Open Prediction Project Ebook

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Time series prediction problems are a difficult type of predictive modeling problem. Unlike regression predictive modeling, time series also adds the complexity of a sequence dependence among the input variables. A powerful type of neural network designed to handle sequence dependence is called. The Long Short-Term Memory network or LSTM network is a type of recurrent neural network used in deep learning because very large architectures can be successfully trained. In this post, you will discover how to develop LSTM networks in Python using the Keras deep learning library to address a demonstration time-series prediction problem.

After completing this tutorial you will know how to implement and develop LSTM networks for your own time series prediction problems and other more general sequence problems. You will know:.

About the International Airline Passengers time-series prediction problem. How to develop LSTM networks for regression, window and time-step based framing of time series prediction problems. How to develop and make predictions using LSTM networks that maintain state (memory) across very long sequences. In this tutorial, we will develop a number of LSTMs for a standard time series prediction problem.

The problem and the chosen configuration for the LSTM networks are for demonstration purposes only they are not optimized. These examples will show you exactly how you can develop your own differently structured LSTM networks for time series predictive modeling problems. Let’s get started. Update Oct/2016: There was an error in the way that RMSE was calculated in each example. Reported RMSEs were just plain wrong.

Now, RMSE is calculated directly from predictions and both RMSE and graphs of predictions are in the units of the original dataset. Models were evaluated using Keras 1.1.0, TensorFlow 0.10.0 and scikit-learn v0.18. Thanks to all those that pointed out the issue, and to Philip O’Brien for helping to point out the fix. Update Mar/2017: Updated example for Keras 2.0.2, TensorFlow 1.0.1 and Theano 0.9.0. Update Apr/2017: For a more complete and better explained tutorial of LSTMs for time series forecasting see the post. Updated LSTM Time Series Forecasting Posts: The example in this post is quite dated, I have better examples available for using LSTMs on time series, see:.

Time Series Prediction with LSTM Recurrent Neural Networks in Python with Keras Photo by, some rights reserved. Problem Description The problem we are going to look at in this post is theInternational Airline Passengers prediction problem. This is a problem where, given a year and a month, the task is to predict the number of international airline passengers in units of 1,000. The data ranges from January 1949 to December 1960, or 12 years, with 144 observations.

The dataset is available for free from the with the filename “ international-airline-passengers.csv“. Below is a sample of the first few lines of the file. '1949-05',121 We can load this dataset easily using the Pandas library. We are not interested in the date, given that each observation is separated by the same interval of one month. Therefore, when we load the dataset we can exclude the first column.

The downloaded dataset also has footer information that we can exclude with the skipfooter argument to pandas.readcsv set to 3 for the 3 footer lines. Once loaded we can easily plot the whole dataset.

The code to load and plot the dataset is listed below. Long Short-Term Memory Network The Long Short-Term Memory network, or LSTM network, is a recurrent neural network that is trained using Backpropagation Through Time and overcomes the vanishing gradient problem. As such, it can be used to create large recurrent networks that in turn can be used to address difficult sequence problems in machine learning and achieve state-of-the-art results. Instead of neurons, LSTM networks have memory blocks that are connected through layers. A block has components that make it smarter than a classical neuron and a memory for recent sequences.

A block contains gates that manage the block’s state and output. A block operates upon an input sequence and each gate within a block uses the sigmoid activation units to control whether they are triggered or not, making the change of state and addition of information flowing through the block conditional. There are three types of gates within a unit:. Forget Gate: conditionally decides what information to throw away from the block. Input Gate: conditionally decides which values from the input to update the memory state.

Output Gate: conditionally decides what to output based on input and the memory of the block. Each unit is like a mini-state machine where the gates of the units have weights that are learned during the training procedure. You can see how you may achieve sophisticated learning and memory from a layer of LSTMs, and it is not hard to imagine how higher-order abstractions may be layered with multiple such layers. LSTM Network for Regression We can phrase the problem as a regression problem. That is, given the number of passengers (in units of thousands) this month, what is the number of passengers next month? We can write a simple function to convert our single column of data into a two-column dataset: the first column containing this month’s (t) passenger count and the second column containing next month’s (t+1) passenger count, to be predicted. Before we get started, let’s first import all of the functions and classes we intend to use.

This assumes a working SciPy environment with the Keras deep learning library installed. Dataset = scaler. Fittransform ( dataset ) After we model our data and estimate the skill of our model on the training dataset, we need to get an idea of the skill of the model on new unseen data. For a normal classification or regression problem, we would do this using cross validation.

