As an introduction to RNN/LSTM (stateless) I'm training a model with sequences of 200 days of previous data (X), including things like daily price change, daily volume change, etc and for the labels/Y I have the % price change from current price to that in 4 months. Basically I want to estimate the market direction, not to be 100% accurate. But I'm getting some odd results...
When I then test my model with the training data, I notice the output from the model is a perfect fit when compared to the actual data, it just lags by exactly 4 months:
When I shift the data by 4 months, you can see it's a perfect fit.
I can obviously understand why the training data would be a very close fit as it has seen it all during training - but why the 4 months lag?
It does the same thing with the validation data (note the area I highlighted with the red box for future reference):
Time-shifted:
It's not as close-fitting as the training data, as you'd expect, but still too close for my liking - I just don't think it can be this accurate (see the little blip in the red rectangle as an example). I think the model is acting as a naive predictor, I just can't work out how/why it's possibly doing it.
To generate this output from the validation data, I input a sequence of 200 timesteps, but there's nothing in the data sequence that says what the %price change will be in 4 months - it's entirely disconnected, so how is it so accurate? The 4-month lag is obviously another indicator that something's not right here, I don't know how to explain that, but I suspect the two are linked.
I tried to explain the observation based on some general underlying concept:
If you don't provide a time-lagged X input dataset (lagged t-k where k is the time steps), then basically you will be feeding the LSTM with like today's closing price to predict the same today's closing price..in the training stage. The model will (over fit) and behave Exactly as the answer is known already (data leakage)
If the Y is the predicted percentage change (ie. X * (1 + Y%) = 4 months future price), the present value Yvalue predicted really is just the future discounted by the Y%
so the predicted value will have 4 months shift
Okay, I realised my error; the way I was using the model to generate the forecast line was naive. For every date in the graph above, I was getting an output from the model, and then apply the forecasted % change to the actual price for that date - that would give predicted price in 4 months' time.
Given the markets usually only move within a margin of 0-3% (plus or minus) over a 4 month period, that would mean my forecasts was always going to closely mirror the current price, just with a 4 month lag.
So at every date the predicted output was being re-based, so the model line would never deviate far from the actual; it'd be the same, but within a margin of 0-3% (plus or minus).
Really, the graph isn't important, and it doesn't reflect the way I'll use the output anyway, so I'm going to ditch trying to get a visual representation, and concentrate on trying to find different metrics that lower the validation loss.
Related
TL;DR:
Can I get Grafana to show me the previous data point, when the currently selected time period does not have a data point? I have an example which sounds ridiculous, but at least it's simple to understand: I send data every 1 minute, and I wish to zoom into the last 30 seconds, and still see data. You may ask "why not just zoom out to 2 minutes" but the reason is that other data is on the same graph that has updated more often, and I wish to compare with that data. Also, for the more lengthy reasons below.
If not, how can I achieve what I want to achieve, see below?
Context
For a few years, I have been monitoring the water level in three of our basement sumps (which have pumps installed) by sending this data from Node-RED to InfluxDB, then visualising the sump levels in Grafana. I have set up three waterproof ultrasonic distance sensors, each pointed down a pipe that is inserted vertically into each sump. The water fills the pipe and the distance sensor, connected to an Arduino, sends me the reading. The Arduino also has other sensors connected (temp / humidity) and deals with distance calibrations to calculate the percent full of each sump. All this data is sent to Node-RED. In total, I am sending 4 values per sump: distance measurement in mm, percent full, temp, humidity. So that's 12 fields. Data is sent every 2 seconds, because I wished to have a reasonably high resolution to see nice curves in graphs.
Also I decided to store all this data so that I could later troubleshoot issues (we have had sewage floods resulting in water not being able to be pumped away, etc...) and design some warning systems for these issues based on data.
Storing 12 values for every 2 seconds, over the course of a number of years, takes up a lot of space (8GB).
