Yanhong Cui

Probabilistic DEAR models

The differential equation associated regression (DEAR) is a flexible and powerful data mining modeling approach, which is intended to catch up the first-order nonlinear trend (i.e., regularity) governing the behavior of the data under investigation. DEAR modeling is a formal mathematical–statistical representation of the so-called grey differential equation model. It should be pointed out that DEAR models were originally proposed on the random fuzzy theoretical foundation. Nevertheless, DEAR models can be defined on any measure theoretic platform, for example, probabilistic, fuzzy, or uncertain measure foundation as long as the model and approximation two constituting components are appropriately specified. In this paper, we re-examine the compositional elements of DEAR models and the potential model selection portfolio in the statistical machine learning (SML) algorithm developments. Then the differential equation backed DEAR may contribute to the SML algorithm significantly, particularly, in developing robot movement system, where the motion laws are expressed directly by a set of differential equations. Under a statistical decision theoretical framework, a DEAR model which is constituted by a random function with a linear difference equation-wise regression as the central tendency and a variance bound specified by Gaussian error analysis theory is developed delicately, in which the prior distribution will be facilitated by a Gaussian process such that the replication of sampling for estimating the weight matrix will be avoided. We not only address the model selection compositional elements of the SML algorithm but also address the optimization scheme, which is called λ-global optimization scheme to make the DEAR learning as one of the fastest, most efficient and accurate SML algorithm.

Imprecise Uncertainty Modelling of Air Pollutant PM10

Particulate matter (PM) refers to solid particles and liquid droplets found in air. Many manmade and natural sources produce PM directly, or produce pollutants that react in the atmosphere to form PM. The resultant solid and liquid particles come in a wide range of sizes, and particles that are 10 micrometers or less in diameter (PM

Climate Change Impact on Quiver Trees in Arid Namibia and South Africa

The climate fluctuates and changes naturally, and adding the common problems of land transformation and deforestation, its impact can be very harsh on the natural environment, and cause a decline in the biodiversity of plants and animals. Aloe dichotoma, common name Quiver tree, is an important part of the arid regions, such as Namaqualand and Bushmanland in South Africa, and in arid parts of southern Namibia. This succulent tree species occurs in rocky areas, and it can grow quite rapidly under the right conditions. Succulents are able to survive long periods of drought conditions, due to the fact succulent plants has special water-storing tissue which makes part of the plant fleshy, and the Quiver tree has succulent leaf and stem (Van Wyk and Smith, 1996). The Quiver tree has a 200 year life span, and can grow up to 9 meters tall, and it occurs in summer and winter rainfall regions, and can live under a variety of climatic conditions (Fig. 1). The Quiver tree is important to the ecosystem due to the fact that it is as a source of moisture for a wide variety of mammals, birds, and insects. Foden’s detailed study of the demographic data of the Quiver trees show that negligible recruitment has occurred in certain populations for 50 years, and the effects of non-climatic variables, such as herbivory, competition, seed availability, fungal pathogens, plant collection... are very small (Foden, 2002). Today, the Quiver trees are threatened by agricultural expansion, overgrazing, and mining, as well as droughts and other climate changes (Foden, 2002). Climate changes is one of the major factors affecting the existence of Quiver trees, while the Quiver tree will unlikely to be affected by small climatic fluctuations, but will be affected larger or long term climatic changes. The Quiver tree can potentially provide a good indication of long term climate changes in the arid regions (Foden, 2002). Previous onsite observations show that Quiver trees are very sensitive to temperature changes, and does not do well under extreme hot and dry conditions. Observations has also shown that the Quiver trees might be responding to higher temperatures by shifting its distribution range towards higher and higher altitudes, showing a preference for slightly cooler regions (Midgley et al., 2009).

An uncertain regression model

In this paper, we propose an uncertain regression model with an intrinsic error structure facilitated by uncertain canonical process. This model is suitable for dealing with experts knowledge ranging from small to medium size data of impreciseness. In order to have a rigorous mathematical treatments on the new regression model, we establish a series of new uncertainty concepts sequentially, such as uncertainty joint multivariate distribution, the uncertainty distribution of uncertainty product variables, and uncertain covariance and correlation based on the axiomatic uncertainty theoretical foundation. Finally, the uncertain regression model is formulated and the estimation of the model coefficients is developed. Two examples is given for illustrating a small data regression analysis.