Interval prediction | MATLAB implements QRCNN convolutional neural network quantile regression time series interval prediction

Interval prediction | MATLAB implements QRCNN convolutional neural network quantile regression time series interval prediction

List of effects

basic introduction

Interval prediction | MATLAB implements QRCNN convolutional neural network quantile regression time series interval prediction
1. Matlab realizes the time series interval prediction model based on QRCNN quantile regression convolutional neural network;
2. Multi-image output, multi-indicator output (MAE , RMSE, MSE, R2), multiple input and single output, including different confidence interval maps and probability density maps;
3. data is a data set, a power data set, using variables from the past period of time to predict the target, the target is the last column, and also Applicable to load forecasting and wind speed forecasting; MainQRCNNTS is the main program, and the rest are function files, no need to run;
4. The code is of high quality, with clear comments, including data preprocessing, and handling missing values. If it is nan, replace it with the previous line, Kernel density estimation is also included.

Model description

QRCNN is a convolutional neural network (CNN) based quantile regression model for time series interval forecasting. Its full name is Quantile Regression Convolutional Neural Network. This model can be used to predict different quantiles of time series data, such as predicting the upper and lower limits of stock prices, the extreme value of wind speed, etc. Since QRCNN adopts the structure of convolutional neural network, it can effectively capture the local and global characteristics of time series data, thereby improving the prediction accuracy.
The main idea of ​​the QRCNN model is to decompose time series data into a series of windows and treat each window as an image. Then, feature extraction and analysis are performed on these images using a convolutional neural network, and a prediction result for each quantile is finally output. The training process of the QRCNN model employs a quantile loss function to minimize the prediction error for all quantiles.

The advantages of the QRCNN model include:
being able to effectively deal with the uncertainty and nonlinear characteristics of time series data;
being able to predict multiple quantiles at the same time, thereby providing more comprehensive prediction results; and
being able to flexibly handle time series data of different lengths.
In conclusion, the QRCNN model is a powerful tool for time series interval forecasting, which can help people better understand and apply time series data.
The formula of the QRCNN model includes input layer, convolutional layer, pooling layer, fully connected layer and output layer. The following are the main formulas of the QRCNN model:

Input layer:
Suppose the time series data is $x_t$, then the input layer will each time step $t$ 's data as an input node$x_t$.
Convolutional layer:
Assuming the $The\; size\; of\; k$ convolution kernels is$d_k$, then the $The\; output\; of\; k$ convolutional layers$z_k$It can be expressed as:

$$z_k=s(W_k\ast x+b_k)$$

Among them, $W_k$is the kkthThe weight matrix of$k$$\ast$ means convolution operation,$b_k$is a bias term, $\sigma$ is the activation function, usually using ReLU or tanh function.
Pooling layer:
Assuming the$The\; size\; of\; k$ pooling operations is$m_k$, then the $The\; output\; of\; k$ pooling layers$y_k$It can be expressed as:

$$y_k=maxpzl(z_k)$$

Among them, $maxpoolrepresentsthe$ maximum pooling operation$.$
Fully connected layer:
Assuming the$The\; output\; of\; l$ fully connected layers is$h_l$, then the $The\; output\; of\; l$ fully connected layers$h_l$It can be expressed as:

$$h_l=s(W_l\ast h_{l-1}+b_l)$$

Among them, $W_l$is the llThe weight matrix of$l$$b_l$is a bias term, $\sigma$ is the activation function.
Output layer:
suppose to predict$q$ quantile,$The\; q$ quantiles are$t_q$, then the output of the output layer $y_q$It can be expressed as:

$$y_q=F_{t_q}(h_L)$$

where, $F_{t_q}\left(h_L\right)$ means theLLThe output of layer$L$$h_L$In quantile $t_q$The cumulative distribution function (CDF) at .
Loss function:
The QRCNN model uses a quantile loss function, which is defined as:

$$L_{}(y,\hat{y})=(1-t)|y-\hat{y}|(y\le \hat{y})+\tau |y-\hat{y}|(y>\hat{y})$$

Among them, $y$ represents the actual value,$\hat{y}$Indicates the predicted value, $\tau$ represents the quantile,$|\cdot {|}_{(\cdot )}$Indicates the indicator function.
Ultimately, the goal of the QRCNN model is to minimize the sum of the prediction errors for all quantiles, namely:

$$min\sum _{i=1}^n\sum _{q=1}^Q{L}_{t_q}(y_i,\widehat{y_i})$$

Among them, $n$ represents the sample size,$Q$ represents the number of quantiles.

programming

• Complete program and data acquisition method: private message blogger.

% Divide the data into training and validation data sets
numTrainFiles = 90;
[imdsTrain,imdsValidation] = splitEachLabel(imds,numTrainFiles,'randomize');
% Define the convolutional neural network architecture.
layers = [
% Image Input Layer An imageInputLayer 
    imageInputLayer([64 64 1])
% Convolutional Layer 
convolution2dLayer(3,8,'Padding','same')
% Batch Normalization 
    batchNormalizationLayer
% ReLU Layer The batch
    reluLayer
% Max Pooling Layer  
    % More values means less weights
    maxPooling2dLayer(4,'Stride',4)
    %------------------------------
    convolution2dLayer(3,8,'Padding','same')
    batchNormalizationLayer
    reluLayer
    maxPooling2dLayer(5,'Stride',5)
    convolution2dLayer(3,8,'Padding','same')
    batchNormalizationLayer
    reluLayer
% Fully Connected Layer (Number of Classes) 
    fullyConnectedLayer(8)
% Softmax Layer 
    softmaxLayer
% Classification Layer The final layer 
    classificationLayer];
% Specify the training options
options = trainingOptions('sgdm', ...
    'InitialLearnRate',0.001, ...
    'MaxEpochs',20, ...
    'Shuffle','every-epoch', ...
    'ValidationData',imdsValidation, ...
    'ValidationFrequency',8, ...
    'Verbose',false, ...
    'Plots','training-progress');
% Train the network 
[net,info]= trainNetwork(imdsTrain,layers,options);

% Converting Serial Network to an Object
netobj = net.saveobj;
% Extracting Fully Connected Layer's Weights To Evolve
FullConn=netobj.Layers(13, 1).Weights;
netbias=netobj.Layers(13, 1).Bias;

%% Data for Each Weight
sizefinal=size(FullConn);
sizefinal=sizefinal(1,1);
for i=1:sizefinal
Inputs=FullConn(i,:);
Targets=Inputs;
data.Inputs=Inputs;
data.Targets=Targets;
datam{
    
    i}=JustLoad(data);
end;

————————————————
版权声明：本文为CSDN博主「机器学习之心」的原创文章，遵循CC 4.0 BY-SA版权协议，转载请附上原文出处链接及本声明。
原文链接：https://blog.csdn.net/kjm13182345320/article/details/128252426

References

[1] https://blog.csdn.net/kjm13182345320/article/details/127931217
[2] https://blog.csdn.net/kjm13182345320/article/details/127418340