This document summarizes an approach to automatic time-series forecasting using neural networks. It describes using a generalized regression neural network (GRNN) that combines three GRNN models with different spread factors. The paper claims this approach shows promising results by winning a time-series forecasting competition against 60 other models. However, the document raises some questions about whether the approach was truly better or just overfitted to that particular competition. It also questions some of the methodological choices.
This presentation contains information about Mann Whitney U test, what is it, when to use it and how to use it. I have also put an example so that it may help you to easily understand it.
Developing visual material can help to recall memory and also be a quick way to show lots of information. Visualization helps us remember (like when we try to picture where we’ve parked our car, and what's in our cupboards when writing a shopping list). We can create diagrams and visual aids depicting module materials and put them up around the house so that we are constantly reminded of our learning
Principal component analysis - application in financeIgor Hlivka
Principal component analysis is a useful multivariate times series method to examine and study the drivers of the changes in the entire dataset. The main advantage of PCA is the reduction of dimensionality where the large sets of data get transformed into few principal factors that explain majority of variability in that group. PCA has found many applications in finance – both in risk and yield curve analytics
This presentation contains information about Mann Whitney U test, what is it, when to use it and how to use it. I have also put an example so that it may help you to easily understand it.
Developing visual material can help to recall memory and also be a quick way to show lots of information. Visualization helps us remember (like when we try to picture where we’ve parked our car, and what's in our cupboards when writing a shopping list). We can create diagrams and visual aids depicting module materials and put them up around the house so that we are constantly reminded of our learning
Principal component analysis - application in financeIgor Hlivka
Principal component analysis is a useful multivariate times series method to examine and study the drivers of the changes in the entire dataset. The main advantage of PCA is the reduction of dimensionality where the large sets of data get transformed into few principal factors that explain majority of variability in that group. PCA has found many applications in finance – both in risk and yield curve analytics
It is rather surprising that in software engineering, standard measurement units have yet to be
widely accepted and used. Every other engineering discipline has their own. By and large, effort
is the most commonly used parameter for measuring software initiatives. The problem of
course is that effort is not an independent variable – it depends on who is doing the work and
how it is done. This presentation looks at an approach that has been used to convert the large
amount of effort data usually collected in an organization into something that can meaningfully
be used for estimation and comparison purposes.
Software of Time Series Forecasting based on Combinations of Fuzzy and Statis...ITIIIndustries
The developed software is a web application with open access and is aimed on forecasting of time series stored in database. We proposed approach of time series forecasting, combined ARIMA models with fuzzy techniques: three fuzzy time series models, fuzzy transformation (F-transform) and ACL-scale. Applications of a proposed web service have demonstrated efficiency in practical time series predictions with suitable accuracy.
The Mann Witney U Test in statistics is related to a testing without considering any assumption as to the parameters of frequently distributed of a valueless hypothesis. It is similar to the value selected randomly from one sample, can be higher than or lesser than a value selected randomly from a second sample. Copy the link given below and paste it in new browser window to get more information on Mann Whitney U Test:- http://www.transtutors.com/homework-help/statistics/mann-whitney-u-test.aspx
Principal Component Analysis and ClusteringUsha Vijay
Identifying the borrower segments from the give bank data set which has 27000 rows and 77 variable using PROC PRINCOMP. variables, it is important to reduce the data set to a smaller set of variables to derive a feasible
conclusion. With the effect of multicollinearity two or more variables can share the same plane in the in dimensions. Each row of the data can
be envisioned as a 77 dimensional graph and when we project the data as orthonormal, it is expected that the certain characteristics of the
data based on the plots to cluster together as principal components. In order to identify these principal components. PROC PRINCOMP is
executed with all the variables except the constant variables(recoveries and collection fees) and we derive a plot of Eigen values of all the
principal components
Brief introduction to graph based pattern recognition. It shows advantages and disantavantages of using graphs and how existing pattern recognition techniques are adapted to graph space.