Nature of the data
Storing this resolution of data has also helped me be able to describe the nature of the data. I will do so here.
(1) Non-meaningful NOISE (see below) - the percent-full reading goes up and down by 1 or 2 percent every couple of seconds:
(2) Meaningful DRIFT (see below) - I don't mean sensor drift, I am referring to actual water levels changing slowly over time, e.g. over 1 day or 1 week. Perhaps condensation on the walls drips down into the sump, or water evaporates from the sump, and the value can waver by a few percent over the course of a day. Each sump has slightly different characteristics.
(3) Meaningful MONITORING DATA - during wet weather, depending on rainfall amount, the sumps fill up over the course of say 30 mins to 3 hours. Then the pumps run and the water level drops again, wavers a bit, then the sumps continue to fill up. If the rain stopped, you can see a lovely curve as the water fills in progressively more slowly (see the green line below):
Solution to downsample
I know Influx has its own downsampling possibilities, however because of the nature of the data (which can hardly vary for 2 months but when it does, I really need to capture it in detail), I don't think lowering the sample rate is a great idea.
I have some understanding of digital filters (e.g. low pass etc) but have never programmed one myself. So I have written a basic filter in javascript (a Node-RED function) to filter the data in realtime as follows: only send each reading when it has changed from the previous one by x amount. (And update the previous one, when that occurs.)
This has already vastly reduced the amount of data being stored, and I can vary x to filter out noise shown in my first graph above, at the expense of resolution when the pumps run. Even if I set the x value to 2, it still vastly reduces data over long periods of dry weather.
So - onto my problem! Now data is not being logged to InfluxDB unless there is some meaningful change. Which means that when I zoom in to e.g. 15 minute timeframe of data, there is nothing to see.
Grafana does have the option of "fill (previous)" but this draws a line between points on the existing graph, rather than showing the previous data as if it hasn't changed since that point. Now my grafana dashboard looks a bit sad :(
One proposed solution is, in addition to sending "delta" data, send "summary" data, that is - send a full suite of data every 1 minute regardless of whether data changed or not. But then we get noise back again, and pointless storage.
Any other ideas?
I would like to use the day of the year in a machine learning model. As the day of the year is not continuous (day 365 of 2019 is followed by day 1 in 2020), I think of performing cyclic (sine or cosine) transformation, following this link.
However, in each year, there are no unique values of the new transformed variable; for example, two values for 0.5 in the same year, see figures below.
I need to be able to use the day of the year in model training and also in prediction. For a value of 0.5 in the sine transformation, it can be on either 31.01.2019 or 31.05.2019, then using 0.5 value can be confusing for the model.
Is it possible to make the model to differentiate between the two values of 0.5 within the same year?
I am modelling the distribution of a species using Maxent software. The species data is continuous every day in 20 years. I need the model to capture the signal of the day or the season, without using either of them explicitly as categorical variable.
Thanks
EDIT1
Based on furcifer's comment below. However, I find the Incremental modelling approach not useful for my application. It solves the issue of consistent difference between subsequent days; e.g. 30.12.2018, 31.12.2018, and 01.01.2019. But it does not differ than counting the number of days from a certain reference day (weight = 1). Having much higher values on the same date for 2019 than 2014 does not make ecological sense. I hope that interannual changes to be captured from the daily environmental conditions used (explanatory variables). The reason for my need to use day in the model is to capture the seasonal trend of the distribution of a migratory species, without the explicit use of month or season as a categorical variable. To predict suitable habitats for today, I need to make this prediction not only depends on the environmental conditions of today but also on the day of the year.
This is a common problem, but I'm not sure if there is a perfect solution. One thing I would note is that there are two things that you might want to model with your date variable:
Seasonal effects
Season-independent trends and autocorrelation
For seasonal effects, the cyclic transformation is sometimes used for linear models, but I don't see the sense for ML models - with enough data, you would expect a nice connection at the edges, so what's the problem? I think the posts you link to are a distraction, or at least they do not properly explain why and when a cyclic transformation is useful. I would just use dYear to model the seasonal effect.
