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Journal articles on the topic 'Conditional sum'

Author: Grafiati

Published: 4 June 2021

Last updated: 12 February 2022

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1

Nagar, Daya K., Edwin Zarrazola, and Alejandro Roldán-Correa. "Conditionally Specified Bivariate Kummer-Gamma Distribution." WSEAS TRANSACTIONS ON MATHEMATICS 20 (April 29, 2021): 196–206. http://dx.doi.org/10.37394/23206.2021.20.21.

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The Kummer-gamma distribution is an extension of gamma distribution and for certain values of parameters slides to a bimodal distribution. In this article, we introduce a bivariate distribution with Kummer-gamma conditionals and call it the conditionally specified bivariate Kummer-gamma distribution/bivariate Kummer-gamma conditionals distribution. Various representations are derived for its product moments, marginal densities, marginal moments, conditional densities, and conditional moments. We also discuss several important properties including, entropies, distributions of sum, and quotient. Most of these representations involve special functions such as the Gauss and the confluent hypergeometric functions. The bivariate Kummer-gamma conditionals distribution studied in this article may serve as an alternative to many existing bivariate models with support on (0, ∞) × (0, ∞).

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2

Bae, Taehan, and Ian Iscoe. "Sum of Bernoulli Mixtures: Beyond Conditional Independence." Journal of Probability and Statistics 2014 (2014): 1–14. http://dx.doi.org/10.1155/2014/838625.

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We consider the distribution of the sum of Bernoulli mixtures under a general dependence structure. The level of dependence is measured in terms of a limiting conditional correlation between two of the Bernoulli random variables. The conditioning event is that the mixing random variable is larger than a threshold and the limit is with respect to the threshold tending to one. The large-sample distribution of the empirical frequency and its use in approximating the risk measures, value at risk and conditional tail expectation, are presented for a new class of models which we calldouble mixtures. Several illustrative examples with a Beta mixing distribution, are given. As well, some data from the area of credit risk are fit with the models, and comparisons are made between the new models and also the classical Beta-binomial model.

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3

Klein, Thierry, Agnés Lagnoux, and Pierre Petit. "A conditional Berry–Esseen inequality." Journal of Applied Probability 56, no. 01 (March 2019): 76–90. http://dx.doi.org/10.1017/jpr.2019.7.

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AbstractAs an extension of a central limit theorem established by Svante Janson, we prove a Berry–Esseen inequality for a sum of independent and identically distributed random variables conditioned by a sum of independent and identically distributed integer-valued random variables.

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4

Janson, Svante. "Moment convergence in conditional limit theorems." Journal of Applied Probability 38, no. 2 (June 2001): 421–37. http://dx.doi.org/10.1239/jap/996986753.

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Consider a sum ∑1NYi of random variables conditioned on a given value of the sum ∑1NXi of some other variables, where Xi and Yi are dependent but the pairs (Xi,Yi) form an i.i.d. sequence. We consider here the case when each Xi is discrete. We prove, for a triangular array ((Xni,Yni)) of such pairs satisfying certain conditions, both convergence of the distribution of the conditioned sum (after suitable normalization) to a normal distribution, and convergence of its moments. The results are motivated by an application to hashing with linear probing; we give also some other applications to occupancy problems, random forests, and branching processes.

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Janson, Svante. "Moment convergence in conditional limit theorems." Journal of Applied Probability 38, no. 02 (June 2001): 421–37. http://dx.doi.org/10.1017/s002190020001994x.

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Consider a sum ∑1 N Y i of random variables conditioned on a given value of the sum ∑1 N X i of some other variables, where X i and Y i are dependent but the pairs (X i ,Y i ) form an i.i.d. sequence. We consider here the case when each X i is discrete. We prove, for a triangular array ((X ni ,Y ni )) of such pairs satisfying certain conditions, both convergence of the distribution of the conditioned sum (after suitable normalization) to a normal distribution, and convergence of its moments. The results are motivated by an application to hashing with linear probing; we give also some other applications to occupancy problems, random forests, and branching processes.

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6

Arrenberg, Jutta. "Natural ranks in the conditional Wilcoxon rank sum test." Computational Statistics & Data Analysis 17, no. 2 (February 1994): 141–52. http://dx.doi.org/10.1016/0167-9473(92)00067-2.

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7

Zabell, S. L. "A limit theorem for expectations conditional on a sum." Journal of Theoretical Probability 6, no. 2 (April 1993): 267–83. http://dx.doi.org/10.1007/bf01047574.

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8

Cho, Keol, and Ki-Seok Chung. "Conditional termination check min-sum algorithm for efficient LDPC decoders." IEICE Electronics Express 12, no. 24 (2015): 20150738. http://dx.doi.org/10.1587/elex.12.20150738.

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9

Koenker, Roger, and Kevin F. Hallock. "Quantile Regression." Journal of Economic Perspectives 15, no. 4 (November 1, 2001): 143–56. http://dx.doi.org/10.1257/jep.15.4.143.

