scholarly journals Calculating CVaR and bPOE for common probability distributions with application to portfolio optimization and density estimation

2019 ◽  
Author(s):  
Matthew Norton ◽  
Valentyn Khokhlov ◽  
Stan Uryasev
Keyword(s):  
Portfolio Optimization ◽  
Density Estimation ◽  
Probability Distributions ◽  
Common Probability

Field-theoretic density estimation for biological sequence space with applications to 5′ splice site diversity and aneuploidy in cancer

2021 ◽  
Vol 118 (40) ◽  
pp. e2025782118
Author(s):  
Wei-Chia Chen ◽  
Juannan Zhou ◽  
Jason M. Sheltzer ◽  
Justin B. Kinney ◽  
David M. McCandlish
Keyword(s):  
Probability Distribution ◽  
Maximum Entropy ◽  
Density Estimation ◽  
Sequence Space ◽  
Chromosomal Abnormalities ◽  
Fundamental Problem ◽  
Probability Distributions ◽  
Biological Sequence ◽  
Point Estimates ◽  
Site Diversity

Density estimation in sequence space is a fundamental problem in machine learning that is also of great importance in computational biology. Due to the discrete nature and large dimensionality of sequence space, how best to estimate such probability distributions from a sample of observed sequences remains unclear. One common strategy for addressing this problem is to estimate the probability distribution using maximum entropy (i.e., calculating point estimates for some set of correlations based on the observed sequences and predicting the probability distribution that is as uniform as possible while still matching these point estimates). Building on recent advances in Bayesian field-theoretic density estimation, we present a generalization of this maximum entropy approach that provides greater expressivity in regions of sequence space where data are plentiful while still maintaining a conservative maximum entropy character in regions of sequence space where data are sparse or absent. In particular, we define a family of priors for probability distributions over sequence space with a single hyperparameter that controls the expected magnitude of higher-order correlations. This family of priors then results in a corresponding one-dimensional family of maximum a posteriori estimates that interpolate smoothly between the maximum entropy estimate and the observed sample frequencies. To demonstrate the power of this method, we use it to explore the high-dimensional geometry of the distribution of 5′ splice sites found in the human genome and to understand patterns of chromosomal abnormalities across human cancers.

Tables of Common Probability Distributions

1970 ◽  
Author(s):  
Peter W. Zehna ◽  
Donald R. Barr
Keyword(s):  
Probability Distributions ◽  
Common Probability

Non-parametric Bayesian density estimation for biological sequence space with applications to pre-mRNA splicing and the karyotypic diversity of human cancer

2020 ◽  
Author(s):  
Wei-Chia Chen ◽  
Juannan Zhou ◽  
Jason M Sheltzer ◽  
Justin B Kinney ◽  
David M McCandlish
Keyword(s):  
Probability Distribution ◽  
Maximum Entropy ◽  
Density Estimation ◽  
Cancer Progression ◽  
Sequence Space ◽  
Chromosomal Abnormalities ◽  
Fundamental Problem ◽  
Human Cancer ◽  
Probability Distributions ◽  
Point Estimates

AbstractDensity estimation in sequence space is a fundamental problem in machine learning that is of great importance in computational biology. Due to the discrete nature and large dimensionality of sequence space, how best to estimate such probability distributions from a sample of observed sequences remains unclear. One common strategy for addressing this problem is to estimate the probability distribution using maximum entropy, i.e. calculating point estimates for some set of correlations based on the observed sequences and predicting the probability distribution that is as uniform as possible while still matching these point estimates. Building on recent advances in Bayesian field-theoretic density estimation, we present a generalization of this maximum entropy approach that provides greater expressivity in regions of sequence space where data is plentiful while still maintaining a conservative maximum entropy char-acter in regions of sequence space where data is sparse or absent. In particular, we define a family of priors for probability distributions over sequence space with a single hyper-parameter that controls the expected magnitude of higher-order correlations. This family of priors then results in a corresponding one-dimensional family of maximum a posteriori estimates that interpolate smoothly between the maximum entropy estimate and the observed sample frequencies. To demonstrate the power of this method, we use it to explore the high-dimensional geometry of the distribution of 5′ splice sites found in the human genome and to understand the accumulation of chromosomal abnormalities during cancer progression.

Nonparametric frequency polygon estimation for modeling input data

2019 ◽  
Author(s):  
Stephen Hague ◽  
Simaan AbouRizk
Keyword(s):  
Density Estimation ◽  
Kernel Density Estimation ◽  
Posterior Distribution ◽  
Input Data ◽  
Probability Distributions ◽  
Kernel Density ◽  
Simulation Environment ◽  
Frequency Polygon ◽  
Density Estimators

To construct valid probability distributions solely from input data, this paper compares three nonparametric density estimators: (1) histograms, (2) Kernel Density Estimation, and (3) Frequency Polygon Estimation. A pseudocode is implemented, a practical example is illustrated, and the Simphony.NET simulation environment is used to fit the nonparametric frequency polygon to a set of data to recreate it as a posterior distribution via the Metropolis-Hastings algorithm.

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