A novel piece-wise linear regression method has been proposed in this work.The method partitions samples into multiple regions from a single attribute.Each region is fitted with a linear regression function.An optimisation model is proposed to decide break-points and regression functions.Benchmark examples have been used to demonstrate its efficiency. In data mining, regression analysis is a computational tool that predicts continuous output variables from a number of independent input variables, by approximating their complex inner relationship. A large number of methods have been successfully proposed, based on various methodologies, including linear regression, support vector regression, neural network, piece-wise regression, etc. In terms of piece-wise regression, the existing methods in literature are usually restricted to problems of very small scale, due to their inherent non-linear nature. In this work, a more efficient piece-wise linear regression method is introduced based on a novel integer linear programming formulation. The proposed method partitions one input variable into multiple mutually exclusive segments, and fits one multivariate linear regression function per segment to minimise the total absolute error. Assuming both the single partition feature and the number of regions are known, the mixed integer linear model is proposed to simultaneously determine the locations of multiple break-points and regression coefficients for each segment. Furthermore, an efficient heuristic procedure is presented to identify the key partition feature and final number of break-points. 7 real world problems covering several application domains have been used to demonstrate the efficiency of our proposed method. It is shown that our proposed piece-wise regression method can be solved to global optimality for datasets of thousands samples, which also consistently achieves higher prediction accuracy than a number of state-of-the-art regression methods. Another advantage of the proposed method is that the learned model can be conveniently expressed as a small number of if-then rules that are easily interpretable. Overall, this work proposes an efficient rule-based multivariate regression method based on piece-wise functions and achieves better prediction performance than state-of-the-arts approaches. This novel method can benefit expert systems in various applications by automatically acquiring knowledge from databases to improve the quality of knowledge base.

This work proposes a novel tree model for multivariate regression analysis.Both node splitting and regression coefficients are optimised in this model.The proposed method achieves improved prediction accuracy than literature methods.The resultant trees are at least as simple as the ones from previous methods. Regression analysis is a machine learning approach that aims to accurately predict the value of continuous output variables from certain independent input variables, via automatic estimation of their latent relationship from data. Tree-based regression models are popular in literature due to their flexibility to model higher order non-linearity and great interpretability. Conventionally, regression tree models are trained in a two-stage procedure, i.e. recursive binary partitioning is employed to produce a tree structure, followed by a pruning process of removing insignificant leaves, with the possibility of assigning multivariate functions to terminal leaves to improve generalisation. This work introduces a novel methodology of node partitioning which, in a single optimisation model, simultaneously performs the two tasks of identifying the break-point of a binary split and assignment of multivariate functions to either leaf, thus leading to an efficient regression tree model. Using six real world benchmark problems, we demonstrate that the proposed method consistently outperforms a number of state-of-the-art regression tree models and methods based on other techniques, with an average improvement of 760% on the mean absolute errors (MAE) of the predictions.

High-frequency synaptic stimulation is thought to cause a rapid and lasting change in the expression of GluR2 subunit-containing AMPA receptors (AMPARs) at synapses in cerebellar stellate cells. We examined whether spontaneous synaptic activity affects the expression of GluR2-containing synaptic AMPARs and whether the change in AMPAR subtypes alters their Ca²⁺permeability and kinetic properties. We used intracellular spermine, which blocks GluR2-lacking receptors at depolarized potentials, to distinguish the presence of GluR2. In most cells, the spontaneous EPSC frequency was low, and evoked EPSCs displayed inwardly rectifyingI–Vrelationships, indicative of the presence of GluR2-lacking AMPARs. However, in cells that displayed a higher rate of spontaneous synaptic activity, EPSCs gave linearI–Vplots, suggesting the presence of GluR2-containingAMPARs. This is consistent with the idea that spontaneous synaptic activity increased the expression of GluR2-containing AMPARs at synapses. The Ca²⁺permeability of AMPARs that gave inwardly rectifying currents in outside-out patches from TTX-treated cells was six times higher than in control cells that gave linear or outwardly rectifyingI–Vplots. However, increased spontaneous synaptic activity did not significantly alter the EPSC decay time. Furthermore, the decay time course ofEPSCs mediated by GluR2-containing receptors was not different from that mediated by a mixed population of receptors at the same synapse. Our results suggest that the level of spontaneous synaptic activity can determine the subunit composition of postsynaptic receptors at this synapse. The activity-induced expression of GluR2-containing receptors significantly reduced the Ca²⁺permeability of AMPARs in stellate cells but did not slow the decay time course of synaptic currents.