With time series data, the sequence of values is important. A simple method that we can use is to split the ordered dataset into train and test datasets. The code below calculates the index of the split point and separates the data into the training datasets with 67% of the observations that we can use to train our model, leaving the remaining 33% for testing the model. Print ( len ( train ), len ( test ) ) Now we can define a function to create a new dataset, as described above. The function takes two arguments: the dataset, which is a NumPy array that we want to convert into a dataset, and the lookback, which is the number of previous time steps to use as input variables to predict the next time period — in this case defaulted to 1.

This default will create a dataset where X is the number of passengers at a given time (t) and Y is the number of passengers at the next time (t + 1). It can be configured, and we will by constructing a differently shaped dataset in the next section. # make predictions trainPredict = model.predict(trainX) testPredict = model.predict(testX) # invert predictions trainPredict = scaler.inversetransform(trainPredict) trainY = scaler.inversetransform(trainY) testPredict = scaler.inversetransform(testPredict) testY = scaler.inversetransform(testY) # calculate root mean squared error trainScore = math.sqrt(meansquarederror(trainY0, trainPredict:,0)) print('Train Score:%.2f RMSE'% (trainScore)) testScore = math.sqrt(meansquarederror(testY0, testPredict:,0)) print('Test Score:%.2f RMSE'% (testScore)). Print ( 'Test Score:%.2f RMSE'% ( testScore ) ) Finally, we can generate predictions using the model for both the train and test dataset to get a visual indication of the skill of the model.

Because of how the dataset was prepared, we must shift the predictions so that they align on the x-axis with the original dataset. Once prepared, the data is plotted, showing the original dataset in blue, the predictions for the training dataset in green, and the predictions on the unseen test dataset in red. # shift train predictions for plotting trainPredictPlot = numpy.emptylike(dataset) trainPredictPlot:,: = numpy.nan trainPredictPlotlookback:len(trainPredict)+lookback,: = trainPredict # shift test predictions for plotting testPredictPlot = numpy.emptylike(dataset) testPredictPlot:,: = numpy.nan testPredictPlotlen(trainPredict)+(lookback.2)+1:len(dataset)-1,: = testPredict # plot baseline and predictions plt.plot(scaler.inversetransform(dataset)) plt.plot(trainPredictPlot) plt.plot(testPredictPlot) plt.show. Test Score: 47.53 RMSE We can see that the model has an average error of about 23 passengers (in thousands) on the training dataset, and about 52 passengers (in thousands) on the test dataset. Not that bad.

LSTM for Regression Using the Window Method We can also phrase the problem so that multiple, recent time steps can be used to make the prediction for the next time step. This is called a window, and the size of the window is a parameter that can be tuned for each problem. For example, given the current time (t) we want to predict the value at the next time in the sequence (t+1), we can use the current time (t), as well as the two prior times (t-1 and t-2) as input variables.

When phrased as a regression problem, the input variables are t-2, t-1, t and the output variable is t+1. The createdataset function we created in the previous section allows us to create this formulation of the time series problem by increasing the lookback argument from 1 to 3. A sample of the dataset with this formulation looks as follows. LSTM Trained on Window Method Formulation of Passenger Prediction Problem LSTM for Regression with Time Steps You may have noticed that the data preparation for the LSTM network includes time steps. Some sequence problems may have a varied number of time steps per sample.

For example, you may have measurements of a physical machine leading up to a point of failure or a point of surge. Each incident would be a sample the observations that lead up to the event would be the time steps, and the variables observed would be the features. Time steps provide another way to phrase our time series problem. Like above in the window example, we can take prior time steps in our time series as inputs to predict the output at the next time step. Instead of phrasing the past observations as separate input features, we can use them as time steps of the one input feature, which is indeed a more accurate framing of the problem. We can do this using the same data representation as in the previous window-based example, except when we reshape the data, we set the columns to be the time steps dimension and change the features dimension back to 1.

LSTM Trained on Time Step Formulation of Passenger Prediction Problem LSTM with Memory Between Batches The LSTM network has memory, which is capable of remembering across long sequences. Normally, the state within the network is reset after each training batch when fitting the model, as well as each call to model.predict or model.evaluate.