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Quantile regression, as introduced by Koenker and Bassett (1978), may be viewed as an extension of classical least squares estimation of conditional mean models to the estimation of an ensemble of models for several conditional quantile functions. The central special case is the median regression estimator which minimizes a sum of absolute errors. Other conditional quantile functions are estimated by minimizing an asymmetrically weighted sum of absolute errors. Quantile regression methods are illustrated with applications to models for CEO pay, food expenditure, and infant birthweight.

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10

Stanghellini, Elena, and Marco Doretti. "On marginal and conditional parameters in logistic regression models." Biometrika 106, no. 3 (May 13, 2019): 732–39. http://dx.doi.org/10.1093/biomet/asz019.

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Summary We derive the exact formula linking the parameters of marginal and conditional logistic regression models with binary mediators when no conditional independence assumptions can be made. The formula has the appealing property of being the sum of terms that vanish whenever parameters of the conditional models vanish, thereby recovering well-known results as particular cases. It also permits the disentangling of direct and indirect effects as well as quantifying the distortion induced by the omission of relevant covariates, opening the way to sensitivity analysis. As the parameters of the conditional models are multiplied by terms that are always bounded, the derivations may also be used to construct reasonable bounds on the parameters of interest when relevant intermediate variables are unobserved. We assume that, conditionally on a set of covariates, the data-generating process can be represented by a directed acyclic graph. We also show how the results presented here lead to the extension of path analysis to a system of binary random variables.

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11

Asimit, Alexandru V., and Yiqing Chen. "Asymptotic results for conditional measures of association of a random sum." Insurance: Mathematics and Economics 60 (January 2015): 11–18. http://dx.doi.org/10.1016/j.insmatheco.2014.10.012.

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12

Berdinazarov, Zafar, Khasanjon Dodoev, Jamshid Mamasalaev, and Jakhongirmirzo Fakhodjonov. "Determinants of Exchange Rate Fluctuations of Uzbek Sum." Business and Management Studies 5, no. 1 (March 20, 2019): 52. http://dx.doi.org/10.11114/bms.v5i1.4162.

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This paper examines the determinants of exchange rate fluctuations of Uzbek sum by using three econometric models OLS (Ordinary Least Squares), ARIMA (Autoregressive Integrated Moving Average) and ML ARCH (Multivariate Long memory Autoregressive Conditional Heteroskadasticity). Model results show that the effects of money supply and remittances to the nominal and real exchange rates (USD/UZS) are found statistically significant; the impacts of inflation and interest rate are not econometrically meaningful. Also, it should be noted that the level of net trade influences to the exchange rate is not conclusive in our econometric analysis.

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13

Mukherjee, Atin, and Anindya Sundar Dhar. "Real-time fault-tolerance with hot-standby topology for conditional sum adder." Microelectronics Reliability 55, no. 3-4 (February 2015): 704–12. http://dx.doi.org/10.1016/j.microrel.2014.12.011.

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14

Keefe, Matthew J., Marco A. R. Ferreira, and Christopher T. Franck. "On the formal specification of sum-zero constrained intrinsic conditional autoregressive models." Spatial Statistics 24 (April 2018): 54–65. http://dx.doi.org/10.1016/j.spasta.2018.03.007.

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15

Rothermel, A., B. J. Hosticka, G. Troster, and J. Arndt. "Realization of transmission-gate conditional-sum (TGCS) adders with low latency time." IEEE Journal of Solid-State Circuits 24, no. 3 (June 1989): 558–61. http://dx.doi.org/10.1109/4.32007.

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16

Klüppelberg, Claudia, and Miriam Isabel Seifert. "Explicit results on conditional distributions of generalized exponential mixtures." Journal of Applied Probability 57, no. 3 (September 2020): 760–74. http://dx.doi.org/10.1017/jpr.2020.26.

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AbstractFor independent exponentially distributed random variables $X_i$ , $i\in {\mathcal{N}}$ , with distinct rates ${\lambda}_i$ we consider sums $\sum_{i\in\mathcal{A}} X_i$ for $\mathcal{A}\subseteq {\mathcal{N}}$ which follow generalized exponential mixture distributions. We provide novel explicit results on the conditional distribution of the total sum $\sum_{i\in {\mathcal{N}}}X_i$ given that a subset sum $\sum_{j\in \mathcal{A}}X_j$ exceeds a certain threshold value $t>0$ , and vice versa. Moreover, we investigate the characteristic tail behavior of these conditional distributions for $t\to\infty$ . Finally, we illustrate how our probabilistic results can be applied in practice by providing examples from both reliability theory and risk management.

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17

Quine, M. P. "Remainder term estimates in a conditional central limit theorem for integer-valued random variables." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 39, no. 1 (August 1985): 75–85. http://dx.doi.org/10.1017/s1446788700022187.

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AbstractA Berry-Esseen type result is given for the conditional distribution of a weighted sum of i.i.d. integer-valued r.v.'s given that their unweighted sum equals its expectation. The examples include the case of sampling without replacement from a finite population.

