scholarly journals Robust Forecast Evaluation of Expected Shortfall*

2019 ◽  
Vol 18 (1) ◽  
pp. 95-120 ◽  
Author(s):  
Johanna F Ziegel ◽  
Fabian Krüger ◽  
Alexander Jordan ◽  
Fernando Fasciati
Keyword(s):  
Value At Risk ◽  
Hypothesis Test ◽  
Scoring Function ◽  
Large Family ◽  
Expected Shortfall ◽  
Basel Iii ◽  
Scoring Functions ◽  
Forecast Method ◽  
Forecast Performance ◽  
Relevant Class

Abstract Motivated by the Basel III regulations, recent studies have considered joint forecasts of Value-at-Risk and Expected Shortfall. A large family of scoring functions can be used to evaluate forecast performance in this context. However, little intuitive or empirical guidance is currently available, which renders the choice of scoring function awkward in practice. We therefore develop graphical checks of whether one forecast method dominates another under a relevant class of scoring functions, and propose an associated hypothesis test. We illustrate these tools with simulation examples and an empirical analysis of S&P 500 and DAX returns.

scholarly journals Preferences Single-Peaked on a Tree: Multiwinner Elections and Structural Results

2022 ◽  
Vol 73 ◽  
pp. 231-276
Author(s):  
Dominik Peters ◽  
Lan Yu ◽  
Hau Chan ◽  
Edith Elkind
Keyword(s):  
Polynomial Time ◽  
Scoring Function ◽  
Large Family ◽  
Np Hard ◽  
Scoring Functions ◽  
Winner Determination ◽  
Polynomial Time Algorithms ◽  
Minimum Number ◽  
Number Of Leaves ◽  
Positive Results

A preference profile is single-peaked on a tree if the candidate set can be equipped with a tree structure so that the preferences of each voter are decreasing from their top candidate along all paths in the tree. This notion was introduced by Demange (1982), and subsequently Trick (1989b) described an efficient algorithm for deciding if a given profile is single-peaked on a tree. We study the complexity of multiwinner elections under several variants of the Chamberlin–Courant rule for preferences single-peaked on trees. We show that in this setting the egalitarian version of this rule admits a polynomial-time winner determination algorithm. For the utilitarian version, we prove that winner determination remains NP-hard for the Borda scoring function; indeed, this hardness results extends to a large family of scoring functions. However, a winning committee can be found in polynomial time if either the number of leaves or the number of internal vertices of the underlying tree is bounded by a constant. To benefit from these positive results, we need a procedure that can determine whether a given profile is single-peaked on a tree that has additional desirable properties (such as, e.g., a small number of leaves). To address this challenge, we develop a structural approach that enables us to compactly represent all trees with respect to which a given profile is single-peaked. We show how to use this representation to efficiently find the best tree for a given profile for use with our winner determination algorithms: Given a profile, we can efficiently find a tree with the minimum number of leaves, or a tree with the minimum number of internal vertices among trees on which the profile is single-peaked. We then explore the power and limitations of this framework: we develop polynomial-time algorithms to find trees with the smallest maximum degree, diameter, or pathwidth, but show that it is NP-hard to check whether a given profile is single-peaked on a tree that is isomorphic to a given tree, or on a regular tree.

Random Forest Refinement of Pairwise Potentials for Protein-ligand Decoy Detection

2019 ◽  
Author(s):  
Jun Pei ◽  
Zheng Zheng ◽  
Hyunji Kim ◽  
Lin Song ◽  
Sarah Walworth ◽  
...  
Keyword(s):  
Machine Learning ◽  
Random Forest ◽  
Probability Function ◽  
Pair Potential ◽  
Scoring Function ◽  
Stable Structure ◽  
Scoring Functions ◽  
Atom Pair ◽  
Data Set ◽  
Atom Pairs

