992 research outputs found
Similarity Measures and Dimensionality Reduction Techniques for Time Series Data Mining
The chapter is organized as follows. Section 2 will introduce the similarity matching
problem on time series. We will note the importance of the use of efficient data structures to
perform search, and the choice of an adequate distance measure. Section 3 will show some
of the most used distance measure for time series data mining. Section 4 will review the
above mentioned dimensionality reduction techniques
Comparing machine learning models to choose the variable ordering for cylindrical algebraic decomposition
There has been recent interest in the use of machine learning (ML) approaches
within mathematical software to make choices that impact on the computing
performance without affecting the mathematical correctness of the result. We
address the problem of selecting the variable ordering for cylindrical
algebraic decomposition (CAD), an important algorithm in Symbolic Computation.
Prior work to apply ML on this problem implemented a Support Vector Machine
(SVM) to select between three existing human-made heuristics, which did better
than anyone heuristic alone. The present work extends to have ML select the
variable ordering directly, and to try a wider variety of ML techniques.
We experimented with the NLSAT dataset and the Regular Chains Library CAD
function for Maple 2018. For each problem, the variable ordering leading to the
shortest computing time was selected as the target class for ML. Features were
generated from the polynomial input and used to train the following ML models:
k-nearest neighbours (KNN) classifier, multi-layer perceptron (MLP), decision
tree (DT) and SVM, as implemented in the Python scikit-learn package. We also
compared these with the two leading human constructed heuristics for the
problem: Brown's heuristic and sotd. On this dataset all of the ML approaches
outperformed the human made heuristics, some by a large margin.Comment: Accepted into CICM 201
A cumulant approach for the first-passage-time problem of the Feller square-root process
The paper focuses on an approximation of the first passage time probability
density function of a Feller stochastic process by using cumulants and a
Laguerre-Gamma polynomial approximation. The feasibility of the method relies
on closed form formulae for cumulants and moments recovered from the Laplace
transform of the probability density function and using the algebra of formal
power series. To improve the approximation, sufficient conditions on cumulants
are stated. The resulting procedure is made easier to implement by the symbolic
calculus and a rational choice of the polynomial degree depending on skewness,
kurtosis and hyperskewness. Some case-studies coming from neuronal and
financial fields show the goodness of the approximation even for a low number
of terms. Open problems are addressed at the end of the paper
Comparing solution methods for dynamic equilibrium economies
This paper compares solution methods for dynamic equilibrium economies. The authors compute and simulate the stochastic neoclassical growth model with leisure choice using Undetermined Coefficients in levels and in logs, Finite Elements, Chebyshev Polynomials, Second and Fifth Order Perturbations and Value Function Iteration for several calibrations. The authors document the performance of the methods in terms of computing time, implementation complexity and accuracy and they present some conclusions about their preferred approaches based on the reported evidence.
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