Week 4 forecasting - time series - smoothing and decomposition - m.awaluddin.tMaling Senk
Forecasting - time series - smoothing and decomposition methods
Smoothing Method as Moving Averages and exponetial methods. The steps for decomposition methods and example of it. Case study for smothing methods in Single Exponential Smoothing, Double Exponential Smoothing and Triple Exponential Smoothing
The assignment problem is a special type of linear programming problem and it is sub class of transportation problem. Assignment problems are defined with two sets of inputs i.e. set of resources and set of demands. Hungarian algorithm is able to solve assignment problems with precisely defined demands and resources.Nowadays, many organizations and competition companies consider markets of their products. They use many salespersons to improve their organizations marketing. Salespersons travel form one city to another city for their markets. There are some problems in travelling which salespeople should go which city in minimum cost. So, travelling assignment problem is a main process for many business functions. Mie Mie Aung | Yin Yin Cho | Khin Htay | Khin Soe Myint "Minimization of Assignment Problems" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-3 | Issue-5 , August 2019, URL: https://www.ijtsrd.com/papers/ijtsrd26712.pdfPaper URL: https://www.ijtsrd.com/computer-science/other/26712/minimization-of-assignment-problems/mie-mie-aung
GRADIENT OMISSIVE DESCENT IS A MINIMIZATION ALGORITHMijscai
This article presents a promising new gradient-based backpropagation algorithm for multi-layer
feedforward networks. The method requires no manual selection of global hyperparameters and is capable
of dynamic local adaptations using only first-order information at a low computational cost. Its semistochastic nature makes it fit for mini-batch training and robust to different architecture choices and data
distributions. Experimental evidence shows that the proposed algorithm improves training in terms of both
convergence rate and speed as compared with other well known techniques.
Automatic algorithms for time series forecastingRob Hyndman
Many applications require a large number of time series to be forecast completely automatically. For example, manufacturing companies often require weekly forecasts of demand for thousands of products at dozens of locations in order to plan distribution and maintain suitable inventory stocks. In these circumstances, it is not feasible for time series models to be developed for each series by an experienced analyst. Instead, an automatic forecasting algorithm is required.
In addition to providing automatic forecasts when required, these algorithms also provide high quality benchmarks that can be used when developing more specific and specialized forecasting models.
I will describe some algorithms for automatically forecasting univariate time series that have been developed over the last 20 years. The role of forecasting competitions in comparing the forecast accuracy of these algorithms will also be discussed.
It is rather surprising that in software engineering, standard measurement units have yet to be
widely accepted and used. Every other engineering discipline has their own. By and large, effort
is the most commonly used parameter for measuring software initiatives. The problem of
course is that effort is not an independent variable – it depends on who is doing the work and
how it is done. This presentation looks at an approach that has been used to convert the large
amount of effort data usually collected in an organization into something that can meaningfully
be used for estimation and comparison purposes.
Software of Time Series Forecasting based on Combinations of Fuzzy and Statis...ITIIIndustries
The developed software is a web application with open access and is aimed on forecasting of time series stored in database. We proposed approach of time series forecasting, combined ARIMA models with fuzzy techniques: three fuzzy time series models, fuzzy transformation (F-transform) and ACL-scale. Applications of a proposed web service have demonstrated efficiency in practical time series predictions with suitable accuracy.
The Mann Witney U Test in statistics is related to a testing without considering any assumption as to the parameters of frequently distributed of a valueless hypothesis. It is similar to the value selected randomly from one sample, can be higher than or lesser than a value selected randomly from a second sample. Copy the link given below and paste it in new browser window to get more information on Mann Whitney U Test:- http://www.transtutors.com/homework-help/statistics/mann-whitney-u-test.aspx
Principal Component Analysis and ClusteringUsha Vijay
Identifying the borrower segments from the give bank data set which has 27000 rows and 77 variable using PROC PRINCOMP. variables, it is important to reduce the data set to a smaller set of variables to derive a feasible
conclusion. With the effect of multicollinearity two or more variables can share the same plane in the in dimensions. Each row of the data can
be envisioned as a 77 dimensional graph and when we project the data as orthonormal, it is expected that the certain characteristics of the
data based on the plots to cluster together as principal components. In order to identify these principal components. PROC PRINCOMP is
executed with all the variables except the constant variables(recoveries and collection fees) and we derive a plot of Eigen values of all the
principal components
Brief introduction to graph based pattern recognition. It shows advantages and disantavantages of using graphs and how existing pattern recognition techniques are adapted to graph space.