We can gain finer control over when the internal state of the LSTM network is cleared in Keras by making the LSTM layer “stateful”. This means that it can build state over the entire training sequence and even maintain that state if needed to make predictions. It requires that the training data not be shuffled when fitting the network.

It also requires explicit resetting of the network state after each exposure to the training data (epoch) by calls to model.resetstates. This means that we must create our own outer loop of epochs and within each epoch call model.fit and model.resetstates. Stateful LSTM Trained on Regression Formulation of Passenger Prediction Problem Stacked LSTMs with Memory Between Batches Finally, we will take a look at one of the big benefits of LSTMs: the fact that they can be successfully trained when stacked into deep network architectures. LSTM networks can be stacked in Keras in the same way that other layer types can be stacked. One addition to the configuration that is required is that an LSTM layer prior to each subsequent LSTM layer must return the sequence. This can be done by setting the returnsequences parameter on the layer to True. We can extend the stateful LSTM in the previous section to have two layers, as follows.

Stacked Stateful LSTMs Trained on Regression Formulation of Passenger Prediction Problem Summary In this post, you discovered how to develop LSTM recurrent neural networks for time series prediction in Python with the Keras deep learning network. Specifically, you learned:. About the international airline passenger time series prediction problem. How to create an LSTM for a regression and a window formulation of the time series problem. How to create an LSTM with a time step formulation of the time series problem. How to create an LSTM with state and stacked LSTMs with state to learn long sequences.

Do you have any questions about LSTMs for time series prediction or about this post? Ask your questions in the comments below and I will do my best to answer. Updated LSTM Time Series Forecasting Posts: The example in this post is quite dated, I have better examples available for using LSTMs on time series, see:. Thanks for this great tutorial Jason. I’m still having trouble figuring out what kind of graph do you get when you do this: # create and fit the LSTM network model = Sequential model.add(LSTM(4, inputshape=(1, lookback))) model.add(Dense(1)) for instance if your lookback=1: the input is one value xt, and the target output is xt+1. How is “LSTM(4, inputshape=(1, lookback))” linking your LSTM blocks with the input? Or do you have 1 input = 1 LSTM block which hidden value (output of the LSTM) is fed to a 4X1 dense MLP?

So that the output of the LSTM is actually the input of a 1x4x1 MLP And if your input is xt-1, xt with target xt+1 (lookback=2), you have two LSTMs blocks (fed with xt-1 and xt respectively) and the hidden value of the second block is the input of a 1x4x1 MLP. I hope I’m being clear, I really have troubles answering this question. Your tutorial helps though! Sorry Alex, you’re question is a little vague. It’s of the order “I have data like this, what is the best way to model this problem”.

It’s a tough StackOverflow question because it’s an open question rather than a specific technical question. Generally, my answer would be “no idea, try lots of stuff and see what works best”. I think your notion of online might also be confused (or I’m confused). Have you seen online implementations of LSTM? Keras does not support it as far as I know. You train your model then you make predictions. Unless of course you mean the maintained state of the model – but this is not online learning, it is just static model with state, the weights are not updated in an online manner unless you re-train your model frequently.

It might be worth stepping back from the code and taking some time to clearly define I/O of the problem and requirements to then figure out the right kind of algorithm/setup you need to solve it. Hi Jason, Interesting post and a very useful website! Can I use LSTMS for time series classification, for a binary supervised problem? My data is arranged as time steps of 1 hr sequences leading up to an event and the occurrence and non-occurrence of the event are labelled in each instance. I have done a bit of research and have not seen many use cases in the literature. Do you think a different recurrent neural net or simpler MLP might work better in this case?

Most of my the research done in my area has got OK results(70% accuracy) from feed forward neural networks and i thought to try out recurrent neural nets, specifically LSTMs to improve my accuracy. Hi Jason, Thanks for this example. I ran the first code example (lookback=1) by just copying the code and can reproduce your train and test scores precisely, however my graph looks differently. Specifically for me the predicted graph (green and red lines) looks as if it is shifted by one to the right in comparison to what I see on this page.

It also looks like the predicted graph starts at x=0 in your example, but my predicted graph starts at 1. So in my case it looks like the prediction is almost like predicting identity? Is there a way for me to verify what I could have done wrong? Thanks, Peter.

Hi Jason, when outputting the train and test score, you scale the output of the model.evaluate with the minmaxscaler to match into the original scale. I am not sure if I understand that correctly. The data values are between 104 and 622, the trainScore (which is the mean squared error) will be scaled into that range using a linear mapping, right?

