# Two loops, one inside the other

I am developing my skills in programming by attacking the general construct of Markov chains and state space. My theory on the bridging between collective intelligence in human societies and artificial neural networks as simulators thereof is that both are intelligent structures. I assume that they learn by producing many alternative versions of themselves whilst staying structurally coherent, and they pitch each such version against a desired output, just to see how fit that particular take on existence is, regarding the requirements in place.

Mathematically, that learning-by-doing is a Markov chain of states, i.e. a sequence of complex states, described by a handful of variables, such that each consecutive state in the sequence is a modification of the preceding state, through a logically coherent σ-algebra. My so-far findings suggest that orienting the intelligent structure on specific outcomes, out of all those available, is crucial for the path of learning that structure takes. In other words, the general hypothesis I am sniffing around and digging into is that the way an intelligent structure learns is principally determined by the desired outcomes which the structure is after, more than by the exact basket of inputs it uses. Stands to reason, for a neural network: the thing optimises inputs so as to make it fit to the outcome it seeks to get as close to as possible.

As I am taking real taste in stepping out of my cavern, I have installed Anaconda on my computer, from https://www.anaconda.com/products/individual/download-success . When I use Anaconda, I use the same JupyterLab online functionality which I have been using so far, with one difference. Anaconda allows me to create a user account with JupyterLab, and to have all my work stored on that account. Probably, there are some storage limits, yet the thing is practical.

Anyway, I want to program in Python, just as I do it in Excel, intelligent structures able to emulate the collective intelligence of human societies. A basic finding of mine, in the so-far research, is that intelligent structures alter their behaviour significantly depending on the outcome they pursue. The initial landscape I start operating in is akin a junkyard of information. I go to the website of World Bank, for example, I mean the one with freely available data, AKA https://data.worldbank.org , and I start rummaging. Quality of life, size of economies, headcount of populations… What else? Oh, yes, there are things about education, energy consumption and whatnot. All that stuff just piled up nicely, each item easy to retrieve, and yet, how does it all make sense together? My take on the thing is that there is stuff going on, like all the time and everywhere. We are part of that ongoing stuff, actually. Out of that stream of happening, we perceptually single out phenomenological cuts , and we isolate those specific cuts because we are able to measure them with some kind of gauge. Data-driven observation of ourselves in the world is closely connected to our science of measuring and counting stuff. Have you noticed that a basic metric, i.e. how many of us is there around, can take a denominator of one – when we count the population of a city – or a denominator of 10 000, when we are interested in the incidence of criminality.

Each quantitative variable I can observe and download the dataset of from https://data.worldbank.org  comes out of that complex process of collective cognition, resembling a huge bunch of psychos walking around with rulers and abacuses, trying to measure everything they perceive. I use data as phenomenological description of both the reality those psychos (me included) live in, and the way they measure that reality. I want to check which among those quantitative variables are particularly suitable to represent the things we are really after, our collectively desired outcomes. The method I use to do it consists in producing as many variations of the original dataset as I have variables. Each variation of the original dataset has one variable singled out as output, and the remaining ones are input. I run such variation through a simple neural network – the simpler, the better – where standardised, randomly weighed and neurally activated input gets compared with the pre-set output. I measure the mean expected values of all the variables in such a transformation, i.e. when I run it through 3000 experimental rounds, I measure those means over the same 3000 rounds. I compute the Euclidean distance between each such vector of means and its cousin computed for the original dataset. I assume that, with rigorously the same logical structure of the neural network, those variations differ from each other just by the output variable they are pegged on. When I say ‘pegged’, by the way, I mean that the output variable is not subject to random weighing, i.e. it is not being experimented with. It comes exogenously, and is taken as it is.

I noticed that each time I do that procedure, with whatever set of variables I take, one or two among them, when taken as output ones, produce variations much closer to the original dataset that other, in terms of Euclidean distance. It looks as if the neural network, when pegged on those particular variables, emulated a process of adaptation particularly similar to what is represented by the original empirical data.

Now, I want to learn how to program, in Python, the production of alternative ‘input <> output’  couplings out of a source dataset. I already know the general drill for producing just one such coupling. Once I have my dataset read out of a CSV file into a Data Frame in Python Pandas, I start with creating a dictionary of all the numerical columns:

>> dict_numerical = [‘numerical_column1’, ‘numerical_column2’, …, ‘numerical column_n’]

A simple way of doing that, with large data frames, is to type in Python:

>> df.columns

… and it yields a string of labels in quotation marks ‘’, separated with commas. I just copy that lot , without the non-numerical columns, into the square brackets of dict_numerical = […], and Bob’s my uncle.

