12 research outputs found
A Central Limit Theorem for the Length of the Longest Common Subsequences in Random Words
Let and be two independent sequences of
independent identically distributed random variables taking their values in a
common finite alphabet and having the same law. Let be the length of the
longest common subsequences of the two random words and
. Under a lower bound assumption on the order of its variance,
is shown to satisfy a central limit theorem. This is in contrast to the
limiting distribution of the length of the longest common subsequences in two
independent uniform random permutations of , which is shown to
be the Tracy-Widom distribution.Comment: Some corrections, typos corrected and improvement
An overview of time series point and interval forecasting based on similarity of trajectories, with an experimental study on traffic flow forecasting
The purpose of this paper is to give an overview of the time series
forecasting problem based on similarity of trajectories. Various methodologies
are introduced and studied, and detailed discussions on hyperparameter
optimization, outlier handling and distance measures are provided. The
suggested new approaches involve variations in both the selection of similar
trajectories and assembling the candidate forecasts. After forming a general
framework, an experimental study is conducted to compare the methods that use
similar trajectories along with some other standard models (such as ARIMA and
Random Forest) from the literature. Lastly, the forecasting setting is extended
to interval forecasts, and the prediction intervals resulting from the similar
trajectories approach are compared with the existing models from the
literature, such as historical simulation and quantile regression. Throughout
the paper, the experimentations and comparisons are conducted via the time
series of traffic flow from the California PEMS dataset.Comment: 32 page
On unfair permutations
In this paper we study the inverse of so-called unfair permutations. Our investigation begins with comparing this class of permutations with uniformly random permutations, and showing that they behave very much alike in case of locally dependent random variables. As an example of a globally dependent statistic we use the number of inversions, and show that this statistic satisfies a central limit theorem after proper centering and scaling.Publisher's Versio
The variance and the asymptotic distribution of the length of longest k-alternating subsequences
We obtain an explicit formula for the variance of the number of k-peaks in a uniformly random permutation. This is then used to obtain an asymptotic formula for the variance of the length of longest k-alternating subsequence in random permutations. Also a central limit is proved for the latter statistic
Mixing time bounds for edge flipping on regular graphs
The edge flipping is a non-reversible Markov chain on a given connected
graph, which is defined by Chung and Graham in [CG12]. In the same paper, its
eigenvalues and stationary distributions for some classes of graphs are
identified. We further study its spectral properties to show a lower bound for
the rate of convergence in the case of regular graphs. Moreover, we show that a
cutoff occurs at \frac{1}{4} n \log n for the edge flipping on the complete
graph by a coupling argument.Comment: 16 pages. An error in the proof of Theorem 1.1 is corrected. The
section on vertex flipping is removed. Presentation is revised. Note the
change in the titl