The decision tree ensembles use a single data feature at each node for splitting the data. However, splitting in this manner may fail to capture the geometric properties of the data. Thus, oblique decision trees generate the oblique hyperplane for splitting the data at each non-leaf node. Oblique decision trees capture the geometric properties of the data and hence, show better generalization. The performance of the oblique decision trees depends on the way oblique hyperplanes are generate and the data used for the generation of those hyperplanes. Recently, multiple classifiers have been used in a heterogeneous random forest (RaF) classifier, however, it fails to generate the trees of proper depth. Moreover, double RaF studies highlighted that larger trees can be generated via bootstrapping the data at each non-leaf node and splitting the original data instead of the bootstrapped data recently. The study of heterogeneous RaF lacks the generation of larger trees while as the double RaF based model fails to take over the geometric characteristics of the data. To address these shortcomings, we propose heterogeneous oblique double RaF. The proposed model employs several linear classifiers at each non-leaf node on the bootstrapped data and splits the original data based on the optimal linear classifier. The optimal hyperplane corresponds to the models based on the optimized impurity criterion. The experimental analysis indicates that the performance of the introduced heterogeneous double random forest is comparatively better than the baseline models. To demonstrate the effectiveness of the proposed heterogeneous double random forest, we used it for the diagnosis of Schizophrenia disease. The proposed model predicted the disease more accurately compared to the baseline models.

Local variable selection has proven to be a powerful technique for ap(cid:173) proximating functions in high-dimensional spaces. It is used in several statistical methods, including CART, ID3, C4, MARS, and others (see the bibliography for references to these algorithms). In this paper I present a tree-structured network which is a generalization of these techniques. The network provides a framework for understanding the behavior of such algorithms and for modifying them to suit particular applications.

Networks for reconstructing a sparse or noisy function often use an edge field to segment the function into homogeneous regions, This approach assumes that these regions do not overlap or have disjoint parts, which is often false. For example, images which contain regions split by an occlud(cid:173) ing object can't be properly reconstructed using this type of network. We have developed a network that overcomes these limitations, using support maps to represent the segmentation of a signal. In our approach, the sup(cid:173) port of each region in the signal is explicitly represented. Results from an initial implementation demonstrate that this method can reconstruct images and motion sequences which contain complicated occlusion.

A three-step method for function approximation with a fuzzy sys(cid:173) tem is proposed. First, the membership functions and an initial rule representation are learned; second, the rules are compressed as much as possible using information theory; and finally, a com(cid:173) putational network is constructed to compute the function value. This system is applied to two control examples: learning the truck and trailer backer-upper control system, and learning a cruise con(cid:173) trol system for a radio-controlled model car.

Selecting a good model of a set of input points by cross validation is a computationally intensive process, especially if the number of possible models or the number of training points is high. Tech(cid:173) niques such as gradient descent are helpful in searching through the space of models, but problems such as local minima, and more importantly, lack of a distance metric between various models re(cid:173) duce the applicability of these search methods. Hoeffding Races is a technique for finding a good model for the data by quickly dis(cid:173) carding bad models, and concentrating the computational effort at differentiating between the better ones. This paper focuses on the special case of leave-one-out cross validation applied to memory(cid:173) based learning algorithms, but we also argue that it is applicable to any class of model selection problems.

In function approximation, example-based learning can be formulated as synthesiz(cid:173) ing an approximation function for data sampled from an unknown target function (Poggio and Girosi, 1990). Active learning describes a class of example-based learning paradigms that seeks out new training examples from specific regions of the input space, instead of passively accepting examples from some data generating source.

We present new results about the temporal-difference learning al(cid:173) gorithm, as applied to approximating the cost-to-go function of a Markov chain using linear function approximators. The algo(cid:173) rithm we analyze performs on-line updating of a parameter vector during a single endless trajectory of an aperiodic irreducible finite state Markov chain. Results include convergence (with probability 1), a characterization of the limit of convergence, and a bound on the resulting approximation error. In addition to establishing new and stronger results than those previously available, our analysis is based on a new line of reasoning that provides new intuition about the dynamics of temporal-difference learning. Furthermore, we discuss the implications of two counter-examples with regards to the Significance of on-line updating and linearly parameterized function approximators.

We present a computationally efficient algorithm for function ap(cid:173) proximation with piecewise linear sigmoidal nodes. A one hidden layer network is constructed one node at a time using the method of fitting the residual. The task of fitting individual nodes is accom(cid:173) plished using a new algorithm that searchs for the best fit by solving a sequence of Quadratic Programming problems. Unique characteristics of this algorithm include: finite step convergence, a simple stop(cid:173) ping criterion, a deterministic methodology for seeking "good" local minima, good scaling properties and a robust numerical implemen(cid:173) tation.

Function approximation is essential to reinforcement learning, but the standard approach of approximating a value function and deter(cid:173) mining a policy from it has so far proven theoretically intractable. In this paper we explore an alternative approach in which the policy is explicitly represented by its own function approximator, indepen(cid:173) dent of the value function, and is updated according to the gradient of expected reward with respect to the policy parameters. Williams's REINFORCE method and actor-critic methods are examples of this approach. Our main new result is to show that the gradient can be written in a form suitable for estimation from experience aided by an approximate action-value or advantage function. Using this result, we prove for the first time that a version of policy iteration with arbitrary differentiable function approximation is convergent to a locally optimal policy.

Many algorithms for approximate reinforcement learning are not known to converge. In fact, there are counterexamples showing that the adjustable weights in some algorithms may oscillate within a region rather than converging to a point. This paper shows that, for two popular algorithms, such oscillation is the worst that can happen: the weights cannot diverge, but instead must converge to a bounded region. The algorithms are SARSA(O) and V(O); the latter algorithm was used in the well-known TD-Gammon program.