Then I make a strictly numerical version of my database, by:

>> df_numerical = pd.DataFrame(df[dict_numerical])

By the way, each time I produce a new data frame, I check its structure with commands ‘df.info()‘ and ‘df.describe()’. At my neophytic level of programming, I want to make sure that what I have in a strictly numerical database is strictly numerical data, i.e. the ‘float64’ type. Here, one hint: when you convert your data from an original Excel file, pay attention to having your decimal point as a point, i.e. as ‘0.0’, not as a comma. With a comma, the Pandas reader tends to interpret such data by default as ‘object’. Annoying.

Once I have that numerical data frame in place, I make another dictionary of the type:

>> dict_for_Input_pegged_on_X_as_output = [‘numerical_input_column1’, ‘numerical_input_column2’, …, ‘numerical_input_column_k’]

… where k = n -1, of course, and the 1 corresponds to the variable X, supposed to be the output one.

I use that dictionary to split df_numerical:

>> df_output_X = df_numerical[‘numerical_column_X’]

>> df_input_for_X = df_numerical[dict_for_Input_pegged_on_X_as_output]

I would like to automatise the process. It means I need a loop. I am looping over a range of numerical columns df_numerical. Let’s dance. I start routinely, in my Anaconda-Jupyter Lab-powered notebook. By the way, I noticed an interesting practical feature of Jupyter Lab. When you start it directly from its website https://jupyter.org , the notebook you can use has somehow limited functionality as compared to the notebook you can create when accessing Jupyter Lab from the Anaconda app on your computer. In the latter case you can create an account with Jupyter Lab, with a very useful functionality of mirroring the content of your cloud account on your hard drive. I know, I know: we use the cloud so as not to collect rubbish on our own disk. Still, Python files are small, they take little space, and I discovered that this mirroring stuff is really useful.

I open up with importing the libraries I think I will need:

>> import numpy as np

>> import pandas as pd

>> import math

>> import os

As I am learning new stuff, I prefer taking known stuff as my data. Once again, I use a dataset which I made out of Penn Tables 9.1., by kicking out all the rows with empty cells [see: Feenstra, Robert C., Robert Inklaar and Marcel P. Timmer (2015), “The Next Generation of the Penn World Table” American Economic Review, 105(10), 3150-3182, www.ggdc.net/pwt ].

I already have that dataset in my working directory. By the way, when you install Anaconda on a MacBook, its working directory is by default the root directory of the user’s profile. For the moment, I keep ip that way. Anyway, I have that dataset and I read it into a Pandas dataframe:

I create my first dictionaries. I type:

>> PWT.columns

… which yields:

Index([‘country’, ‘year’, ‘rgdpe’, ‘rgdpo’, ‘pop’, ’emp’, ’emp / pop’, ‘avh’,

‘hc’, ‘ccon’, ‘cda’, ‘cgdpe’, ‘cgdpo’, ‘cn’, ‘ck’, ‘ctfp’, ‘cwtfp’,

‘rgdpna’, ‘rconna’, ‘rdana’, ‘rnna’, ‘rkna’, ‘rtfpna’, ‘rwtfpna’,

‘labsh’, ‘irr’, ‘delta’, ‘xr’, ‘pl_con’, ‘pl_da’, ‘pl_gdpo’, ‘csh_c’,

‘csh_i’, ‘csh_g’, ‘csh_x’, ‘csh_m’, ‘csh_r’, ‘pl_c’, ‘pl_i’, ‘pl_g’,

‘pl_x’, ‘pl_m’, ‘pl_n’, ‘pl_k’],

dtype=’object’)

…and I create the dictionary of quantitative variables:

>> Variables=[‘rgdpe’, ‘rgdpo’, ‘pop’, ’emp’, ’emp / pop’, ‘avh’,

‘hc’, ‘ccon’, ‘cda’, ‘cgdpe’, ‘cgdpo’, ‘cn’, ‘ck’, ‘ctfp’, ‘cwtfp’,

‘rgdpna’, ‘rconna’, ‘rdana’, ‘rnna’, ‘rkna’, ‘rtfpna’, ‘rwtfpna’,

‘labsh’, ‘irr’, ‘delta’, ‘xr’, ‘pl_con’, ‘pl_da’, ‘pl_gdpo’, ‘csh_c’,

‘csh_i’, ‘csh_g’, ‘csh_x’, ‘csh_m’, ‘csh_r’, ‘pl_c’, ‘pl_i’, ‘pl_g’,

‘pl_x’, ‘pl_m’, ‘pl_n’, ‘pl_k’]

The ‘Variables’ dictionary serves me to mutate the ‘PWT’ dataframe into its close cousin, obsessed with numbers, namely into ‘PWT_Numerical’:

>> PWT_Numerical = pd.DataFrame(PWT[Variables])

I quickly check the PWT_Numerical’s driving licence, by typing ‘PWT_Numerical.info()’ and  ‘PWT_Numerical.shape’. All is well, data is in the ‘float64’ format, there are 42 columns and 3006 rows, the guy is cleared to go.