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18

Fristedt, Bert, and Donald A. Berry. "Optimality of myopic stopping times for geometric discounting." Journal of Applied Probability 25, no. 2 (June 1988): 437–43. http://dx.doi.org/10.2307/3214454.

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Consider a sequence of conditionally independent Bernoulli random variables taking on the values 1 and − 1. The objective is to stop the sequence in order to maximize the discounted sum. Suppose the Bernoulli parameter has a beta distribution with integral parameters. It is optimal to stop when the conditional expectation of the next random variable is negative provided the discount factor is less than or equal to . Moreover, is best possible. The case where the parameters of the beta distribution are arbitrary positive numbers is also treated.

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19

Fristedt, Bert, and Donald A. Berry. "Optimality of myopic stopping times for geometric discounting." Journal of Applied Probability 25, no. 02 (June 1988): 437–43. http://dx.doi.org/10.1017/s0021900200041103.

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Consider a sequence of conditionally independent Bernoulli random variables taking on the values 1 and − 1. The objective is to stop the sequence in order to maximize the discounted sum. Suppose the Bernoulli parameter has a beta distribution with integral parameters. It is optimal to stop when the conditional expectation of the next random variable is negative provided the discount factor is less than or equal to . Moreover, is best possible. The case where the parameters of the beta distribution are arbitrary positive numbers is also treated.

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20

Sugimoto, S., Y. Kubo, and N. Munetomo. "A Quasi-Linear Filter with Conditional Gaussian Sum Distributions for Nonlinear Dynamical Systems." IFAC Proceedings Volumes 44, no. 1 (January 2011): 7797–802. http://dx.doi.org/10.3182/20110828-6-it-1002.01911.

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21

Armendáriz, Inés, and Michail Loulakis. "Conditional distribution of heavy tailed random variables on large deviations of their sum." Stochastic Processes and their Applications 121, no. 5 (May 2011): 1138–47. http://dx.doi.org/10.1016/j.spa.2011.01.011.

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22

Lo, Hao‐Yung. "An implementation of the conditional‐sum scheme embedded in a signed digital adder." Journal of the Chinese Institute of Engineers 19, no. 5 (July 1996): 633–43. http://dx.doi.org/10.1080/02533839.1996.9677827.

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23

DI NOLA, ANTONIO, and ROMANO SCOZZAFAVA. "PARTIAL ALGEBRAIC CONDITIONAL SPACES." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 12, no. 06 (December 2004): 781–89. http://dx.doi.org/10.1142/s021848850400320x.

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Conditioning plays a central role, both from a theoretical and practical point of view, in domains such as logic and probability, or rule–based expert systems. In classical approaches to probability, there is the notion of "conditional probability" P(E|H), but usually there is no meaning given to E|H itself. In 1935 de Finetti 5 was the first to mention "conditional events" outside the function P. We shall refer to a concept of conditional event extensively discussed in 4, where the idea of de Finetti of looking at E|H, with H≠∅ (the impossible event), as a three–valued logical entity (true when both E and H are true, false when H is true and E is false, "undetermined" when H is false) is generalized (or better, in a sense, is given up) by letting the third "value" t(E, H)suitably depend on the given ordered pair(E, H) and not being just an undetermined common value for all pairs. Here an axiomatic definition is given of Partial Algebraic Conditional Spaces (PACS), that is a set of conditional events endowed with two partial operations (denoted by ⊕ and ⊙): we then show that the structure discussed through a betting scheme in 4 (i.e., a class of particular random variables with suitable partial sum and product) is a "natural" model of a PCAS. Moreover, it turns out that the map t(E, H) can be looked on – with this choice of the two operations ⊕ and ⊙ – as a conditional probability (in its most general sense related to the concept of coherence) satisfying the classic de Finetti – Popper axioms.

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24

Nielsen, Morten Ørregaard. "Asymptotics for the Conditional-Sum-of-Squares Estimator in Multivariate Fractional Time-Series Models." Journal of Time Series Analysis 36, no. 2 (November 28, 2014): 154–88. http://dx.doi.org/10.1111/jtsa.12100.

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25

Chung, Ching-Fan, and Richard T. Baillie. "Small sample bias in conditional sum-of-squares estimators of fractionally integrated ARMA models." Empirical Economics 18, no. 4 (December 1993): 791–806. http://dx.doi.org/10.1007/bf01205422.

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26

Tabak, Esteban G., and Giulio Trigila. "Conditional expectation estimation through attributable components." Information and Inference: A Journal of the IMA 7, no. 4 (March 15, 2018): 727–54. http://dx.doi.org/10.1093/imaiai/iax023.

