URL of this paper: ftp://ftp.cs.colorado.edu/pub/Time-Series/MyPapers/experts.ps.Z, or http://www.cs.colorado.edu/~andreas/Time-Series/MyPapers/experts.ps.Z University of Colorado Computer Science Technical Report CU-CS-798-95. In the analysis and prediction of real-world systems, two of the key problems are nonstationarity(often in the form of switching between regimes), and overfitting (particularly serious for noisy processes). This article addresses these problems using gated experts, consisting of a (nonlinear) gating network, and several (also nonlinear) competing experts. Each expert learns to predict the conditional mean, and each expert adapts its width to match the noise level in its regime. The gating network learns to predict the probability of each expert, given the input. This article focuses on the case where the gating network bases its decision on information from the inputs. This can be contrasted to hidden Markov models where the decision is based on the previous state(s) (i.e., on the output of the gating network at the previous time step), as well as to averaging over several predictors. In contrast, gated experts soft-partition the input space. This article discusses the underlying statistical assumptions, derives the weight update rules, and compares the performance of gated experts to standard methods on three time series: (1) a computer-generated series, obtained by randomly switching between two nonlinear processes, (2) a time series from the Santa Fe Time Series Competition (the light intensity of a laser in chaotic state), and (3) the daily electricity demand of France, a real-world multivariate problem with structure on several time scales. The main results are (1) the gating network correctly discovers the different regimes of the process, (2) the widths associated with each expert are important for the segmentation task (and they can be used to characterize the sub-processes), and (3) there is less overfitting compared to single networks (homogeneous multi-layer perceptrons), since the experts learn to match their variances to the (local) noise levels. This can be viewed as matching the local complexity of the model to the local complexity of the data. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #25702. 	[Title] Nonlinear Prediction of Chaotic Time Series Using Support Vector Machines [Abstract] A novel method for regression has been recently proposed by V. Vapnik et al. [8, 9]. The technique, called Support Vector Machine (SVM), is very well founded from the mathematical point of view and seems to provide a new insight in function approximation. We implemented the SVM and tested it on the same data base of chaotic time series that was used in [1] to compare the performances of different approximation techniques, including polynomial and rational approximation, local polynomial techniques, Radial Basis Functions, and Neural Networks. The SVM performs better than the approaches presented in [1]. We also study, for a particular time series, the variability in performance with respect to the few free parameters of SVM. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #675847. 	[Title] NONLINEAR TRADING MODELS THROUGH SHARPE RATIO MAXIMIZATION [Abstract] Working Paper IS-97-005, Leonard N. Stern School of Business, New York University. In: Decision Technologies for Financial Engineering (Proceedings of the Fourth International Conference on Neural Networks in the Capital Markets, NNCM-96), pp. 3-22. Edited by A.S.Weigend, Y.S.Abu-Mostafa, and A.-P.N.Refenes. Singapore: World Scientific, 1997. http://www.stern.nyu.edu/~aweigend/Research/Papers/SharpeRatio While many trading strategies are based on price prediction, traders in financial markets are typically interested in risk-adjusted performance such as the Sharpe Ratio, rather than price predictions themselves. This paper introduces an approach which generates a nonlinear strategy that explicitly maximizes the Sharpe Ratio. It is expressed as a neural network model whose output is the position size between a risky and a risk-free asset. The iterative parameter update rules are derived and compared to alternative approaches. The resulting trading strategy is evaluated and analyzed on both computer-generated data and real world data (DAX, the daily German equity index). Trading based on Sharpe Ratio maximization compares favorably to both profit optimization and probability matching (through cross-entropy optimization). The results show that the goal of optimizing out-of-sample risk-adjusted profit can be achieved with this nonlinear approach. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #675756. 	[Title] A Bootstrap Evaluation of the Effect of Data Splitting on Financial Time Series [Abstract] This article exposes problems of the commonly used technique of splitting the available data into training, validation, and test sets that are held fixed, warns about drawing too strong conclusions from such static splits, and shows potential pitfalls of ignoring variability across splits. Using a bootstrap or resampling method, we compare the uncertainty in the solution stemming from the data splitting with neural network specific uncertainties (parameter initialization, choice of number of hidden units, etc.). We present two results on data from the New York Stock Exchange. First, the variation due to different resamplings is significantly larger than the variation due to different network conditions. This result implies that it is important to not over-interpret a model (or an ensemble of models) estimated on one specific split of the data. Second, on each split, the neural network solution with early stopping is very close to a linear model; no significant nonlinearities are extracted. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #910. 	[Title] Learning networks for face analysis and synthesis [Abstract] This paper presents an overview of the face-related projects in our group. The unifying theme underlying our work is the use of example-based learning methods for both analyzing and synthesizing face images. We label the example face images (and for the problem of face detection, "near miss" faces as well) with descriptive parameters for pose, expression, identity, and face vs. non-face. Then, by using example-based learning techniques, we develop networks for performing analysis tasks such as pose and expression estimation, face recognition, and face detection in cluttered scenes. In addition to these analysis applications, we show how the example-based technique can also be used as a novel method for image synthesis that is for computer graphics. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #6130. 	[Title] ``Learning Local Error Bars for Nonlinear Regression.''  Learning Local Error Bars for Nonlinear Regression [Abstract] We present a new method for obtaining local error bars for nonlinear regression, i.e., estimates of the confidence in predicted values that depend on the input. We approach this problem by applying a maximum-likelihood framework to an assumed distribution of errors. We demonstrate our method first on computer-generated data with locally varying, normally distributed target noise. We then apply it to laser data from the Santa Fe Time Series Competition where the underlying system noise is known quantization error and the error bars give local estimates of model misspecification. In both cases, the method also provides a weighted-regression effect that improves generalization performance. Please summarise all the given information.