So your transformed trainscore can never be lower than the minimum of the dataset, i.e. Shouldn’t the square root of the trainScore be transformed and then the minimum of the range be subtracted and squared again to get the mean square error in the original domain range? Like numpy.square(scalar.inversetransform(nump.sqrt(trainScore))-scaler.datamin) Thanks, Peter. If I understand correctly, you want more elaboration on time steps vs features? Features are your input variables.

In this airline example we only have one input variable, but we can contrive multiple input variables using past time steps in what is called the window method. Normally, multiple features would be a multivariate time series.

Timesteps are the sequence through time for a give attribute. As we comment in the tutorial, this is the natural mapping of the problem onto LSTMs for this airline problem. You always need a 3D array as input for LSTMs samples, features, timesteps, but you can reduce each dimension to one if needed. We explore this ability in reframe the problem in the tutorial above.

You also ask about the point of stateful. It is helpful to have memory between batches over one training run. If we keep all of out time series samples in order, the method can learn the relationships between values across batches. If we did not enable the stateful parameter, the algorithm we no knowledge beyond each batch, much like a MLP. I hope that helps, I’m happy to dig into a specific topic further if you have more questions. So does that mean (in reference to the LSTM diagram in ) that the cell memory is not passed between consecutive lstms if stateful=false (i.e.

Set to zero)? Or do you mean cell memory is reset to zero between consecutive batches (In this tutorial batchsize is 1). Although I guess I should point out that the hidden layer values are passed on, so it will still be different to a MLP (wouldn’t it?) On a side note, the fact that the output has to be a factor of batchsize seems to be confounding. Feels like it limits me to using a batchsize of one. If stateful is set to false (the default), then I understand according to the Keras documentation that the state within each LSTM node is reset after each batch, either for prediction or training.

This is useful if you do not want to use LSTMs in a stateful manner of you want to train with all of the required memory to learn from within each batch. This does tie into the limit on batch size for prediction. The TF/Theano structures created from this network definition are optimized for the batch size. I’m super confused here. If the LSTM node is reset after each batch (in this case batchsize 1), does that mean in each forward-backprop session, the LSTM starts with a fresh state without any memory of previous inputs, and it’s only input is a single value?

If that’s the case, how could it possibly learn anything? E.g., let’s say on both time step 10 and 15 the input value is 150, how does the network predict step (10+1) to be 180 and step (15+1) to be 130 while the only input is 150 and the LSTM start with a fresh state? First of all, thank you for that great post I have just one small question: For some research work i am working on, I need to make a prediction, so I’ve been looking for the best possible solution and I am guessing its LSTM The app. Hi Liu, after investigating a bit, I have concluded that the 1 time-step LSTM is indeed the trivial identity function (you can convince yourself by reducing the layer to 1 neuron, and adding ad-hoc data to the test set, as you have). But if we think about it, this makes alot of sense that the ‘mimic’ function would minimize MSE for such a simple network – it doesn’t see enough time steps to learn the sequence, anyways. However, if you increase the number of timesteps, you will see that it can reach lower MSE on the test set by slowly moving away from the mimic function to actually learning the sequence, although for low #’s of neurons the approximation will be rougher-looking. I recommend experimenting with the lookback amount, and adding more layers to see how the MSE can be reduced further!

Hi Nicholas, Thanks for the comment! I guess the problem (or feature you can say) in the first example is that ‘time-step’ is set to 1 if I understand the API correctly: trainX = numpy.reshape(trainX, (trainX.shape0, 1, trainX.shape1)) It means it is feeding sequence of length 1 to the network in each training. Therefore, the RNN/LSTM is not unrolled. The updated internal state is not used anywhere (as it is also resetting the states of the machine in each batch).

I agree with what you said. But by setting timestep and lookback to be 1 as in the first example, it is not learning a sequence at all. For other readers, I think it worths to look. Great question Chris. The batchsize is the number of samples from your train dataset shown to the model at a time. After batchsize samples are run through the network and error calculated, an update to the weights is performed. Too many and the updates are too big, too few, and the updates are too noisy.

The hardware you use is also a factor for batchsize and you want to ensure you can fit the batch of samples in memory (e.g. So your GPU can get at them). I chose a batchsize of 1 because I want to explore and demonstrate LSTMs on time series working with only one sample at a time, but potentially vary the number of features or time steps. Hi Jason, Thanks for this series. I have a question for you. I want to apply a multi-classification problem for videos using LSTM.