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Abstract A general methodology is proposed for the explanation of variability in a quantity of interest x in terms of covariates z = (z1, …, zL). It provides the conditional mean $\bar{x}(z)$ as a sum of components, where each component is represented as a product of non-parametric one-dimensional functions of each covariate zl that are computed through an alternating projection procedure. Both x and the zl can be real or categorical variables; in addition, some or all values of each zl can be unknown, providing a general framework for multi-clustering, classification and covariate imputation in the presence of confounding factors. The procedure can be considered as a preconditioning step for the more general determination of the full conditional distribution $\boldsymbol{\rho}(x|z) $ through a data-driven optimal-transport barycenter problem. In particular, just iterating the procedure once yields the second order structure (i.e. the covariance) of $\boldsymbol{\rho}(x|z) $. The methodology is illustrated through examples that include the explanation of variability of ground temperature across the continental United States and the prediction of book preference among potential readers.

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27

Desarbo, Wayne S., Venkatram Ramaswamy, and Rabikar Chatterjee. "Analyzing Constant-Sum Multiple Criterion Data: A Segment-level Approach." Journal of Marketing Research 32, no. 2 (May 1995): 222–32. http://dx.doi.org/10.1177/002224379503200209.

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The authors propose a methodology for determining the segment-level impact of explanatory variables on multiple criterion measures obtained on a constant-sum scale. These explanatory variables could characterize different product, situation, or person related conditions that either occur naturally or are experimentally manipulated. Their proposed methodology simultaneously estimates market segment membership and multivariate segment-level parameters for each dependent criterion, using finite mixtures of conditional Dirichlet distributions. They conduct a modest Monte Carlo simulation analysis to investigate the performance of the proposed methodology. The authors also provide an empirical application to industrial buying decisions that examines the impact of the type of buying situation on multiple vendor selection criteria such as economic cost, functional performance, vendor cooperation, and vendor capability.

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28

Cressie, Noel, and Subhash Lele. "New models for Markov random fields." Journal of Applied Probability 29, no. 4 (December 1992): 877–84. http://dx.doi.org/10.2307/3214720.

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The Hammersley–Clifford theorem gives the form that the joint probability density (or mass) function of a Markov random field must take. Its exponent must be a sum of functions of variables, where each function in the summand involves only those variables whose sites form a clique. From a statistical modeling point of view, it is important to establish the converse result, namely, to give the conditional probability specifications that yield a Markov random field. Besag (1974) addressed this question by developing a one-parameter exponential family of conditional probability models. In this article, we develop new models for Markov random fields by establishing sufficient conditions for the conditional probability specifications to yield a Markov random field.

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29

Cressie, Noel, and Subhash Lele. "New models for Markov random fields." Journal of Applied Probability 29, no. 04 (December 1992): 877–84. http://dx.doi.org/10.1017/s0021900200043758.

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The Hammersley–Clifford theorem gives the form that the joint probability density (or mass) function of a Markov random field must take. Its exponent must be a sum of functions of variables, where each function in the summand involves only those variables whose sites form a clique. From a statistical modeling point of view, it is important to establish the converse result, namely, to give the conditional probability specifications that yield a Markov random field. Besag (1974) addressed this question by developing a one-parameter exponential family of conditional probability models. In this article, we develop new models for Markov random fields by establishing sufficient conditions for the conditional probability specifications to yield a Markov random field.

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30

Johansen, Søren, and Morten Ørregaard Nielsen. "THE ROLE OF INITIAL VALUES IN CONDITIONAL SUM-OF-SQUARES ESTIMATION OF NONSTATIONARY FRACTIONAL TIME SERIES MODELS." Econometric Theory 32, no. 5 (May 11, 2015): 1095–139. http://dx.doi.org/10.1017/s0266466615000110.

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In this paper, we analyze the influence of observed and unobserved initial values on the bias of the conditional maximum likelihood or conditional sum-of-squares (CSS, or least squares) estimator of the fractional parameter,d, in a nonstationary fractional time series model. The CSS estimator is popular in empirical work due, at least in part, to its simplicity and its feasibility, even in very complicated nonstationary models.We consider a process,Xt, for which data exist from some point in time, which we call –N0+ 1, but we only start observing it at a later time,t= 1. The parameter (d,μ,σ2) is estimated by CSS based on the model${\rm{\Delta }}_0^d \left( {X_t - \mu } \right) = \varepsilon _t ,t = N + 1, \ldots ,N + T$, conditional onX1,...,XN. We derive an expression for the second-order bias of$\hat d$as a function of the initial values,Xt,t= –N0+ 1,...,N, and we investigate the effect on the bias of setting aside the firstNobservations as initial values. We compare$\hat d$with an estimator,$\hat d_c $, derived similarly but by choosingμ=C. We find, both theoretically and using a data set on voting behavior, that in many cases, the estimation of the parameterμpicks up the effect of the initial values even for the choiceN= 0.IfN0= 0, we show that the second-order bias can be completely eliminated by a simple bias correction. If, on the other hand,N0> 0, it can only be partly eliminated because the second-order bias term due to the initial values can only be diminished by increasingN.

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31

Brüdern, Jörg. "On Waring's problem for cubes and biquadrates. II." Mathematical Proceedings of the Cambridge Philosophical Society 104, no. 2 (September 1988): 199–206. http://dx.doi.org/10.1017/s0305004100065385.