Week 4 forecasting - time series - smoothing and decomposition - m.awaluddin.tMaling Senk
Forecasting - time series - smoothing and decomposition methods
Smoothing Method as Moving Averages and exponetial methods. The steps for decomposition methods and example of it. Case study for smothing methods in Single Exponential Smoothing, Double Exponential Smoothing and Triple Exponential Smoothing
The assignment problem is a special type of linear programming problem and it is sub class of transportation problem. Assignment problems are defined with two sets of inputs i.e. set of resources and set of demands. Hungarian algorithm is able to solve assignment problems with precisely defined demands and resources.Nowadays, many organizations and competition companies consider markets of their products. They use many salespersons to improve their organizations marketing. Salespersons travel form one city to another city for their markets. There are some problems in travelling which salespeople should go which city in minimum cost. So, travelling assignment problem is a main process for many business functions. Mie Mie Aung | Yin Yin Cho | Khin Htay | Khin Soe Myint "Minimization of Assignment Problems" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-3 | Issue-5 , August 2019, URL: https://www.ijtsrd.com/papers/ijtsrd26712.pdfPaper URL: https://www.ijtsrd.com/computer-science/other/26712/minimization-of-assignment-problems/mie-mie-aung
GRADIENT OMISSIVE DESCENT IS A MINIMIZATION ALGORITHMijscai
This article presents a promising new gradient-based backpropagation algorithm for multi-layer
feedforward networks. The method requires no manual selection of global hyperparameters and is capable
of dynamic local adaptations using only first-order information at a low computational cost. Its semistochastic nature makes it fit for mini-batch training and robust to different architecture choices and data
distributions. Experimental evidence shows that the proposed algorithm improves training in terms of both
convergence rate and speed as compared with other well known techniques.
Automatic algorithms for time series forecastingRob Hyndman
Many applications require a large number of time series to be forecast completely automatically. For example, manufacturing companies often require weekly forecasts of demand for thousands of products at dozens of locations in order to plan distribution and maintain suitable inventory stocks. In these circumstances, it is not feasible for time series models to be developed for each series by an experienced analyst. Instead, an automatic forecasting algorithm is required.
In addition to providing automatic forecasts when required, these algorithms also provide high quality benchmarks that can be used when developing more specific and specialized forecasting models.
I will describe some algorithms for automatically forecasting univariate time series that have been developed over the last 20 years. The role of forecasting competitions in comparing the forecast accuracy of these algorithms will also be discussed.
This presentations includes the basic fundamentals of time series data forecasting. It starts with basic naive, regression models and then explains advanced ARIMA models.
Data Science - Part X - Time Series ForecastingDerek Kane
This lecture provides an overview of Time Series forecasting techniques and the process of creating effective forecasts. We will go through some of the popular statistical methods including time series decomposition, exponential smoothing, Holt-Winters, ARIMA, and GLM Models. These topics will be discussed in detail and we will go through the calibration and diagnostics effective time series models on a number of diverse datasets.
MULTI-OBJECTIVE ENERGY EFFICIENT OPTIMIZATION ALGORITHM FOR COVERAGE CONTROL ...ijcseit
Many studies have been done in the area of Wireless Sensor Networks (WSNs) in recent years. In this kind of networks, some of the key objectives that need to be satisfied are area coverage, number of active sensors and energy consumed by nodes. In this paper, we propose a NSGA-II based multi-objective algorithm for optimizing all of these objectives simultaneously. The efficiency of our algorithm is demonstrated in the simulation results. This efficiency can be shown as finding the optimal balance point among the maximum coverage rate, the least energy consumption, and the minimum number of active nodes while maintaining the connectivity of the network
A Mathematical Programming Approach for Selection of Variables in Cluster Ana...IJRES Journal
Data clustering is a common technique for statistical data analysis; it is defined as a class of
statistical techniques for classifying a set of observations into completely different groups. Cluster analysis
seeks to minimize group variance and maximize between group variance. In this study we formulate a
mathematical programming model that chooses the most important variables in cluster analysis. A nonlinear
binary model is suggested to select the most important variables in clustering a set of data. The idea of the
suggested model depends on clustering data by minimizing the distance between observations within groups.
Indicator variables are used to select the most important variables in the cluster analysis.