Also, video samples have a different number of frames. Dataset: samples of videos for actions like boxing, jumping, hand waving, etc. (Dataset like UCF1101). Each class of action has one label. So, each video has a label. Really, I do not know how to describe the data set to LSTM when a number of frames sequence are different from one action to another and I do not know how to use it when a number of frames are fixed as well.

If you have any example of how to use: LSTM, stacked of LSTM, or CNN with LSTM with this problem this will help me too much. I wait for your recommendations Thanks.

Hi Jason, First off, thanks again for this great blog, without you I would be nowhere, with LSTM, and life! I am running a LSTM model that works, but when I make predictions with “model.predict” it spits out 4000 predictions, which look fine.

However, when I run “model.predict” again and save those 4000 predictions again, they are different. From prediction 50 onward, they are all essentially the same, but the first few (that are very important to me) are very different. To give you an idea, the correlation between the first 10 predictions of both rounds is 0.11. I am a little bit confused regarding the “statefulness”. If I use a Sequential Model with LSTM layers and stateful set to false. Will this still be a recurrent network that feeds back into my nodes?

How would I compare it to the standard LSTM model proposed by Hochreiter et al. Do I have to use the stateful layers to mimic the behaviour presented in the original paper? In essence, I have a simple time series of sales forecasts that show a weekly and partly a yearly pattern. It was easy to create a simple MLP with the Dense layer and the time window method.

I put some sales values from the last week, the same week day a few weeks back and the sales of the days roughly a year before into my feature vector. Results are pretty good so far. I now want to compare it to an LSTM approach. I am however not sure how I can model the weekly and yearly pattern correctly and if I need to use the stateful LSTM or not.

Basically I want to use the power of an LSTM to predict a sequence of a longer period of time and hope that the forecasts will be better than with a standard (and much faster) MLP. These lines don’t make sense to me: # reshape input to be samples, time steps, features trainX = numpy.reshape(trainX, (trainX.shape0, 1, trainX.shape1)) testX = numpy.reshape(testX, (testX.shape0, 1, testX.shape1)) Isn’t it samples, fetaures, timesteps? When you switch to lookback = 3, you still use trainX.shape0, 1, trainX.shape1 as your reshape, and aren’t the timesteps the lookback? I noticed the Keras model doesn’t work unless you reshape in this way, which is really strange to me. Why do we have to have a matrix full of 1×1 vectors which hold another vector inside of them? Is this in case we have more features or something? Are there ever any cases where the ‘1’ in the reshape would be any other number?

I think the example given here is wrong in the sense, that each data point represents a sample with one single timestep. This doesn’t make sense at all if you think about the strengths of recurrent networks and especially LSTM.

How is the LSTM going to memorize if there’s only one timestep for each sample? Since we are working on a single time series, it should probably be the other way around, with one sample and n timesteps. One could also try and reduce the number of timesteps and split the time series up into samples of a week or a month depending on the data. Not sure if this is all correct what I just said, but I get the feeling that this popular tutorial isn’t a 100% correct and therefore a bit misleading for the community. Hi Jason, Nice blog post. I noticed however, that when you do not scale the input data and switch the activation of the LSTMs to ReLu, you are able to get performance comparable to the feedforward models in your other blog post.

The performance becomes: Train Score: 23.07 RMSE, Test Score: 48.59 RMSE Moreover, when you run the feedforward models in the other blog post with scaling of the input data their performance degrades. Any idea why scaling the dataset seems to worsen the performance performance?

Cheers, Stijn. Hey Jason, As far as I can tell (and you’ll have to excuse me if I’m being naive) this isn’t predicting the next timestep at all? Merely doing a good job at mimicking the previous timestep? For example the with the first example, if we take the first timestep of trainX (trainX0) the prediction from the model doesn’t seem to be trying to predict what t+1 (trainX1) is, but merely mimics what it thinks fits the model at that particular timestep (trainX0) i.e. Tries to copy the current timestep.

Same for trainX1, the prediction is not a prediction of trainX2 but a guess at trainX1 Hence which the graphs in the post (which as you mentioned above you need to update) look like they’re forwardlooking, but running the code actually produces graphs which have the predictions shifted t+lookback. How would you make this a forward looking graph? Hence also, I tried to predict multiple future timesteps with your first model by initialising the first prediction with testX0 and then feeding the next predictions with the prior predictions but the predictions just plummeted downwards into a downwards curve. Not predicting the next timesteps at all. Am I being naive to the purpose of this blog post here?

