In this article, we strengthen the proof methods of some previously weakly consistent variants of random forests into strongly consistent proof methods, and improve the data utilization of these variants, in order to obtain better theoretical properties and experimental performance. In addition, based on the multinomial random forest (MRF) and Bernoulli random forest (BRF), we propose a data-driven multinomial random forest (DMRF) algorithm, which has lower complexity than MRF and higher complexity than BRF while satisfying strong consistency. It has better performance in classification and regression problems than previous RF variants that only satisfy weak consistency, and in most cases even surpasses standard random forest. To the best of our knowledge, DMRF is currently the most excellent strongly consistent RF variant with low algorithm complexity.

Regression trees are one of the oldest forms of AI models, and their predictions can be made without a calculator, which makes them broadly useful, particularly for high-stakes applications. Within the large literature on regression trees, there has been little effort towards full provable optimization, mainly due to the computational hardness of the problem. This work proposes a dynamic-programming-with-bounds approach to the construction of provably-optimal sparse regression trees. We leverage a novel lower bound based on an optimal solution to the k-Means clustering algorithm in 1-dimension over the set of labels. We are often able to find optimal sparse trees in seconds, even for challenging datasets that involve large numbers of samples and highly-correlated features.

Crops are constantly challenged by different environmental conditions. Seed treatment by nanomaterials is a cost-effective and environmentally-friendly solution for environmental stress mitigation in crop plants. Here, 56 seed nanopriming treatments are used to alleviate environmental stresses in maize. Seven selected nanopriming treatments significantly increase the stress resistance index (SRI) by 13.9% and 12.6% under salinity stress and combined heat-drought stress, respectively. Metabolomics data reveals that ZnO nanopriming treatment, with the highest SRI value, mainly regulates the pathways of amino acid metabolism, secondary metabolite synthesis, carbohydrate metabolism, and translation. Understanding the mechanism of seed nanopriming is still difficult due to the variety of nanomaterials and the complexity of interactions between nanomaterials and plants. Using the nanopriming data, we present an interpretable structure-activity relationship (ISAR) approach based on interpretable machine learning for predicting and understanding its stress mitigation effects. The post hoc and model-based interpretation approaches of machine learning are combined to provide complementary benefits and give researchers or policymakers more illuminating or trustworthy results. The concentration, size, and zeta potential of nanoparticles are identified as dominant factors for correlating root dry weight under salinity stress, and their effects and interactions are explained. Additionally, a web-based interactive tool is developed for offering prediction-level interpretation and gathering more details about specific nanopriming treatments. This work offers a promising framework for accelerating the agricultural applications of nanomaterials and may profoundly contribute to nanosafety assessment.

In this paper, after some introductory remarks into the classification prob(cid:173) lem as considered in various research communities, and some discussions concerning some of the reasons for ascertaining the performances of the three chosen algorithms, viz., CART (Classification and Regression Tree), C4.5 (one of the more recent versions of a popular induction tree tech(cid:173) nique known as ID3), and a multi-layer perceptron (MLP), it is proposed to compare the performances of these algorithms under two criteria: classi(cid:173) fication and generalisation. It is found that, in general, the MLP has better classification and generalisation accuracies compared with the other two algorithms.

In this paper, we incorporate the Hierarchical Mixtures of Experts (HME) method of probability estimation, developed by Jordan [1], into an HMM(cid:173) based continuous speech recognition system. The resulting system can be thought of as a continuous-density HMM system, but instead of using gaussian mixtures, the HME system employs a large set of hierarchically organized but relatively small neural networks to perform the probability density estimation. The hierarchical structure is reminiscent of a decision tree except for two important differences: each "expert" or neural net performs a "soft" decision rather than a hard decision, and, unlike ordinary decision trees, the parameters of all the neural nets in the HME are automatically trainable using the EM algorithm. We report results on the ARPA 5,OOO-word and 4O,OOO-word Wall Street Journal corpus using HME models.

Conventional binary classification trees such as CART either split the data using axis-aligned hyperplanes or they perform a compu(cid:173) tationally expensive search in the continuous space of hyperplanes with unrestricted orientations. We show that the limitations of the former can be overcome without resorting to the latter. For every pair of training data-points, there is one hyperplane that is orthog(cid:173) onal to the line joining the data-points and bisects this line. Such hyperplanes are plausible candidates for splits. In a comparison on a suite of 12 datasets we found that this method of generating candidate splits outperformed the standard methods, particularly when the training sets were small.

We introduce a constructive, incremental learning system for regression problems that models data by means of locally linear experts. In contrast to other approaches, the experts are trained independently and do not compete for data during learning. Only when a prediction for a query is required do the experts cooperate by blending their individual predic(cid:173) tions. Each expert is trained by minimizing a penalized local cross vali(cid:173) dation error using second order methods. In this way, an expert is able to find a local distance metric by adjusting the size and shape of the recep(cid:173) tive field in which its predictions are valid, and also to detect relevant in(cid:173) put features by adjusting its bias on the importance of individual input dimensions.

Predictions oflifetimes of dynamically allocated objects can be used to improve time and space efficiency of dynamic memory manage(cid:173) ment in computer programs. Barrett and Zorn [1993] used a simple lifetime predictor and demonstrated this improvement on a variety of computer programs. In this paper, we use decision trees to do lifetime prediction on the same programs and show significantly better prediction . Our method also has the advantage that during training we can use a large number of features and let the decision tree automatically choose the relevant subset. Dynamic memory allocation is used in many computer applications.

We study a time series model that can be viewed as a decision tree with Markov temporal structure. The model is intractable for exact calculations, thus we utilize variational approximations. We consider three different distributions for the approximation: one in which the Markov calculations are performed exactly and the layers of the decision tree are decoupled, one in which the decision tree calculations are performed exactly and the time steps of the Markov chain are decoupled, and one in which a Viterbi-like assumption is made to pick out a single most likely state sequence.

An adaptive on-line algorithm is proposed to estimate hierarchical data structures for non-stationary data sources. The approach is based on the principle of minimum cross entropy to derive a decision tree for data clustering and it employs a metalearning idea (learning to learn) to adapt to changes in data characteristics. Its efficiency is demonstrated by grouping non-stationary artifical data and by hierarchical segmentation of LANDSAT images.