Once I have that nailed down, I mess around a bit with creating names for my cloned datasets. I practice with the following loop:

>> for i in range(42):

print(“Input_for_”+PWT_Numerical.iloc[:,i].name)

It yields a list of names for input databases in various ‘input <> output’ configurations of my experiment with the PWT 9.1 dataset. The ‘print’ command gives a string of 42 names: Input_for_rgdpe, Input_for_rgdpo, Input_for_pop etc.

In my next step, I want to make that outcome durable. The ‘print’ command just prints the output of the loop, it does not store it in any logical structure. The output is gone as soon as it is printed. I create a loop that makes a dictionary, this time with names of output data frames:

>> Names_Output_Data=[] # Here, I create an empty dictionary

>> for i in range(42): # I design the loop

>> Name_Output_Data=PWT_Numerical.iloc[:,i].name # I create a mechanism for generating strings to fill the dictionary up.

>> Names_Output_Data.append(Name_Output_Data) # This is the mechanism of appending   the dictionary with names generated in the previous command

I check the result by typing the name of the dictionary – ‘Names_Output_Data’ – and executing (Shift + Enter in Jupyter Lab). It yields a full dictionary, filled with column names from PWT_Numerical

Now,  pass to designing my Markov chain of states, i.e. into making an intelligent structure, which produces many alternative versions of itself and tests them for fitness to meet a pre-defined desired outcome. In my neophyte’s logic, I see it as two loops, one inside the other.

The big, external loop is the one which clones the initial ‘PWT_Numerical’ into pairs of data frames of the style: ’Input variables’ plus ‘Output variable’. I make as many such cloned pairs as there are numerical variables in PWT_Numerical, i.e. 42. Thus, my loop opens up as ‘for i in range(42):’. Inside each iteration of that loop, there is an internal loop of passing the input variables  through a very simple perceptron, assessing the error in estimating the output variable, and then feeding the error forward. Now, I will present below the entire code for those two loops, and then discuss what works, what doesn’t, and what I have no idea how to check whether it works or not. The code is grammatically correct in Python, i.e. it does not yield any error message when put to execution (Shift + Enter in JupyterLab, by the way).  After I present the entire code, I will discuss, further below, its particular parts. Anyway, here it is:

>> List_of_Output_DB=[]

>>Names_Output_Data=[]

>>MEANS=[]

>> Source_means=np.array(PWT_Numerical.mean())

>> EUC=[]

>>for i in range(42):

>> Name_Output_Data=PWT_Numerical.iloc[:,i].name

>> Names_Output_Data.append(Name_Output_Data)

>> Output=pd.DataFrame(PWT_Numerical.iloc[:,i])

>> Mean=Output.mean()

>> MEANS.append(Mean)

>> Input=pd.DataFrame(PWT_Numerical.drop(Output,axis=1))

>> Input_STD=pd.DataFrame(Input/Input.max(axis=0))

>> ER=[]

>> Transformed=[]

>> for j in range(30):

>> Input_STD_randomized=Input.iloc[j]*np.random.rand(41)

>> Input_STD_summed=Input_STD_randomized.sum(axis=0)

>> T=math.tanh(Input_STD_summed)

>> D=1-(T**2)

>> E=(Output.iloc[j]-T)*D

>> E_vector=np.array(np.repeat(E,41))

>> Next_row_with_error=Input_STD.iloc[j+1]+E_vector

>> Next_row_DESTD=Next_row_with_error*Input.max(axis=0)

>> ER.append(E)

>> ERROR=pd.DataFrame(ER)

>> Transformed.append(Next_row_DESTD)

>> CLONE=pd.DataFrame(Transformed).mean()

>> frames=[CLONE,MEANS[i]]

>> CLONE_Means=np.array(pd.concat(frames))

>> Euclidean=np.linalg.norm(Source_means-CLONE_Means)

>> EUC.append(Euclidean)

>> print(‘Finished’)

Here is a shareable link to my Python file with that code inside: http://localhost:8880/lab/tree/Practice%20Dec%208%202020.ipynb  . I hope it works.