All the best, love your work, Jakob. Hi Jakob, I believe you are correct. I have tried these methods on many different time series and the same mimicking behavior occurs – the training loss is somehow minimized by outputting the previous timestep. A similar mimicking behavior occurs when predicting multiple time steps ahead as well (for example, if predicting two steps ahead, the model learns to output the previous two timesteps). There is a small discussion on this issue found here – – but besides that I haven’t discovered any ways to combat this (or if there is some underlying problem with Keras, my code, etc.). I am in the process of writing a blog to uncover this phenomenon in more detail. Will follow up when I am done.

Any other advancements or suggestions would be greatly appreciated! Thanks, Jeremy.

Sir, Awesome work!!! I am very interested in cross-sectional time series estimation How can that be done? I am starting your Python track, but will eventually target data with say 50 explanatory variables, with near infinite length of time series observations available on each one. Since the explanatory variables are not independent normal OLS is useless and wish to learn your methods. I would be most interested in your approach to deriving an optimal sampling temporal window and estimation procedure. This is a nice tutorial for starters. However, I have some concerns about the createdataset function.

I think it just make a simple problem complicated (or even wrong). When lookback=1, the function is simply equivalent to: dataX = dataset:len(dataset)-lookback, dataY = datasetlookback:. When lookback is larger than 1, the function is wrong: after each iteration, dataX is appended by more than 1 data, but dataY is appended by just 1 data. Finally, dataX will be lookback times larger than dataY. Is that what createdataset supposed to do? Def createdataset(dataset, lookback=1): dataX, dataY = for i in range(len(dataset)-lookback-1): a = dataseti:(i+lookback), 0 dataX.append(a) dataY.append(dataseti + lookback, 0) return numpy.array(dataX), numpy.array(dataY). Thanks for your great article!

I have a question that when I use the model “Stacked LSTMs With Memory Between Batches” with my own data, I found that cpu is much faster than gpu. May data contains many files and each files’ size is about 3M. I put each file into the model to trian one by one. I guess that the data is too small so the gpu is useless, but I can’t sure. I use thano backend and I can sure that the type of the data is float32. So I want to know what reason would make this happen, or the only reason is the data too small?

Thank you very much and best wishes to you. Hi, Great article on LSTM and keras. I was really struggling with this, until I read through your examples.

Now I have a much better understanding and can use LSTM on my own data. One thing I’d like to point out. The reuse of trainY and trainX on lines 55 & 57. Line 55 trainY = scaler.inversetransform(trainY) This confused me a lot, because the model can’t run fit or predict again, after this is done. I was struggling to understand why it could not do a second predict or fit. Until i very carefully read each line of code. I think renaming the above variables would make the example code clearer.

Unless I am missing something. And being a novice programmer that’s very possible. Thanks again for the great work. I’m a total newbie to Keras and LSTM and most things NN, but if you’ll excuse that, I’d like to run this idea past you just to see if I’m talking the same language let alone on the same page: I’m interested in time-series prediction, mostly stocks / commodities etc, and have encountered the same problem as others in these comments, namely, how is it prediction if it’s mostly constrained to within the time-span for which we already have data? With most ML algorithms I could train the model and implement a shuffle, ie get the previous day’s prediction for today and append it in the input-variable column, get another prediction, repeat. The worst that would happen is a little fudge around the last day in the learning dataset.

That seems rather laborious if we want to predict how expensive gold is going to be in 6 months’ time. (Doubly so, since in other worlds (R + RSNNS + elman or jordan), the prediction is bound-up with training so a prediction would involve rebuilding the entire NN for every day’s result, but we digress.) I saw somewhere Keras has a notion of “masking”, assigning a dummy value that tells the training the values are missing. Would it be possible to use this with LSTM, just append a bunch of 180 mask zeroes, let it train itself on this and then use the testing phase to impute the last values, thereby filling in the blanks for the next 6 months? It would also be possible to run an ensemble of these models and draw a pretty graph similar to arima.predict with varying degrees of confidence as to what might happen. Dear Jason, I am trying to implement your code in order to make forecasting on a time-series that i am receiving from a server. My only problem is that the length of my dataset is continuously increasing. Is there any way to read the last N rows from my csv file?