Covariance matrices are central to many adaptive filtering and optimisation problems. In practice, they have to be estimated from a finite number of samples; on this, I will review some known results from spectrum estimation and multiple-input multiple-output communications systems, and how properties that are assumed to be inherent in covariance and power spectral densities can easily be lost in the estimation process. I will discuss new results on space-time covariance estimation, and how the estimation from finite sample sets will impact on factorisations such as the eigenvalue decomposition, which is often key to solving the introductory optimisation problems. The purpose of the presentation is to give you some insight into estimating statistics as well as to provide a glimpse on classical signal processing challenges such as the separation of sources from a mixture of signals.
Abstract : Motivated by the recovery and prediction of electricity consumption time series, we extend Nonnegative Matrix Factorization to take into account external features as side information. We consider general linear measurement settings, and propose a framework which models non-linear relationships between external features and the response variable. We extend previous theoretical results to obtain a sufficient condition on the identifiability of NMF with side information. Based on the classical Hierarchical Alternating Least Squares (HALS) algorithm, we propose a new algorithm (HALSX, or Hierarchical Alternating Least Squares with eXogeneous variables) which estimates NMF in this setting. The algorithm is validated on both simulated and real electricity consumption datasets as well as a recommendation system dataset, to show its performance in matrix recovery and prediction for new rows and columns.
A Fast Multi-objective Evolutionary Approach for Designing Large-Scale Optica...Annibale Panichella
Spatial mode division de-multiplexing of optical signals has many real-world applications, such as quantum computing and both classical and quantum optical communication. In this context, it is crucial to develop devices able to efficiently sort optical signals according to the optical mode they belong to and route them on different paths. Depending on the mode selected, this problem can be very hard to tackle. Recently, researchers have proposed using multi-objective evolutionary algorithms (MOEAs) ---and NSGA-II in particular--- combined with Linkage Learning (LL) to automate the process of design mode sorter. However, given the very large-search scale of the problem, the existing evolutionary-based solutions have a very slow convergence rate. In this paper, we proposed a novel approach for mode sorter design that combines (1) stochastic linkage learning, (2) the adaptive geometry estimation-based MOEA (AGE-MOEA-II), and (3) an adaptive mutation operator. Our experiments with two- and three-objectives (beams) show that our approach is faster (better convergence rate) and produces better mode sorters (closer to the ideal solutions) than the state-of-the-art approach. A direct comparison with the vanilla NSGA-II and AGE-MOEA-II also further confirms the importance of adopting LL in this domain.
APPLYING DYNAMIC MODEL FOR MULTIPLE MANOEUVRING TARGET TRACKING USING PARTICL...IJITCA Journal
In this paper, we applied a dynamic model for manoeuvring targets in SIR particle filter algorithm for improving tracking accuracy of multiple manoeuvring targets. In our proposed approach, a color distribution model is used to detect changes of target's model. Our proposed approach controls deformation of target's model. If deformation of target's model is larger than a predetermined threshold, then the model will be updated. Global Nearest Neighbor (GNN) algorithm is used as data association algorithm. We named our proposed method as Deformation Detection Particle Filter (DDPF). DDPF approach is compared with basic SIR-PF algorithm on real airshow videos. Comparisons results show that, the basic SIR-PF algorithm is not able to track the manoeuvring targets when the rotation or scaling is occurred in target's model. However, DDPF approach updates target's model when the rotation or scaling is occurred. Thus, the proposed approach is able to track the manoeuvring targets more efficientlyand accurately.
A NEW ALGORITHM FOR SOLVING FULLY FUZZY BI-LEVEL QUADRATIC PROGRAMMING PROBLEMSorajjournal
This paper is concerned with new method to find the fuzzy optimal solution of fully fuzzy bi-level non-linear (quadratic) programming (FFBLQP) problems where all the coefficients and decision variables of both objective functions and the constraints are triangular fuzzy numbers (TFNs). A new method is based on decomposed the given problem into bi-level problem with three crisp quadratic objective functions and bounded variables constraints. In order to often a fuzzy optimal solution of the FFBLQP problems, the concept of tolerance membership function is used to develop a fuzzy max-min decision model for generating satisfactory fuzzy solution for FFBLQP problems in which the upper-level decision maker (ULDM) specifies his/her objective functions and decisions with possible tolerances which are described by membership functions of fuzzy set theory. Then, the lower-level decision maker (LLDM) uses this preference information for ULDM and solves his/her problem subject to the ULDMs restrictions. Finally, the decomposed method is illustrated by numerical example.