I start explaining this code casually, from its end. This is a little trick I discovered as regards looping on datasets. Looping takes time and energy. In my struggles to learn Python, I have already managed to make a loop which kept looping forever. All I did was to call the loop as ‘for i in range PWT.index:’, without putting any ‘break’ command at the end. Yes, the index of a data frame is a finite number, yet it is also a sequence. When you don’t break explicitly the looping over that sequence, it will loop over and over again.

Anyway, the trick. I put the command ‘print(‘Finished’)’ at the very end of the code, after all the loops. When the thing is done with being an intelligent structure at work, it simply prints ‘Finished’ in the next line. Among other things, it allows me to count the time it needs to deal with a given amount of data. As you might have already noticed, whilst I have a dataset with index = 3005 rows, I made the internal loop of the code to go just over 30 rows: ‘for j in range (30)’. The code took some 4 seconds in total to create 42 big loops (‘for i in range (42)’) , and then to loop over 30 rows of data inside each of them. It gives like 42*30 = 1260 experimental rounds in 10 seconds, thus something like 0,0079 seconds per one round. If I took the full dataset of 3005 rows, it would be like 42*3000*0,0079 = 1000 seconds, i.e. 16,6666 minutes. Satanic. I like it.

Before opening each level of looping, I create empty lists. You can see:

>> List_of_Output_DB=[]

>>Names_Output_Data=[]

>>MEANS=[]

>> Source_means=np.array(PWT_Numerical.mean())

>> EUC=[]

… before I open the external loop, and…

>> ER=[]

>> Transformed=[]

… before the internal loop.

I noticed that I create those empty lists in a loop, essentially. This is more than just a play on words. When I code a loop, I have output of the loop. The loop does something, and as it does, I discover I want to store that particular outcome in some kind of repository vessel, and I go back to the lines of code before the loop opens and I add an empty list, just in case. I come up with a smart name for the   list, e.g. MEANS, which stands for the mean values of numerical variables, such as they are after being transformed by the perceptron. Mathematically, it is the most basic representation of expected state in a particular transformation of the source dataset “PWT’.

I code it as ‘MEANS=[]’, and, once I have done that, I add a mechanism of updating a list, inside the loop. This, in turn, goes in two steps. First, I code the variable which should be stored in that list. In the case of ‘MEANS’, as this list is created before I open the big loop of 42 ‘input <> output’ mutations, I append it in that loop. Logically, is must be appended with the mean expected values of output variables in each instance of the big loop. I code it in the big loop, and before opening the internal loop, as:

>> Output=pd.DataFrame(PWT_Numerical.iloc[:,i])  # Here, I define the data frame for the output variable in this specific instance of the big loop

>> Mean=Output.mean() # Now, I define the function to generate values, which later append the ‘MEANS’ list

>> MEANS.append(Mean) # Finally, I append the ‘MEANS’ list with values generated in the previous line of the code.

It is a good thing for me to write about the things I do. I have just noticed that I use two different methods of storing partial outcomes of my loops. The first one is the one I have just presented. The second one is visible in the part of code presented below, included in the internal loop ‘for j in range(number of rows experimented with)’, range(30) in the occurrence tested.

In this situation, I need to store in some kind of repository the values of input variables transformed by the neural network, i.e. with local error from each experimental round fed forward to the next experimental round. I need to store the way my data looks under each possible orientation of the intelligent structure I assume it represents. I denote that data under the general name ‘Transformed’, and, before opening the internal loop, just at the end of the big external loop, I define an empty list: ‘Transformed=[]’, which is supposed to contain those values I want.

In other words, when I structure the big external loop, I go like:

# Step 1: for each variables in the dataset, i.e. ‘for i in range(number of variables)’, split the overall dataset into into this variable as the output, in a separate data frame, and all the other variables grouped separately as input. These are the lines of code:

>> Output=pd.DataFrame(PWT_Numerical.iloc[:,i])  # I define the output variable

[…]

>> Input=pd.DataFrame(PWT_Numerical.drop(Output,axis=1)) # I drop the output from the entire dataset and I group the remaining columns as ‘Input’

# Step 2: I standardise the input data by denominating it over the respective maximums for each variable:

>> Input_STD=pd.DataFrame(Input/Input.max(axis=0))

# Step 3: I define, at the end of the big external loop, containers for data which I want to store from each round of the big loop:

>> ER=[] # This is the list of local errors generated by the perceptron when working with each ‘Input <> Output’ configuration

>> Transformed=[] # That’s the container for input data transformed by the perceptron

# Step 4: I open the internal loop, with ‘for j in range(number of rows to experiment with)’, and I start by coding the computational procedure of the perceptron:

>> Input_STD_randomized=Input.iloc[j]*np.random.rand(41) # I weigh each empirical, standardised value in this specific row with a random weight

>> Input_STD_summed=Input_STD_randomized.sum(axis=0) # I sum the randomised values from that specific row of input. This line of code together with the preceding one are equivalent to the mathematical structure ‘∑x*random’.