What changes do i have to make in code below in order to succeed it. Def createdataset(dataset, lookback=1): dataX, dataY = for i in range(len(dataset)-lookback-1): a = dataseti:(i+lookback), 0 dataX.append(a) dataY.append(dataseti + lookback, 0) return numpy.array(dataX), numpy.array(dataY) # fix random seed for reproducibility numpy.random.seed(7) # load the dataset dataframe = pandas.readcsv(‘timeseries.csv’, usecols=1, engine=’python’, skipfooter=3) dataset = dataframe.values dataset = dataset.astype(‘float32’).

Hi Jason, Thanks for your great content. As you did i upgraded to Keras 1.1.0 and scikit-learn v0.18.

However i run Theano v.0.9.0dev3 as im on Windows 10. Also im on Anaconda 3.5. (installed from this article: ) Your examples run fine on my setup – but i seem to be getting slightly different results. For eamples in your first example: # LSTM for international airline passengers problem with window regression framing – i get: Train Score: 22.79 RMSE Test Score: 48.80 RMSE Should i be getting exact the same results as in your tutorial? If yes, any idea what i should be looking at changing? Best regards Soren.

The Project Gutenberg eBook of The Personal History of David Copperfield, by Charles Dickens The Project Gutenberg eBook, The Personal History of David Copperfield, by Charles Dickens, Illustrated by H. Browne This eBook is for the use of anyone anywhere at no cost and with almost no restrictions whatsoever. I do not find it easy to get sufficiently far away from this Book, in the first sensations of having finished it, to refer to it with the composure which this formal heading would seem to require. My interest in it, is so recent and strong; and my mind is so divided between pleasure and regret—pleasure in the achievement of a long design, regret in the separation from many companions—that I am in danger of wearying the reader whom I love, with personal confidences, and private emotions.

Besides which, all that I could say of the Story, to any purpose, I have endeavoured to say in it. It would concern the reader little, perhaps, to know, how sorrowfully the pen is laid down at the close of a two-years’ imaginative task; or how an Author feels as if he were dismissing some portion of himself into the shadowy world, when a crowd of the creatures of his brain are going from him for ever. Yet, I have nothing else to tell; unless, indeed, I were to confess (which might be of less moment still) that no one can ever believe this Narrative, in the reading, more than I have believed it in the writing. Instead of looking back, therefore, I will look forward.

I cannot close this Volume more agreeably to myself, than with a hopeful glance towards the time when I shall again put forth my two green leaves once a month, and with a faithful remembrance of the genial sun and showers that have fallen on these leaves of David Copperfield, and made me happy. London, October, 1850. Contents 1 I AM BORN. 10 I OBSERVE. 21 I HAVE A CHANGE.

33 I FALL INTO DISGRACE. 46 I AM SENT AWAY FROM HOME. 59 I ENLARGE MY CIRCLE OF ACQUAINTANCE. 65 MY “FIRST HALF” AT SALEM HOUSE. 78 MY HOLIDAYS. ESPECIALLY ONE HAPPY AFTERNOON. 88 I HAVE A MEMORABLE BIRTHDAY.

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97 I BECOME NEGLECTED, AND AM PROVIDED FOR. 111 I BEGIN LIFE ON MY OWN ACCOUNT, AND DON’T LIKE IT. 122 LIKING LIFE ON MY OWN ACCOUNT NO BETTER, I FORM A GREAT RESOLUTION. 129 THE SEQUEL OF MY RESOLUTION. 143 MY AUNT MAKES UP HER MIND ABOUT ME. 154 I MAKE ANOTHER BEGINNING.

161 I AM A NEW BOY IN MORE SENSES THAN ONE. 176 SOMEBODY TURNS UP. 188 A RETROSPECT. 193 I LOOK ABOUT ME, AND MAKE A DISCOVERY. 205 STEERFORTH’S HOME.

211 LITTLE EM’LY. 225 SOME OLD SCENES, AND SOME NEW PEOPLE. 240 I CORROBORATE MR. DICK, AND CHOOSE A PROFESSION. 251 MY FIRST DISSIPATION. 257 GOOD AND BAD ANGELS. 271 I FALL INTO CAPTIVITY.

283 TOMMY TRADDLES. MICAWBER’S GAUNTLET. 303 I VISIT STEERFORTH AT HIS HOME, AGAIN. 314 A GREATER LOSS. 321 THE BEGINNING OF A LONG JOURNEY.