Comparison of Cost Estimation Methods using Hybrid Artificial Intelligence on...IJERA Editor
Cost estimating at schematic design stage as the basis of project evaluation, engineering design, and cost
management, plays an important role in project decision under a limited definition of scope and constraints in
available information and time, and the presence of uncertainties. The purpose of this study is to compare the
performance of cost estimation models of two different hybrid artificial intelligence approaches: regression
analysis-adaptive neuro fuzzy inference system (RANFIS) and case based reasoning-genetic algorithm (CBRGA)
techniques. The models were developed based on the same 50 low-cost apartment project datasets in
Indonesia. Tested on another five testing data, the models were proven to perform very well in term of accuracy.
A CBR-GA model was found to be the best performer but suffered from disadvantage of needing 15 cost drivers
if compared to only 4 cost drivers required by RANFIS for on-par performance.
Similar to Time Series Forecasting using Neural Nets (GNNNs) (20)
Nutraceutical market, scope and growth: Herbal drug technologyLokesh Patil
As consumer awareness of health and wellness rises, the nutraceutical market—which includes goods like functional meals, drinks, and dietary supplements that provide health advantages beyond basic nutrition—is growing significantly. As healthcare expenses rise, the population ages, and people want natural and preventative health solutions more and more, this industry is increasing quickly. Further driving market expansion are product formulation innovations and the use of cutting-edge technology for customized nutrition. With its worldwide reach, the nutraceutical industry is expected to keep growing and provide significant chances for research and investment in a number of categories, including vitamins, minerals, probiotics, and herbal supplements.
Introduction:
RNA interference (RNAi) or Post-Transcriptional Gene Silencing (PTGS) is an important biological process for modulating eukaryotic gene expression.
It is highly conserved process of posttranscriptional gene silencing by which double stranded RNA (dsRNA) causes sequence-specific degradation of mRNA sequences.
dsRNA-induced gene silencing (RNAi) is reported in a wide range of eukaryotes ranging from worms, insects, mammals and plants.
This process mediates resistance to both endogenous parasitic and exogenous pathogenic nucleic acids, and regulates the expression of protein-coding genes.
What are small ncRNAs?
micro RNA (miRNA)
short interfering RNA (siRNA)
Properties of small non-coding RNA:
Involved in silencing mRNA transcripts.
Called “small” because they are usually only about 21-24 nucleotides long.
Synthesized by first cutting up longer precursor sequences (like the 61nt one that Lee discovered).
Silence an mRNA by base pairing with some sequence on the mRNA.
Discovery of siRNA?
The first small RNA:
In 1993 Rosalind Lee (Victor Ambros lab) was studying a non- coding gene in C. elegans, lin-4, that was involved in silencing of another gene, lin-14, at the appropriate time in the
development of the worm C. elegans.
Two small transcripts of lin-4 (22nt and 61nt) were found to be complementary to a sequence in the 3' UTR of lin-14.
Because lin-4 encoded no protein, she deduced that it must be these transcripts that are causing the silencing by RNA-RNA interactions.
Types of RNAi ( non coding RNA)
MiRNA
Length (23-25 nt)
Trans acting
Binds with target MRNA in mismatch
Translation inhibition
Si RNA
Length 21 nt.
Cis acting
Bind with target Mrna in perfect complementary sequence
Piwi-RNA
Length ; 25 to 36 nt.
Expressed in Germ Cells
Regulates trnasposomes activity
MECHANISM OF RNAI:
First the double-stranded RNA teams up with a protein complex named Dicer, which cuts the long RNA into short pieces.
Then another protein complex called RISC (RNA-induced silencing complex) discards one of the two RNA strands.
The RISC-docked, single-stranded RNA then pairs with the homologous mRNA and destroys it.
THE RISC COMPLEX:
RISC is large(>500kD) RNA multi- protein Binding complex which triggers MRNA degradation in response to MRNA
Unwinding of double stranded Si RNA by ATP independent Helicase
Active component of RISC is Ago proteins( ENDONUCLEASE) which cleave target MRNA.
DICER: endonuclease (RNase Family III)
Argonaute: Central Component of the RNA-Induced Silencing Complex (RISC)
One strand of the dsRNA produced by Dicer is retained in the RISC complex in association with Argonaute
ARGONAUTE PROTEIN :
1.PAZ(PIWI/Argonaute/ Zwille)- Recognition of target MRNA
2.PIWI (p-element induced wimpy Testis)- breaks Phosphodiester bond of mRNA.)RNAse H activity.