>> T=math.tanh(Input_STD_summed) # I compute the hyperbolic tangent of summed, randomised input data

>> D=1-(T**2) # I compute the local first derivative of the hyperbolic tangent

>> E=(Output.iloc[j]-T)*D # I compute the error, as: (Expected Output minus Hyperbolic Tangent of Randomised Input) times local derivative of the Hyperbolic Tangent

>> E_vector=np.array(np.repeat(E,41)) # I create a NumPy array, with the error repeated as many times as there are input variables.

>> Next_row_with_error=Input_STD.iloc[j+1]+E_vector # I feed the error forward. In the next experimental row ‘j+1’, error from row ‘j’ is added to the value of each standardised input variable. This is probably the most elementary representation of learning: I include into my input for the next go the knowledge about what I f**ked up in the previous go. This line creates the transformed input data I want to store later on.

# Step 5: I collect and store information about the things my perceptron did to input data in the given j-th round of the internal loop:

>> Next_row_DESTD=Next_row_with_error*Input.max(axis=0) # I destandardise the data transformed by the perceptron. It is like translating the work of the perceptron, which operates on standardised values, back into the measurement scale proper to each variable. In a sense, I deneuralise that data.

>> ER.append(E) # I collect and store error in the ER list

>> ERROR=pd.DataFrame(ER) #I transform the ER list into a data frame, which I name ‘ERROR’. I do it a few times with different data, and, quite honestly, I do it intuitively. I already know that data frames defines in Pandas are somehow handier to do statistics with than lists defined in the basic code of Python. Just as honestly: I know too little yet about programming to know whether this turn of code makes sense at all.

>> Transformed.append(Next_row_DESTD) # I collect and store the destandardized, transformed input data in the ‘Transformed’ list.

# Step 6: I step out of both loops, and I start putting some order in the data I generated and collected. Stepping out of both loops means that in my code, the lines presented below have no indent. They all start at the left margin, just as the definition of the big external loop.

>> CLONE=pd.DataFrame(Transformed).mean() # I transform the ‘Transformed’ list into a data frame. Same procedure as two lines of code earlier, only now, I know why I do it. I intend to put together the mean values of destandardised input with the mean value of output, and I am going to do it by concatenation of data frames.

>> frames=[CLONE,MEANS[i]] # I define the data frames for concatenation. I put together mean values in the input variables, generated in this specific, i-th round of the big external loop, with the mean value of the output variable corresponding to the same i-th round. You can notice that in the full code, such as I presented it earlier in this update, at this verse of code I move back by one indent. In other words, this definition is already outside of the internal loop, and still inside the big external loop.

>> CLONE_Means=np.array(pd.concat(frames)) # I concatenate the data I defined in the previous line.

>> Euclidean=np.linalg.norm(Source_means-CLONE_Means) # Something I need for my science. I estimate the mathematical similarity between the source data set ‘PWT_Numerical’, and the data set created by the perceptron, in the given i-th round of the big external loop. I do it by computing the Euclidean distance between the respective vectors of mean expected values in this specific pair of datasets, i.e. the pair ‘source vs i-th clone’.

>> EUC.append(Euclidean) # I collect and store information generated in the ‘Euclidean’ line. I store it in the EUC list, which I opened as empty before starting the big external loop.

# One step out of the cavern

I have made one step further in my learning of programming. I finally have learn’t at least one method of standardising numerical values in a dataset. In a moment, I will show what exact method did I nail down. First, I want to share a thought of more general nature. I learn programming in order to enrich my research on the application of artificial intelligence for simulating collective intelligence in human societies. I have already discovered the importance of libraries, i.e. ready-made pieces of code, possible to call with a simple command, and short-cutting across many verses of code which I would have to write laboriously. I mean libraries such as NumPy, Pandas, Math etc. It is very similar to human consciousness. Using pre-constructed cognitive structures, i.e. using language and culture is a turbo boost for whatever we do of things that humans are supposed to do when being a civilisation.