However, the discontinuity might be a problem for modelling trends / autocorrelation / variation in the time series that is not seasonal, or common between years. For that reason, I would add an absolute date to the model, so use
y = dYear + dAbsolute + otherPredictors
A well-tuned ML model should be able to do the rest, with the usual caveats, and if you have enough data.
This may not the right choice depending on your needs, there are two choices that comes to my mind.
Incremental modeling
In this case, the dates are modeled in a linear fashion, so say 12 Dec, 2018 < 12, Dec, 2019.
For this you just need some form of transformation function that converts dates to numeric values.
As there are many dates that need to be converted to numeric representation, the first thing to make sure is that the output list also has the same order as Lukas mentioned. The easiest way to do this is by adding weight to each unit (weight_year > weight_month > weight_day).
def date2num(date_time):
d, m, y = date_time.split('-')
num = int(d)*10 + int(m)*100 + int(y)*1000 # these weights can be anything as long as
# they are ordered
return num
Now, it's important to normalize the numeric values.
import numpy as np
date_features = []
for d in list(df['date_time']):
date_features.append(date2num(d))
date_features = np.array(date_features)
date_features_normalized = (date_features - np.min(date_features))/(np.max(date_features) - np.min(date_features))
Using the day, month, year as separate features. So, instead of considering the date as whole, we segregate. The motivation is that maybe there will be some relations between the output and a specific date, month, etc. Like, maybe the output suddenly increases in the summer season (specific months) or maybe on weekends (specific days)
I'm writing a program to predict when will something happens. I don't know which activation function to get output in day of week (1-7).
I tried sigmoid function but i need to input the predicted day and it output probability of it, I don't want it to be this way.
I expect the activation function returning 0 to infinite, is ReLU the best activation function for this task?
EDIT:
also, what if i wanted output more than 7 days, for example, x will hapen in 9th day from today, or 15th day from today, etc? I'm looking for dynamic ways to do this
What you are trying to do is solving a classification problem with a regression approach. That's at least unconventional.
You can use any activation function you want and define your output as you want. E.g. linear, relu with output range from 1 to 7 or something between -1(or 0) and 1 like tanh or sigmoid and map the output (-1 -> 1; -0.3 -> 2; ...).
The problem for you will be that you get a floatingpoint number as a result. So your model not only has to learn how to classify correctly but also how to predict the (allmost) exact number you want in your output neuron. That makes the problem more complicated than it has to be. With a model like that it also will be likley that for some outlier datapoints you might get unexpected return values like 0, -1 or 8. What do you do then?
To sum it up: Listen to #venkata krishnan, use softmax and seven output neurons and map this result to a number between 1 and 7 outside the neural network if you have to.
EDIT
What comes to my mind after reading the comments again would be a mix of what you want and what you should do.
You could try to make the second last layer a 7 neuron softmax layer and map those output to a single neuron in the last layer.
Niether did i ever try that nor have i ever read about something like that so i can't tell you if thats a good idea, likely not, but you might consider it worth a try.
I want to add onto the point of #venkata krishnan, which raises a valid point in your problem setting. You will find an answer to your original question further down, but I strongly suggeste you read the following comment first.
Generally, you want to discern between categorical, ordinal and interval variables. I have given a relatively lengthy explanation in a different answer on Stackoverflow, it might be helpful to understand this concept in more detail.
In your scenario, you mostly want to have an understanding of "how wrong" you are. Of course, it is perfectly reasonable to assume what you are doing and interpret it as a interval variable, and therefore have an assumed ordering (and a distance) between different values.
What is problematic, though, is the fact that you are assuming a continuous space on a discrete variable. E.g., it does not make any sense to interpret the output of 4.3, since you can only tell between 4 (Friday, assuming you start numbering your days at 0), or 5 (Saturday). Any value in between would have to be rounded, which is perfectly fine - until you want to perform backpropagation on this loss.