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In discussing the consequences of a conditional estimate for the sixth moment of cubic Weyl sums, Hooley [4] established asymptotic formulae for the number ν(n) of representations of n as the sum of a square and five cubes, and for ν(n), defined similarly with six cubes and two biquadrates. The condition here is the truth of the Riemann Hypothesis for a certain Hasse–Weil L-function. Recently Vaughan [8] has shown unconditionally , a lower bound of the size suggested by the conditional asymptotic formula. In the corresponding problem for ν(n) the author [1] was able to deduce ν(n) > 0, as a by-product of the result that almost all numbers can be expressed as the sum of three cubes and one biquadrate. As promised in the first paper of this series we return to the problem of bounding ν(n) from below.

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32

Suzuki, Yuta. "A remark on the conditional estimate for the sum of a prime and a square." Functiones et Approximatio Commentarii Mathematici 57, no. 1 (September 2017): 61–76. http://dx.doi.org/10.7169/facm/1616.

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33

Broström, Göran, and Leif Nilsson. "Acceptance–Rejection Sampling from the Conditional Distribution of Independent Discrete Random Variables, given their Sum." Statistics 34, no. 3 (January 2000): 247–57. http://dx.doi.org/10.1080/02331880008802716.

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34

Becker, Bernd, and Reiner Kolla. "On the Construction of Optimal Time Adders." Fundamenta Informaticae 12, no. 2 (April 1, 1989): 205–20. http://dx.doi.org/10.3233/fi-1989-12207.

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In this paper we present the design of a novel optimal time adder: the conditional carry adder. In order to perform addition a tree-like combination of multiplexer cells is used in the carry computation part. We show that, for the complete conditional carry adder, this results in an overall computation time which seems to be substantially shorter than for any other known (optimal time) adder (e.g. carry look ahead adders ([5]) or conditional sum adders ([12])). The second part of this paper contains a uniform approach to the computation of the carry function resulting in seven different classes of optimal time adders. It is shown that the conditional carry adder and the carry look ahead adder are representatives of two different classes. While section 1 defines the conditional carry adder and proposes a realization which is very time efficient, section 2 provides the possibility to compare this choice with other possible realizations and to choose a different design depending e.g. on specific properties of a given technology.

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35

Friederichs, P., and A. Hense. "Statistical Downscaling of Extreme Precipitation Events Using Censored Quantile Regression." Monthly Weather Review 135, no. 6 (June 1, 2007): 2365–78. http://dx.doi.org/10.1175/mwr3403.1.

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Abstract A statistical downscaling approach for extremes using censored quantile regression is presented. Conditional quantiles of station data (e.g., daily precipitation sums) in Germany are estimated by means of the large-scale circulation as represented by the NCEP reanalysis data. It is shown that a mixed discrete–continuous response variable, such as a daily precipitation sum, can be statistically modeled by a censored variable. Furthermore, a conditional quantile skill score is formulated to assess the relative gain of a quantile forecast compared with a reference forecast. Just like multiple regression for expectation values, quantile regression provides a tool to formulate a model output statistics system for extremal quantiles.

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36

Francis, Charles. "The Hilbert space of conditional clauses." International Journal of Quantum Information 13, no. 03 (April 2015): 1550026. http://dx.doi.org/10.1142/s0219749915500264.

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In the absence of a satisfactory interpretation of quantum theory, physical law lacks physical basis. This paper reviews the orthodox, or Dirac–von Neumann interpretation, and makes explicit that Hilbert space describes propositions about measurement results. Kets are defined as conditional clauses referring to measurements in a formal language. It is seen that these clauses are elements of a Hilbert space, such that addition is logical disjunction, the dual space consists of consequent clauses, and the inner product is a set of statements in the subjunctive mood. The probability interpretation gives truth values for corresponding future tense statements when the initial state is actually prepared and the final state is to be measured. The mathematical structure of quantum mechanics is formulated in terms of discrete measurement results at finite level of accuracy and does not depend on an assumption of a substantive, or background, space–time continuum. A continuum of kets, ∣x〉 for x ∈ ℝ3, is constructed from linear combinations of kets in a finite basis. The inner product can be expressed either as a finite sum or as an integral. Discrete position functions are uniquely embedded into smooth wave functions in such a way that differential operators are defined. It is shown that the choice of basis has no effect on underlying physics (quantum covariance). The Dirac delta has a representation as a smooth function. Operators do not in general have an integral form. The Schrödinger equation is shown from the requirements of the probability interpretation. It is remarked that a formal construction of quantum electrodynamics (qed) avoiding divergence problems has been completed using finite dimensional Hilbert space. I conclude that quantum mechanics makes statements about the world with clear physical meaning, such that space is emergent from particle interactions and has no fundamental role.

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37

Smith, Noah A., and Mark Johnson. "Weighted and Probabilistic Context-Free Grammars Are Equally Expressive." Computational Linguistics 33, no. 4 (December 2007): 477–91. http://dx.doi.org/10.1162/coli.2007.33.4.477.