Anyway, I kept working with the dataset which I had already mentioned in my earlier updates, namely a version of Penn Tables 9.1., cleaned of all the rows with empty cells [see: Feenstra, Robert C., Robert Inklaar and Marcel P. Timmer (2015), “The Next Generation of the Penn World Table” American Economic Review, 105(10), 3150-3182, www.ggdc.net/pwt ]. Thus I started by creating an online notebook at JupyterLab (https://jupyter.org/try), with Python 3 as its kernel. Then I imported what I needed from Python in terms of ready-cooked culture, i.e. I went:

>> import numpy as np

>> import pandas as pd

>> import os

I uploaded the ‘PWT 9_1 no empty cells.csv’ file from my computer, and, just in case, I checked its presence in the working directory, with >> os.listdir(). I read the contents of the file into a Pandas Data Frame, which spells: PWT = pd.DataFrame(pd.read_csv(‘PWT 9_1 no empty cells.csv’)). Worked.

In my next step, as I planned to mess up a bit with the columns of that dataset, I typed: PWT.columns. The thing nicely gave me back a list of columns, i.e. literally a list of labels in quotation marks [‘’]. I used that list to create a dictionary of columns with numerical values, and therefore the most interesting to me. I went:

>> Variables=[‘rgdpe’, ‘rgdpo’, ‘pop’, ’emp’, ’emp / pop’, ‘avh’,

‘hc’, ‘ccon’, ‘cda’, ‘cgdpe’, ‘cgdpo’, ‘cn’, ‘ck’, ‘ctfp’, ‘cwtfp’,

‘rgdpna’, ‘rconna’, ‘rdana’, ‘rnna’, ‘rkna’, ‘rtfpna’, ‘rwtfpna’,

‘labsh’, ‘irr’, ‘delta’, ‘xr’, ‘pl_con’, ‘pl_da’, ‘pl_gdpo’, ‘csh_c’,

‘csh_i’, ‘csh_g’, ‘csh_x’, ‘csh_m’, ‘csh_r’, ‘pl_c’, ‘pl_i’, ‘pl_g’,

‘pl_x’, ‘pl_m’, ‘pl_n’, ‘pl_k’]

The ‘Variables’ dictionary served me to make a purely numerical mutation of my dataset, namely: PWTVar=pd.DataFrame(PWT[Variables]).

I generated the fixed components of standardisation in my data, i.e. maximums, means, and standard deviations across columns in PWTVar. It looked like this:

>> Maximums=PWTVar.max(axis=0)

>> Means=PWTVar.mean(axis=0)

>> Deviations=PWTVar.std(axis=0)

The ‘axis=0’ part means that I want to generate those values across columns, not rows. Once that done, I made my two standardisations of data from PWTVar, namely: a) standardisation over maximums, like s(x) = x/max(x) and b) standardisation by mean-reversion, where s(x) = [x – avg(x)]/std(x)]. I did it as:

>> Standardized=pd.DataFrame(PWTVar/Maximums)

>> MR=pd.DataFrame((PWTVar-Means)/Deviations)

I used here the in-built function of Python Pandas, i.e. the fact that they automatically operate data frames as matrices. When, for example, I subtract ‘Means’ from ‘PWTVar’, the one-row matrix of ‘Means’ gets subtracted from each among the 3005 rows of ‘PWTVar’ etc. I checked those two data frames with commands such as ‘df.describe()’, ’df.shape’, and df.info(), just to make sure they are what I think they are. They are, indeed.

Standardisation allowed me to step out of my cavern, in terms of programming artificial neural networks. The next step I took was to split my numerical dataset PWTVar into one output variable, on the one hand, and all the other variables grouped as input. As output, I took a variable which, as I have already found out in my research, is extremely important in social change seen through the lens of Penn Tables 9.1. This is ‘avh’ AKA the average number of hours worked per person per year. I did:

>> Output_AVH=pd.DataFrame(PWTVar[‘avh’])

>> Input_dict=[‘rgdpe’, ‘rgdpo’, ‘pop’, ’emp’, ’emp / pop’, ‘hc’, ‘ccon’, ‘cda’,

‘cgdpe’, ‘cgdpo’, ‘cn’, ‘ck’, ‘ctfp’, ‘cwtfp’, ‘rgdpna’, ‘rconna’,

‘rdana’, ‘rnna’, ‘rkna’, ‘rtfpna’, ‘rwtfpna’, ‘labsh’, ‘irr’, ‘delta’,

‘xr’, ‘pl_con’, ‘pl_da’, ‘pl_gdpo’, ‘csh_c’, ‘csh_i’, ‘csh_g’, ‘csh_x’,

‘csh_m’, ‘csh_r’, ‘pl_c’, ‘pl_i’, ‘pl_g’, ‘pl_x’, ‘pl_m’, ‘pl_n’,

‘pl_k’]