334 BLISSFUL. 346 MY AUNT ASTONISHES ME. 353 DEPRESSION. 367 ENTHUSIASM. 379 A LITTLE COLD WATER. 385 A DISSOLUTION OF PARTNERSHIP. 397 WICKFIELD AND HEEP.

411 THE WANDERER. 417 DORA’S AUNTS. 428 MISCHIEF. 443 ANOTHER RETROSPECT.

449 OUR HOUSEKEEPING. DICK FULFILS MY AUNT’S PREDICTION. 471 INTELLIGENCE.

489 DOMESTIC. 497 I AM INVOLVED IN MYSTERY. PEGGOTTY’S DREAM COMES TRUE. 513 THE BEGINNING OF A LONGER JOURNEY. 525 I ASSIST AT AN EXPLOSION. 541 ANOTHER RETROSPECT. MICAWBER’S TRANSACTIONS.

564 THE NEW WOUND, AND THE OLD. 569 THE EMIGRANTS. 600 I AM SHOWN TWO INTERESTING PENITENTS. 609 A LIGHT SHINES ON MY WAY. 615 A VISITOR. 621 A LAST RETROSPECT. Whether I shall turn out to be the hero of my own life, or whether that station will be held by anybody else, these pages must show.

To begin my life with the beginning of my life, I record that I was born (as I have been informed and believe) on a Friday, at twelve o’clock at night. It was remarked that the clock began to strike, and I began to cry, simultaneously. In consideration of the day and hour of my birth, it was declared by the nurse, and by some sage women in the neighbourhood who had taken a lively interest in me several months before there was any possibility of our becoming personally acquainted, first, that I was destined to be unlucky in life; and secondly, that I was privileged to see ghosts and spirits; both these gifts inevitably attaching, as they believed, to all unlucky infants of either gender, born towards the small hours on a Friday night. I need say nothing here, on the first head, because nothing can show better than my history whether that prediction was verified or falsified by the result.

On the second branch of the question, I will only remark, that unless I ran through that part of my inheritance while I was still a baby, I have not come into it yet. But I do not at all complain of having been kept out of this property; and if anybody else should be in the present enjoyment of it, he is heartily welcome to keep it.

I was born with a caul, which was advertised for sale, in the newspapers, at the low price of fifteen guineas. Whether sea-going people were short of money about that time, or were short of faith and preferred cork-jackets, I don’t know; all I know is, that there was but one solitary bidding, and that was from an attorney connected with the bill-broking business, who offered two pounds in cash, and the balance in sherry, but declined to be guaranteed from drowning on any higher bargain. Consequently the advertisement was withdrawn at a dead loss—for as to sherry, my poor dear mother’s own sherry was in the market then—and ten years afterwards the caul was put up in a raffle down in our part of the country, to fifty members at half-a-crown a head, the winner to spend five shillings. I was present myself, and I remember to have felt quite uncomfortable and confused, at a part of myself being disposed of in that way. The caul was won, I recollect, by an old lady with a hand-basket, who, very reluctantly, produced from it the stipulated five shillings, all in halfpence, and twopence halfpenny short—as it took an immense time and a great waste of arithmetic, to endeavour without any effect to prove to her. It is a fact which will be long remembered as remarkable down there, that she was never drowned, but died triumphantly in bed, at ninety-two. I have understood that it was, to the last, her proudest boast, that she never had been on the water in her life, except upon a bridge; and that over her tea (to which she was extremely partial) she, to the last, expressed her indignation at the impiety of mariners and others, who had the presumption to go “meandering” about the world.

It was in vain to represent to her that some conveniences, tea perhaps included, resulted from this objectionable practice. She always returned, with greater emphasis and with an instinctive knowledge of the strength of her objection, “Let us have no meandering.” Not to meander, myself, at present, I will go back to my birth. I was born at Blunderstone, in Suffolk, or “thereby,” as they say in Scotland. I was a posthumous child. My father’s eyes had closed upon the light of this world six months, when mine opened on it. There is something strange to me, even now, in the reflection that he never saw me; and something stranger yet in the shadowy remembrance that I have of my first childish associations with his white grave-stone in the church-yard, and of the indefinable compassion I used to feel for it lying out alone there in the dark night, when our little parlor was warm and bright with fire and candle, and the doors of our house were—almost cruelly, it seemed to me sometimes—bolted and locked against it.