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This article studies the relationship between weighted context-free grammars (WCFGs), where each production is associated with a positive real-valued weight, and probabilistic context-free grammars (PCFGs), where the weights of the productions associated with a nonterminal are constrained to sum to one. Because the class of WCFGs properly includes the PCFGs, one might expect that WCFGs can describe distributions that PCFGs cannot. However, Z. Chi (1999, Computational Linguistics, 25(1):131–160) and S. P. Abney, D. A. McAllester, and P. Pereira (1999, In Proceedings of the 37th Annual Meeting of the Association for Computational Linguistics, pages 542–549, College Park, MD) proved that every WCFG distribution is equivalent to some PCFG distribution. We extend their results to conditional distributions, and show that every WCFG conditional distribution of parses given strings is also the conditional distribution defined by some PCFG, even when the WCFG's partition function diverges. This shows that any parsing or labeling accuracy improvement from conditional estimation of WCFGs or conditional random fields (CRFs) over joint estimation of PCFGs or hidden Markov models (HMMs) is due to the estimation procedure rather than the change in model class, because PCFGs and HMMs are exactly as expressive as WCFGs and chain-structured CRFs, respectively.

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38

Hu, Mengxiao, Jinlong Li, Maolin Hu, and Tao Hu. "Hierarchical Modes Exploring in Generative Adversarial Networks." Proceedings of the AAAI Conference on Artificial Intelligence 34, no. 07 (April 3, 2020): 10981–88. http://dx.doi.org/10.1609/aaai.v34i07.6732.

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In conditional Generative Adversarial Networks (cGANs), when two different initial noises are concatenated with the same conditional information, the distance between their outputs is relatively smaller, which makes minor modes likely to collapse into large modes. To prevent this happen, we proposed a hierarchical mode exploring method to alleviate mode collapse in cGANs by introducing a diversity measurement into the objective function as the regularization term. We also introduced the Expected Ratios of Expansion (ERE) into the regularization term, by minimizing the sum of differences between the real change of distance and ERE, we can control the diversity of generated images w.r.t specific-level features. We validated the proposed algorithm on four conditional image synthesis tasks including categorical generation, paired and un-paired image translation and text-to-image generation. Both qualitative and quantitative results show that the proposed method is effective in alleviating the mode collapse problem in cGANs, and can control the diversity of output images w.r.t specific-level features.

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Lee, Sangyeol, Chang Kyeom Kim, and Sangjo Lee. "Hybrid CUSUM Change Point Test for Time Series with Time-Varying Volatilities Based on Support Vector Regression." Entropy 22, no. 5 (May 20, 2020): 578. http://dx.doi.org/10.3390/e22050578.

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This study considers the problem of detecting a change in the conditional variance of time series with time-varying volatilities based on the cumulative sum (CUSUM) of squares test using the residuals from support vector regression (SVR)-generalized autoregressive conditional heteroscedastic (GARCH) models. To compute the residuals, we first fit SVR-GARCH models with different tuning parameters utilizing a time series of training set. We then obtain the best SVR-GARCH model with the optimal tuning parameters via a time series of the validation set. Subsequently, based on the selected model, we obtain the residuals, as well as the estimates of the conditional volatility and employ these to construct the residual CUSUM of squares test. We conduct Monte Carlo simulation experiments to illustrate its validity with various linear and nonlinear GARCH models. A real data analysis with the S&P 500 index, Korea Composite Stock Price Index (KOSPI), and Korean won/U.S. dollar (KRW/USD) exchange rate datasets is provided to exhibit its scope of application.

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Revenko, V. P. "Method of finite bodies for determination of the plane stressed state of rectangular plates with a rectangular hole." Bulletin of Taras Shevchenko National University of Kyiv. Series: Physics and Mathematics, no. 1 (2019): 170–73. http://dx.doi.org/10.17721/1812-5409.2019/1.39.

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The paper is devoted to the determination of the stress-deformed state of structurally heterogeneous bearing rectangular plates with a rectangular hole. The new analytical-numerical method (finite bodies) was used, to find the stress state of the plate with a hole. The method of finite bodies uses the conditional partition of the doubly-connected surface of the plate into simpler connected rectangular parts. On the lines of conditional contact, the conditions of ideal contact are taken into account, which ensure the equality of stresses, deformations and displacements. The perturbed stressed state, which is presented in the form of a series of functions, which is rapidly intercepted at a distance from the outline of the hole, is considered. A finite sum of solutions of a plane problem is used and the stress state of a perturbed state is given as a sum of a series for nonorthogonal functions. The components of vector of displacements and stresses are written. The determination of the coefficients of the sum of a series is based on the proposed method of satisfying all boundary conditions and the conditions of ideal contact to find the minimum of a generalized quadratic form. The numerical criterion for the convergence of the method is theoretically established. It is shown that the accuracy of satisfaction of boundary conditions and conditions of ideal contact is estimated by one number – the minimum of a generalized quadratic form.