#As you can see, ‘avh’ is absent from the ‘Input-dict’ dictionary

>> Input = pd.DataFrame(PWT[Input_dict])

The last thing that worked, in this episode of my learning, was to multiply the ‘Input’ dataset by a matrix of random float values generated with NumPy:

>> Randomized_input=pd.DataFrame(Input*np.random.rand(3006,41))

## Gives an entire Data Frame of randomized values

# It works again

I intend to work on iterations. My general purpose with learning to program in Python is to create my own algorithms of artificial neural networks, in line with what I have already done in that respect using just Excel. Iteration is the essence of artificial intelligence, to the extent that the latter manifests as an intelligent structure producing many alternative versions of itself. Many means one at a time over many repetitions.

When I run my neural networks in Excel, they do a finite number of iterations. That would be a Definite Iteration in Python, thus the structure based on the ‘for’ expression. I am helping myself  with the tutorial available at https://realpython.com/python-for-loop/ . Still, as programming is supposed to enlarge my Excel-forged intellectual horizons, I want to understand and practice the ‘while’ loop in Python, thus Indefinite Iteration (https://realpython.com/python-while-loop/ ).

Anyway, programming a loop is very different from looping over multiple rows of an Excel sheet. The latter simply makes a formula repeat over many rows, whilst the former requires defining the exact operation to iterate, the input domain which the iteration takes as data, and the output dataset to store the outcome of iteration.

It is time, therefore, to describe exactly the iteration I want to program in Python. As a matter of fact, we are talking about a few different iterations. The first one is the standardisation of my source data. I can use two different ways of standardising it, depending on the neural activation function I use. The baseline method is to standardise each variable over its maximum, and then it fits every activation function I use. It is standardised value of x, AKA s(x), being calculated as s(x) = x/max(x)

If I focus just on the hyperbolic tangent as activation function, I can use the first method, or I can standardise by mean-reversion, where s(x) = [x – avg(x)]/std(x). In a first step, I subtract from x the average expected value of x – this is the the [x – avg(x)] expression – and then I divide the resulting difference by the standard deviation of x, or std(x)

The essential difference between those two modes of standardisation is the range of standardised values. When denominated in units of the max(x), standardised values range in 0 ≥ std(x) ≥ 1. When I standardise by mean-reversion, I have -1 ≥ std(x) ≥ 1.

The piece of programming I start that specific learning of mine with consists in transforming my source Data Frame ‘df’ into its standardised version ’s_df’ by dividing values in each column of df by their maximums. As I think of all that, it comes to my mind what I have recently learnt, namely that operations on Numpy arrays, in Python, are much faster than the same operations on data frames built with Python Pandas. I check if I can make a Data Frame out of an imported CSV file, and then turn it into a Numpy array.

Let’s walse. I start by opening JupyterLab at https://hub.gke2.mybinder.org/user/jupyterlab-jupyterlab-demo-nocqldur/lab and creating a notebook with Python 3 as its kernel. Then, I import the libraries which I expect to use one way or another: NumPy, Pandas, Matplot, OS, and Math. In other words, I do:

>> import numpy as np

>> import pandas as pd

>> import matplotlib.pyplot as plt

>> import math

>> import os

Then, I upload a CSV file and I import it into a Data Frame. It is a database I used in my research on cities and urbanization, its name is ‘DU_DG database.csv’, and, as it is transformed from an Excel file, I take care to specify that separators are semi-columns.

The resulting Data Frame is structured as:

Index([‘Index’, ‘Country’, ‘Year’, ‘DU/DG’, ‘Population’,

‘GDP (constant 2010 US\$)’, ‘Broad money (% of GDP)’,

‘urban population absolute’,

‘Energy use (kg of oil equivalent per capita)’, ‘agricultural land km2’,

‘Cereal yield (kg per hectare)’],

dtype=’object’)

Import being successful (I just check with commands ‘DU_DG.shape’ and ‘DU_DG.head()’), I am trying to create a NumPy array. Of course, there is not much sense in translating names of countries and labels of years into a NumPy array. I try to select numerical columns ‘DU/DG’, ‘Population’, ‘GDP (constant 2010 US\$)’, ‘Broad money (% of GDP)’, ‘urban population absolute’, ‘Energy use (kg of oil equivalent per capita)’, ‘agricultural land km2’, and ‘Cereal yield (kg per hectare)’, by commanding:

>> DU_DGnumeric=np.array(DU_DG[‘DU/DG’,’Population’,’GDP (constant 2010 US\$)’,’Broad money (% of GDP)’,’urban population absolute’,’Energy use (kg of oil equivalent per capita)’,’agricultural land km2′,’Cereal yield (kg per hectare)’])

The answer I get from Python 3 is a gentle ‘f**k you!’, i.e. an elaborate error message.