MiRNA:
The Double-stranded RNAs are naturally produced in eukaryotic cells during development, and they have a key role in regulating gene expression .
Richard's aventures in two entangled wonderlandsRichard Gill
Since the loophole-free Bell experiments of 2020 and the Nobel prizes in physics of 2022, critics of Bell's work have retreated to the fortress of super-determinism. Now, super-determinism is a derogatory word - it just means "determinism". Palmer, Hance and Hossenfelder argue that quantum mechanics and determinism are not incompatible, using a sophisticated mathematical construction based on a subtle thinning of allowed states and measurements in quantum mechanics, such that what is left appears to make Bell's argument fail, without altering the empirical predictions of quantum mechanics. I think however that it is a smoke screen, and the slogan "lost in math" comes to my mind. I will discuss some other recent disproofs of Bell's theorem using the language of causality based on causal graphs. Causal thinking is also central to law and justice. I will mention surprising connections to my work on serial killer nurse cases, in particular the Dutch case of Lucia de Berk and the current UK case of Lucy Letby.
Multi-source connectivity as the driver of solar wind variability in the heli...Sérgio Sacani
The ambient solar wind that flls the heliosphere originates from multiple
sources in the solar corona and is highly structured. It is often described
as high-speed, relatively homogeneous, plasma streams from coronal
holes and slow-speed, highly variable, streams whose source regions are
under debate. A key goal of ESA/NASA’s Solar Orbiter mission is to identify
solar wind sources and understand what drives the complexity seen in the
heliosphere. By combining magnetic feld modelling and spectroscopic
techniques with high-resolution observations and measurements, we show
that the solar wind variability detected in situ by Solar Orbiter in March
2022 is driven by spatio-temporal changes in the magnetic connectivity to
multiple sources in the solar atmosphere. The magnetic feld footpoints
connected to the spacecraft moved from the boundaries of a coronal hole
to one active region (12961) and then across to another region (12957). This
is refected in the in situ measurements, which show the transition from fast
to highly Alfvénic then to slow solar wind that is disrupted by the arrival of
a coronal mass ejection. Our results describe solar wind variability at 0.5 au
but are applicable to near-Earth observatories.
THE IMPORTANCE OF MARTIAN ATMOSPHERE SAMPLE RETURN.Sérgio Sacani
The return of a sample of near-surface atmosphere from Mars would facilitate answers to several first-order science questions surrounding the formation and evolution of the planet. One of the important aspects of terrestrial planet formation in general is the role that primary atmospheres played in influencing the chemistry and structure of the planets and their antecedents. Studies of the martian atmosphere can be used to investigate the role of a primary atmosphere in its history. Atmosphere samples would also inform our understanding of the near-surface chemistry of the planet, and ultimately the prospects for life. High-precision isotopic analyses of constituent gases are needed to address these questions, requiring that the analyses are made on returned samples rather than in situ.
This presentation explores a brief idea about the structural and functional attributes of nucleotides, the structure and function of genetic materials along with the impact of UV rays and pH upon them.
Professional air quality monitoring systems provide immediate, on-site data for analysis, compliance, and decision-making.
Monitor common gases, weather parameters, particulates.
What is greenhouse gasses and how many gasses are there to affect the Earth.moosaasad1975
What are greenhouse gasses how they affect the earth and its environment what is the future of the environment and earth how the weather and the climate effects.
2. Relationship to Research
Currently analyzing the performance of NEAT for Time Series
Forecasting (TSF)
Paper summarizes common approaches, and issues, using ANNs for
TSF
2 / 19
3. Claims of the Paper
Develops an automatic TSF model using a Generalized Regression
Neural Network (GRNN)
Shows promising results by winning NN3 time-series competition
against 60 different models
3 / 19
4. General Problems with ANN
Most approaches are ad hoc meaning they do some type of
preprocessing of the data
Typically try different ANN architectures to see which one performs
better
Nelson et al. : ANN inconsistency on TSF is the result of different
preprocessing strategies
Balkin et al. : ANNs require larger number of samples to be trained.
Real-world examples, financial etc., are short training samples.
