An obvious way to speed up the process of discovering association rules is to generate them from a small sample of the database rather than the database itself. The primary challenge in developing sampling-based algorithms stems from the fact that the support of an itemset in a sample almost always deviates from the support in the entire database. We present FAST (Finding Associations from Samp...

The problem of controlling the capacity of decision trees is considered for the case where the decision nodes implement linear threshold functions. In addition to the standard early stopping and pruning procedures, we implement a strategy based on the margins of the decision boundaries at the nodes. The approach is motivated by bounds on generalization error obtained in terms of the margins of ...

In this work we study numerical construction of optimal clinical diagnostic tests for detecting sporadic Creutzfeldt-Jakob disease (sCJD). A cerebrospinal fluid sample (CSF) from a suspected sCJD patient is subjected to a process which initiates the aggregation of a protein present only in cases of sCJD. This aggregation is indirectly observed in real-time at regular intervals, so that a longit...

This paper is concerned with solving Cauchy problem for parabolic equation by minimizing an energy-like error functional and by taking into account noisy Cauchy data. After giving some fundamental results, numerical convergence analysis of the energy-like minimization method is carried out and leads to an adapted stopping criterion depending on noise rate for the minimization process. Numerical...

We study tltt' problem of when to stop If'arning a class of feedforward networks networks with linear outputs I1PUrOIl and fixed input weights when they are trained with a gradient descent algorithm on a finite number of examples. Under general regularity conditions, it is shown that there a.re in general three distinct phases in the generalization performance in the learning process, and in pa...

In blind detection, a set of candidates has to be decoded within a strict time constraint, to identify which transmissions are directed at the user equipment. Blind detection is required by the 3GPP LTE/LTE-Advanced standard, and it will be required in the 5th generation wireless communication standard (5G) as well. Polar codes have been selected for use in 5G: thus, the issue of blind detectio...

The restoration problem deals with images in which information has been destroyed or obscured. In this paper, we present a framework for addressing image restoration problems in which the goal is to recover information about the image. Restoration algorithms often use tentative assumptions to compensate for the information lost in the degradation process. We propose cross-validation as a method...

We formulate and solve a problem that combines the features of the so-called monotone follower of singular stochastic control theory with optimal stopping. In particular, we consider a stochastic system whose uncontrolled state dynamics are modelled by a general one-dimensional Itô diffusion. The aim of the problem that we solve is to maximise the utility derived from the system’s state at the ...

Many materials processes and properties depend on the anisotropy of energy grain boundaries, i.e. fact that this is a function five geometric degrees freedom (DOF) interface. To access parameter space in an efficient way to discover cusps unexplored regions, method was recently established, which combines atomistic simulations with statistical methods (kroll et al., 2022). This sequential sampl...