An accurate scoring function is expected to correctly select the most stable structure from a set of pose candidates. One can hypothesize that a scoring function’s ability to identify the most stable structure might be improved by emphasizing the most relevant atom pairwise interactions. However, it is hard to evaluate the relevant importance for each atom pair using traditional means. With the introduction of machine learning methods, it has become possible to determine the relative importance for each atom pair present in a scoring function. In this work, we use the Random Forest (RF) method to refine a pair potential developed by our laboratory (GARF6) by identifying relevant atom pairs that optimize the performance of the potential on our given task. Our goal is to construct a machine learning (ML) model that can accurately differentiate the native ligand binding pose from candidate poses using a potential refined by RF optimization. We successfully constructed RF models on an unbalanced data set with the ‘comparison’ concept and, the resultant RF models were tested on CASF-2013.5 In a comparison of the performance of our RF models against 29 scoring functions, we found our models outperformed the other scoring functions in predicting the native pose. In addition, we used two artificial designed potential models to address the importance of the GARF potential in the RF models: (1) a scrambled probability function set, which was obtained by mixing up atom pairs and probability functions in GARF, and (2) a uniform probability function set, which share the same peak positions with GARF but have fixed peak heights. The results of accuracy comparison from RF models based on the scrambled, uniform, and original GARF potential clearly showed that the peak positions in the GARF potential are important while the well depths are not. <br>

scholarly journals ASFP (Artificial Intelligence based Scoring Function Platform): a web server for the development of customized scoring functions

2021 ◽  
Vol 13 (1) ◽  
Author(s):  
Xujun Zhang ◽  
Chao Shen ◽  
Xueying Guo ◽  
Zhe Wang ◽  
Gaoqi Weng ◽  
...  
Keyword(s):  
High Efficiency ◽  
Low Cost ◽  
Pearson Correlation ◽  
Scoring Function ◽  
Web Server ◽  
Scoring Functions ◽  
Protein Ligand Interactions ◽  
Prediction Module ◽  
Ligand Interactions ◽  
Benchmark Datasets

AbstractVirtual screening (VS) based on molecular docking has emerged as one of the mainstream technologies of drug discovery due to its low cost and high efficiency. However, the scoring functions (SFs) implemented in most docking programs are not always accurate enough and how to improve their prediction accuracy is still a big challenge. Here, we propose an integrated platform called ASFP, a web server for the development of customized SFs for structure-based VS. There are three main modules in ASFP: (1) the descriptor generation module that can generate up to 3437 descriptors for the modelling of protein–ligand interactions; (2) the AI-based SF construction module that can establish target-specific SFs based on the pre-generated descriptors through three machine learning (ML) techniques; (3) the online prediction module that provides some well-constructed target-specific SFs for VS and an additional generic SF for binding affinity prediction. Our methodology has been validated on several benchmark datasets. The target-specific SFs can achieve an average ROC AUC of 0.973 towards 32 targets and the generic SF can achieve the Pearson correlation coefficient of 0.81 on the PDBbind version 2016 core set. To sum up, the ASFP server is a powerful tool for structure-based VS.

scholarly journals Optimisation of Time-Varying Asset Pricing Models with Penetration of Value at Risk and Expected Shortfall

Mathematics ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 394
Author(s):  
Adeel Nasir ◽  
Kanwal Iqbal Khan ◽  
Mário Nuno Mata ◽  
Pedro Neves Mata ◽  
Jéssica Nunes Martins
Keyword(s):  
At Risk ◽  
Asset Pricing ◽  
Stock Returns ◽  
Value At Risk ◽  
Expected Shortfall ◽  
Time Varying ◽  
Pricing Models ◽  
Asset Pricing Model ◽  
Asset Pricing Models ◽  
Market Beta

This study aims to apply value at risk (VaR) and expected shortfall (ES) as time-varying systematic and idiosyncratic risk factors to address the downside risk anomaly of various asset pricing models currently existing in the Pakistan stock exchange. The study analyses the significance of high minus low VaR and ES portfolios as a systematic risk factor in one factor, three-factor, and five-factor asset pricing model. Furthermore, the study introduced the six-factor model, deploying VaR and ES as the idiosyncratic risk factor. The theoretical and empirical alteration of traditional asset pricing models is the study’s contributions. This study reported a strong positive relationship of traditional market beta, value at risk, and expected shortfall. Market beta pertains its superiority in estimating the time-varying stock returns. Furthermore, value at risk and expected shortfall strengthen the effects of traditional beta impact on stock returns, signifying the proposed six-factor asset pricing model. Investment and profitability factors are redundant in conventional asset pricing models.

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