4 / 19
5. RBF
RBF can be viewed as local linear regression model
Apply Gaussian kernel to input data. All inputs go to node of form:
G(x) = exp
−x − c
σ2
(1)
Find center points by assigning c (center point) to each point in data
set (measuring the distance to center point).
This is equivalent to doing a local regression (sigma affects the
smoothing of the approximation).
Output layer (the weights) are trained using least-squares regression
5 / 19
6. Generalized Definition for Regression
Computation of most probable value of Y for each value of X based
on finite number of possibly noisy measurements of X
Conditional mean of y given X (regression of y on X ) is given by:
E[y|X] =
∞
−∞
yf (X, y)dy
∞
−∞
f (X, y)dy
(2)
Since we don’t typically know the density function f(X, y) it can be
estimated using a Parzen window density estimator.
6 / 19
7. Generalized Definition for Regression
The generalized definition yields the following regression function:
ˆY (X) =
n
i=1
Y i exp −
D2
i
2σ2
n
i=1
exp −
D2
i
2σ2
(3)
Where D2
i = (X − Xi
)T (X − Xi
)
In the case of GRNN X is the input data and Xi
are the centers.
7 / 19
8. GRNN
G(x, xi ) are the standard radial basis functions
wi is the generalized regression equation
The spread factor dictates the performance
8 / 19
9. Claimed Benefits of GRNN
Easy to train
Can accurately approximate functions from sparse and noisy data
Note: Recent paper, Ahmed et al., claim GRNN inferior to MLP for
TSF
9 / 19
10. Methodology Requirements
Minimal human intervention
Computationally efficient for a large number of series
Good forecasting over range of data sets
10 / 19
11. Preprocessing: Outliers
Real-world time series has outliers
Outliers identified by
|x| ≥ 4max(|ma|, |mb|) (4)
where ma = median(xi−3, xi−2, xi−1) and
mb = median(xi+1, xi+2, xi+3)
If x is an outlier the value is replaced with average value of two points
before and after x
11 / 19
12. Preprocessing: Trends
Real-world time series has trends. Could be due to seasonality or other
factors.
Common approaches are curve fitting, filtering, and differencing.
Identifying trends is difficult to do algorithmically
Proposes detrending scheme:
Split series into segments. If monthly split into 12 if quarterly split into
4
Mean of historical observations within each segment is subtracted from
every historical observation in segment.
If x is an outlier the value is replaced with average value of two points
before and after x
12 / 19
13. Preprocessing: Seasonality
Identifying seasonality is typically a manual process
Author used a simple approach and defined short series as n ≤ 60 and
long n ≥ 60
Uses autocorrelation coefficients at one and two seasonal lags to
decide if seasonal
Uses a standard method for subtracting out seasonality from series
data
13 / 19
14. ANN Modeling
Aspects of ANN modeling
Spread Factor. Typically found empirically since no good analytic
approach has been found. Some guidance was given by Haykin
σ = dmax√
2n
where dmax is max distance between the training points.
Proposes spread factor be set to d50, d75, d95 (percentiles) of the
nearest distance of all training samples to rest of points.
Uses three GRNNs that all take the same input and are combined to
give the final output.
Choice of combining three GRNNs is based on previous success in
literature
14 / 19
15. ANN Modeling Cont’d
Input selection is considered one of the most important aspects in
TSF
Two general approaches: filter and wrapper
Filtering selects features based on data itself (independent of learning
algorithm)
Wrapping approaches use the learning algorithm. Wrapper typically
performs better.
Author uses contiguous lag and limits to one full season for 12 month
data.
15 / 19
16. Experimental Results
Use NN3 time-series competition dataset which has composed of
Dataset A and Dataset B
Dataset A is 111 monthly time series data drawn from empirical
business time series
Dataset B is a small subset of Dataset A which consists of 11 time
series
Error is measured using sMAPE
16 / 19
19. Discussion
Are TSF competitions just a demonstration of the no free lunch
theorem? Why is the theorem not mentioned?
Did he prove his approach was “better” or did this approach just
outperform on a particular contest?
Why doesn’t the training of the GRNN factor out outliers and
seasonality on its own? Isn’t that what training is for?
Why did he choose a GRNN? Previous papers said they perform
poorly.
What kind of bias does the detrending scheme introduce?
Paper was “rule of thumb” oriented. Is there a way to make an
automatic approach more rigorous?
19 / 19