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Model Parsimony and Overfitting
Published in Norman Matloff, Probability and Statistics for Data Science, 2019
Suppose we have just one predictor, and n data points. If we fit a polynomial model of degree n − 1, the resulting curve will pass through all n points, a “perfect” fit. For instance: > x <- rnorm(6) > y <- rnorm(6) # unrelated to x! > df <- data. frame(x, y) > df$x2 <- x ^ 2 > df$x3 <- x ^ 3 > df $x4 <- x ^ 4 > df$x5 <- x ^ 5 > df x y x2 x3 1 -0.9808202 0.9898205 0.9620082 -0.94355703 2 -0.5115071 0.5725953 0.2616395 -0.13383047 3 -0.6824555 -0.1354214 0.4657456 -0 .31785063 4 0.8113214 1.0621229 0.6582425 0.53404620 5 -0.7352366 0.1920320 0.5405728 -0.39744891 6 0.3600138 0.7356633 0.1296100 0.04666137 x4 x5 1 0.92545975 -0.907709584 2 0.06845524 -0.035015341 3 0.21691892 -0.148037517 4 0.43328312 0.351531881 5 0.29221897 -0.214850074 6 0.01679874 0.006047779 > lmo <- lm (y~., data = df) > lmo $fitted. values 1 2 3 4 0.9898205 0.5725953 -0.1354214 1.0621229 5 6 0. 1920320 0. 7356633 > df $y [1] 0.9898205 0.5725953 -0.1354214 1.0621229 [5] 0.1920320 0.7356633
Energy efficient optimal hop transmission using minimum power least cost algorithm in cooperative routing for wireless sensor network
Published in Automatika, 2023
Immanuvel Arokia James K., Manjula P., Guga Priya G., Karthikeyan A.
The relay channels usually do Amplify and Forward (AF) or Decode and Forward (DF) user cooperation [12]. By relay channel, consider that in addition to the source to relay and to the destination (PN → PA → PM) there may be a direct communication (PN → PM) from source to the destination node. In such cases, the transmission between the end to the endpoint, and the transmission in a single description. According to the distortion theorem and the steps of decoding, encoding protocol given in Equation (2). λr = Hr, where Hr is the number of channels used between the PN → PM. and Ch represents the channel. It may be a single relay or multiple relay distortion according to the distortion algorithm.
Performance analysis of multihop wireless systems with decode and forward relays over Fisher– Snedecor F fading channels
Published in International Journal of Electronics Letters, 2022
A multihop wireless system is examined for the number of hops, as depicted in Figure 1. Messages are transmitted from a source node employing regenerative as well as DF-type intervening nodes (relays) to the destination node or user . The half-duplex mode of communication is considered for the system. A node transmits signals only to a closer node at one-time slot, and thus total communication time is divided into time slots. The intermediary relays are positioned at an identical separation, and consequently, whole the -hops are at an equal span. The user receives the signals from the th relay. The instantaneous SNR of the th hop is represented by where . The channel of the th hop experiences flat Fisher–Snedecor F fading distribution. The PDF relating to instantaneous SNR concerning the Fisher–Snedecor F channel is formulated as Yoo et al. (2017)
Outage Trade-Offs Between Full/Half-Duplex Relaying for NOMA Aided Multicarrier Cooperative D2D Communications System
Published in IETE Technical Review, 2022
FD mode and NOMA are an integral part of the B5G cellular networks, and hence, the integration of both promising technologies will exhibit high throughput and spectral efficiency [10, 23–25]. In [26], authors proposed a hybrid FD/HD cooperative NOMA system wherein the near user works as a DF relay for a far user. Analytical results of ergodic sum rate and OP showed that FD NOMA outperforms the HD NOMA for the low SNR values. Additionally, the authors also discussed energy efficiencies for FD and HD relaying. However, the proposed model is limited to only two users within the cell. The proposed model has not been tested for the multiuser environment. Similarly, in [27], an FD D2D aided cooperative NOMA system comprising of one BS and two users is proposed. Here, the NOMA strong user (a user having better channel condition) operates as an FD relay to assist the NOMA weak user to improve the outage performance. The OP expressions are derived to evaluate the performance of proposed system model.