It is problematic, because you are essentially introducing a non-convex and non-continous function, no matter how you "round" your values. Again, to exemplify this, you could assume to round to the nearest number; then, at the value of 4.5, you would see a sudden increase in the loss, which is non-differentialbe, and will therefore put a hard time on your optimizer, potentially limiting convergence of your system.
If, instead, you utilize several output neurons, as suggested by #venkata krishnan, you might lose the information of distance (how many days you are off) on paper, but you can of course still interpret your loss in any way you like. This would certainly be the better option for a discrete-valued variable.
To answer your original question: I personally would make sure that your loss function is bounded both in the upper and lower level, as you could otherwise have undefined/inconsistent loss values, that might lead to subpar optimization. One way to do this is to re-scale a Sigmoid function (the co-domain of sigmoid(R) is [0,1]. Eventually, you can then just multiply your output by 6, to get a value range that is [0,6], and could (after rounding) cover all the values you want.
As far I know, there is no such thing like an activation function which will yield 0 to infinite. You can apply 7 output nodes with a "Softmax" activation function which will return the probability. There is another solution which may work. You can you 3 output nodes with "Binary" activation function which will return either 0 or 1. That means you can have 8 different outputs with only 3 nodes which are 000, 001, 010, 011, 100, 101, 110 and 111. You can use 7 of them.
I am trying to validate a district heating model I built using Dymola.
In this case, I am trying to find the mass flow during a year period. I have two models running. both with the same loads and pipes with same characteristics as this picture:
pipes
Both models are as follows:
models
My results are making sense at least regarding the time of the year my flow should be higher, I am getting very high values during January, February and March, then again by the end of the year.
However those high peaks are VERY different, the first model on the picture is giving me peaks of almost 400kg/s whereas the second one is reaching up to 70kg/s.
Can anyone suggest a way to validate the model? I have the heat loads for the year hour by hour (this is the input I am giving to Dymola), I know that the min temperature of the water is 70 and the max is 85 celsius.
But I am really struggling to validate my model. Any suggestions?
In the course of testing an algorithm I computed option prices for random input values using the standard pricing function blsprice implemented in MATLAB's Financial Toolbox.
Surprisingly ( at least for me ) ,
the function seems to return negative option prices for certain combinations of input values.
As an example take the following:
> [Call,Put]=blsprice(67.6201,170.3190,0.0129,0.80,0.1277)
Call =-7.2942e-15
Put = 100.9502
If I change time to expiration to 0.79 or 0.81, the value becomes non-negative as I would expect.
Did anyone of you ever experience something similar and can come up with a short explanation why that happens?
I don't know which version of the Financial Toolbox you are using but for me (TB 2007b) it works fine.
When running:
[Call,Put]=blsprice(67.6201,170.3190,0.0129,0.80,0.1277)
I get the following:
Call = 9.3930e-016
Put = 100.9502
Which is indeed positive
Bit late but I have come across things like this before. The small negative value can be attributed to numerical rounding error and / or truncation error within the routine used to compute the cumulative normal distribution.
As you know computers are not perfect and small numerical error always persists in all calculations, in my view therefore the question one should must ask instead is - what is the accuracy of the input parameters being used and therefore what is the error tolerance for outputs.
The way I thought about it when I encountered it before was that, in finance, typical annual stock price return variance are of the order of 30% which means the mean returns are typically sampled with standard error of roughly 30% / sqrt(N) which is roughly of the order of +/- 1% assuming 2 years worth of data (so N = 260 x 2 = 520, any more data you have the other problem of stationarity assumption). Therefore on that basis the answer you got above could have been interpreted as zero given the error tolerance.
Also we typically work to penny / cent accuracy and again on that basis the answer you had could be interpreted as zero.
Just thought I'd give my 2c hope this is helpful in some ways if you are still checking for answers!