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Hualde, Javier, and Morten Ørregaard Nielsen. "TRUNCATED SUM OF SQUARES ESTIMATION OF FRACTIONAL TIME SERIES MODELS WITH DETERMINISTIC TRENDS." Econometric Theory 36, no. 4 (July 1, 2019): 751–72. http://dx.doi.org/10.1017/s0266466619000161.

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We consider truncated (or conditional) sum of squares estimation of a parametric model composed of a fractional time series and an additive generalized polynomial trend. Both the memory parameter, which characterizes the behavior of the stochastic component of the model, and the exponent parameter, which drives the shape of the deterministic component, are considered not only unknown real numbers but also lying in arbitrarily large (but finite) intervals. Thus, our model captures different forms of nonstationarity and noninvertibility. As in related settings, the proof of consistency (which is a prerequisite for proving asymptotic normality) is challenging due to nonuniform convergence of the objective function over a large admissible parameter space, but, in addition, our framework is substantially more involved due to the competition between stochastic and deterministic components. We establish consistency and asymptotic normality under quite general circumstances, finding that results differ crucially depending on the relative strength of the deterministic and stochastic components. Finite-sample properties are illustrated by means of a Monte Carlo experiment.

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Ross, Sheldon M., and Kyle Y. Lin. "APPLYING VARIANCE REDUCTION IDEAS IN QUEUING SIMULATIONS." Probability in the Engineering and Informational Sciences 15, no. 4 (October 2001): 481–94. http://dx.doi.org/10.1017/s0269964801154045.

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Variance reduction techniques are often underused in simulation studies. In this article, we indicate how certain ones can be efficiently employed when analyzing queuing models. The first technique considered is that of dynamic stratified sampling; the second is the utilization of multiple control variates; the third concerns the replacement of random variables by their conditional expectations when trying to estimate the expected value of a sum of random variables.

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Coffey, Mark W. "On certain sums over the non-trivial zeta zeroes." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 466, no. 2124 (June 2, 2010): 3679–92. http://dx.doi.org/10.1098/rspa.2010.0064.

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We study coefficients b n , expressible as sums over the Li/Keiper constants λ j , that contain information on the Riemann xi function. We present a number of relations for and representations of b n . These include the expression of b n as a sum over non-trivial zeroes of the Riemann zeta function, as well as integral representations. Conditional on the Riemann hypothesis, we provide the asymptotic form of .

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Zhang, N. L., and D. Poole. "Exploiting Causal Independence in Bayesian Network Inference." Journal of Artificial Intelligence Research 5 (December 1, 1996): 301–28. http://dx.doi.org/10.1613/jair.305.

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A new method is proposed for exploiting causal independencies in exact Bayesian network inference. A Bayesian network can be viewed as representing a factorization of a joint probability into the multiplication of a set of conditional probabilities. We present a notion of causal independence that enables one to further factorize the conditional probabilities into a combination of even smaller factors and consequently obtain a finer-grain factorization of the joint probability. The new formulation of causal independence lets us specify the conditional probability of a variable given its parents in terms of an associative and commutative operator, such as ``or'', ``sum'' or ``max'', on the contribution of each parent. We start with a simple algorithm VE for Bayesian network inference that, given evidence and a query variable, uses the factorization to find the posterior distribution of the query. We show how this algorithm can be extended to exploit causal independence. Empirical studies, based on the CPCS networks for medical diagnosis, show that this method is more efficient than previous methods and allows for inference in larger networks than previous algorithms.

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Ramirez-Silva, Ivonne, Juan A. Rivera, Belem Trejo-Valdivia, Aryeh D. Stein, Reynaldo Martorell, Isabelle Romieu, Albino Barraza-Villarreal, Laura Avila-Jiménez, and Usha Ramakrishnan. "Relative Weight Gain Through Age 4 Years Is Associated with Increased Adiposity, and Higher Blood Pressure and Insulinemia at 4–5 Years of Age in Mexican Children." Journal of Nutrition 148, no. 7 (June 19, 2018): 1135–43. http://dx.doi.org/10.1093/jn/nxy068.