Paper #1132505 has the title `TO IMPROVE FORECASTING  
` and the abstract `Working Paper IS-97-007, Leonard N. Stern School of Business, New York University. In: Journal of Computational Intelligence in Finance 6 (1998) 14-23. (Special Issue on "Improving Generalization of Nonlinear Financial Forecasting Models".) http://www.stern.nyu.edu/~aweigend/Research/Papers/InteractionLayer Abstract. Predictive models for financial data are often based on a large number of plausible inputs that are potentially nonlinearly combined to yield the conditional expectation of a target, such as a daily return of an asset. This paper introduces a new architecture for this task: On the output side, we predict dynamical variables such as first derivatives and curvatures on different time spans. These are subsequently combined in an interaction output layer to form several estimates of the variable of interest. Those estimates are then averaged to yield the final prediction. Independently from this idea, on the input side, we propose a new internal preprocessing layer connected with a diagonal matrix of positive weights to a layer of squashing functions. These weights adapt for each input individually and learn to squash outliers in the input. We apply these two ideas to the real world example of the daily predictions of the German stock index DAX (Deutscher Aktien Index), and compare the results to a network with a single output. The new six layer architecture is more stable in training due to two facts: (1) More information is flowing back from the outputs to the input in the backward pass; (2) The constraint of predicting first and second derivatives focuses the learning on the relevant variables for the dynamics. The architectures are compared from both the training perspective (squared errors, robust errors), and from the trading perspective (annualized returns, percent correct, Sharpe ratio). 
`.
Question: Which category should Paper #1132505 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].


Paper #1132505 has the title `TO IMPROVE FORECASTING  
` and the abstract `Working Paper IS-97-007, Leonard N. Stern School of Business, New York University. In: Journal of Computational Intelligence in Finance 6 (1998) 14-23. (Special Issue on "Improving Generalization of Nonlinear Financial Forecasting Models".) http://www.stern.nyu.edu/~aweigend/Research/Papers/InteractionLayer Abstract. Predictive models for financial data are often based on a large number of plausible inputs that are potentially nonlinearly combined to yield the conditional expectation of a target, such as a daily return of an asset. This paper introduces a new architecture for this task: On the output side, we predict dynamical variables such as first derivatives and curvatures on different time spans. These are subsequently combined in an interaction output layer to form several estimates of the variable of interest. Those estimates are then averaged to yield the final prediction. Independently from this idea, on the input side, we propose a new internal preprocessing layer connected with a diagonal matrix of positive weights to a layer of squashing functions. These weights adapt for each input individually and learn to squash outliers in the input. We apply these two ideas to the real world example of the daily predictions of the German stock index DAX (Deutscher Aktien Index), and compare the results to a network with a single output. The new six layer architecture is more stable in training due to two facts: (1) More information is flowing back from the outputs to the input in the backward pass; (2) The constraint of predicting first and second derivatives focuses the learning on the relevant variables for the dynamics. The architectures are compared from both the training perspective (squared errors, robust errors), and from the trading perspective (annualized returns, percent correct, Sharpe ratio). 
`.
Question: Which category should Paper #1132505 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].

This paper should be classified into: Neural_Networks