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AbstractBackgroundRapid early weight gain has been associated with increased risk of obesity and cardiometabolic alterations, but evidence in low and middle-income countries is inconclusive.ObjectiveWe evaluated the relation between relative weight gain from 1 to 48 mo with adiposity and cardiometabolic risk factors at 4–5 y of age, and determined if adiposity is a mediator for cardiometabolic alterations.MethodsWe studied 428 Mexican children with anthropometric and blood pressure (BP) information from birth to 5 y of age from POSGRAD (Prenatal Omega-3 fatty acid Supplementation and child GRowth And Development), of whom 334 provided measures of adiposity and cardiometabolic risk markers at 4 y. We estimated relative weight gain by means of conditional weight-for-height z scores for the age intervals 1–6, 6–12, 12–24, and 24–48 mo. Associations between relative weight gain and adiposity and cardiometabolic risk markers (lipid profile, triglycerides, insulin, glucose, and BP) were analyzed by multivariate multiple linear models and path analysis.ResultsA 1-unit increase in conditional weight-for-height z score within each age interval was positively associated with adiposity at 5 y, with coefficients of 0.43–0.89 for body mass index (BMI) z score, 1.08–3.65 mm for sum of skinfolds, and 1.21–3.87 cm for abdominal circumference (all P < 0.01). Positive associations were documented from ages 6 to 48 mo with systolic BP (coefficient ranges: 1.19–1.78 mm Hg; all P < 0.05) and from ages 12 to 48 mo with diastolic BP (1.28–0.94 mm Hg; P < 0.05) at 5 y. Conditional weight-for-height z scores at 12–24 and 24–48 mo of age were more strongly associated with adiposity and BP relative to younger ages. A unit increase in conditional weight-for-height z scores from 12 to 24 mo was associated with 14% higher insulin levels (P < 0.05) at 4 y. Path analyses documented that the associations of conditional weight gain with BP were mediated by BMI and sum of skinfolds.ConclusionRelative weight gain at most periods during the first 4 y of life was associated with greater adiposity and higher systolic and diastolic BP at 5 y. These associations with BP were mediated by adiposity. Relative weight gain from 12 to 24 mo was associated with increased serum insulin concentrations at 4 y, but there were no associations with lipid profiles or glucose concentration.

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Zhu, Hong, Yujian Pan, Weiwei Wu, Ning Tai, and Naichang Yuan. "Effects of Compound K-Distributed Sea Clutter on Angle Measurement of Wideband Monopulse Radar." Mathematical Problems in Engineering 2017 (2017): 1–19. http://dx.doi.org/10.1155/2017/2081718.

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The effects of compound K-distributed sea clutter on angle measurement of wideband monopulse radar are investigated in this paper. We apply the conditional probability density function (pdf) of monopulse ratio (MR) error to analyze these effects. Based on the angle measurement procedure of the wideband monopulse radar, this conditional pdf is first deduced in detail for the case of compound K-distributed sea clutter plus noise. Herein, the spatial correlation of the texture components for each channel clutter and the correlation of the texture components between the sum and difference channel clutters are considered, and two extreme situations for each of them are tackled. Referring to the measured sea clutter data, angle measurement performances in various K-distributed sea clutter plus noise circumstances are simulated, and the effects of compound K-distributed sea clutter on angle measurement are discussed.

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Longla, Martial, Costel Peligrad, and Magda Peligrad. "On the Functional Central Limit Theorem for Reversible Markov Chains with Nonlinear Growth of the Variance." Journal of Applied Probability 49, no. 04 (December 2012): 1091–105. http://dx.doi.org/10.1017/s0021900200012894.

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In this paper we study the functional central limit theorem (CLT) for stationary Markov chains with a self-adjoint operator and general state space. We investigate the case when the variance of the partial sum is not asymptotically linear in n, and establish that conditional convergence in distribution of partial sums implies the functional CLT. The main tools are maximal inequalities that are further exploited to derive conditions for tightness and convergence to the Brownian motion.

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Hasebe, Takahiro, and Hayato Saigo. "On operator-valued monotone independence." Nagoya Mathematical Journal 215 (September 2014): 151–67. http://dx.doi.org/10.1017/s002776300001093x.

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AbstractWe investigate operator-valued monotone independence, a noncommutative version of independence for conditional expectation. First we introduce operator-valued monotone cumulants to clarify the whole theory and show the moment-cumulant formula. As an application, one can obtain an easy proof of the central limit theorem for the operator-valued case. Moreover, we prove a generalization of Muraki’s formula for the sum of independent random variables and a relation between generating functions of moments and cumulants.

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Hasebe, Takahiro, and Hayato Saigo. "On operator-valued monotone independence." Nagoya Mathematical Journal 215 (September 2014): 151–67. http://dx.doi.org/10.1215/00277630-2741151.

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AbstractWe investigate operator-valued monotone independence, a noncommutative version of independence for conditional expectation. First we introduce operator-valued monotone cumulants to clarify the whole theory and show the moment-cumulant formula. As an application, one can obtain an easy proof of the central limit theorem for the operator-valued case. Moreover, we prove a generalization of Muraki’s formula for the sum of independent random variables and a relation between generating functions of moments and cumulants.

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50

Longla, Martial, Costel Peligrad, and Magda Peligrad. "On the Functional Central Limit Theorem for Reversible Markov Chains with Nonlinear Growth of the Variance." Journal of Applied Probability 49, no. 4 (December 2012): 1091–105. http://dx.doi.org/10.1239/jap/1354716659.

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In this paper we study the functional central limit theorem (CLT) for stationary Markov chains with a self-adjoint operator and general state space. We investigate the case when the variance of the partial sum is not asymptotically linear in n, and establish that conditional convergence in distribution of partial sums implies the functional CLT. The main tools are maximal inequalities that are further exploited to derive conditions for tightness and convergence to the Brownian motion.

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