KeyError                                  Traceback (most recent call last)

/srv/conda/envs/notebook/lib/python3.7/site-packages/pandas/core/indexes/base.py in get_loc(self, key, method, tolerance)

2656             try:

-> 2657                 return self._engine.get_loc(key)

2658             except KeyError:

pandas/_libs/index.pyx in pandas._libs.index.IndexEngine.get_loc()

pandas/_libs/index.pyx in pandas._libs.index.IndexEngine.get_loc()

pandas/_libs/hashtable_class_helper.pxi in pandas._libs.hashtable.PyObjectHashTable.get_item()

pandas/_libs/hashtable_class_helper.pxi in pandas._libs.hashtable.PyObjectHashTable.get_item()

KeyError: (‘DU/DG’, ‘Population’, ‘GDP (constant 2010 US\$)’, ‘Broad money (% of GDP)’, ‘urban population absolute’, ‘Energy use (kg of oil equivalent per capita)’, ‘agricultural land km2’, ‘Cereal yield (kg per hectare)’)

During handling of the above exception, another exception occurred:

KeyError                                  Traceback (most recent call last)

<ipython-input-18-e438a5ba1aa2> in <module>

—-> 1 DU_DGnumeric=np.array(DU_DG[‘DU/DG’,’Population’,’GDP (constant 2010 US\$)’,’Broad money (% of GDP)’,’urban population absolute’,’Energy use (kg of oil equivalent per capita)’,’agricultural land km2′,’Cereal yield (kg per hectare)’])

/srv/conda/envs/notebook/lib/python3.7/site-packages/pandas/core/frame.py in __getitem__(self, key)

2925             if self.columns.nlevels > 1:

2926                 return self._getitem_multilevel(key)

-> 2927             indexer = self.columns.get_loc(key)

2928             if is_integer(indexer):

2929                 indexer = [indexer]

/srv/conda/envs/notebook/lib/python3.7/site-packages/pandas/core/indexes/base.py in get_loc(self, key, method, tolerance)

2657                 return self._engine.get_loc(key)

2658             except KeyError:

-> 2659                 return self._engine.get_loc(self._maybe_cast_indexer(key))

2660         indexer = self.get_indexer([key], method=method, tolerance=tolerance)

2661         if indexer.ndim > 1 or indexer.size > 1:

pandas/_libs/index.pyx in pandas._libs.index.IndexEngine.get_loc()

pandas/_libs/index.pyx in pandas._libs.index.IndexEngine.get_loc()

pandas/_libs/hashtable_class_helper.pxi in pandas._libs.hashtable.PyObjectHashTable.get_item()

pandas/_libs/hashtable_class_helper.pxi in pandas._libs.hashtable.PyObjectHashTable.get_item()

KeyError: (‘DU/DG’, ‘Population’, ‘GDP (constant 2010 US\$)’, ‘Broad money (% of GDP)’, ‘urban population absolute’, ‘Energy use (kg of oil equivalent per capita)’, ‘agricultural land km2’, ‘Cereal yield (kg per hectare)’)

Didn’t work, obviously. I try something else. I proceed in two steps. First, I create a second Data Frame out of the numerical columns of DU_DG. I go:

>> DU_DGNumCol=pd.DataFrame(DU_DG.columns[‘DU/DG’, ‘Population’,’GDP (constant 2010 US\$)’, ‘Broad money (% of GDP)’,’urban population absolute’,’Energy use (kg of oil equivalent per capita)’, ‘agricultural land km2’,’Cereal yield (kg per hectare)’])

Python seems to have accepted the command without reserves, and yet something strange happens. Informative commands about that second Data Frame, i.e. DU_DGNumCol, such as ‘DU_DGNumCol.head()’, ‘DU_DGNumCol.shape’ or ‘DU_DGNumCol.info‘ don’t work, as if DU_DGNumCol had no structure at all.

Cool. I investigate. I want to check how does Python see data in my DU_DG data frame. I do ‘DU_DG.describe()’ first, and, to my surprise, I can see descriptive statistics just for columns ‘Index’ and ‘Year’. The legitimate WTF? question pushes me to type ‘DU_DG.info()’ and here is what I get:

<class ‘pandas.core.frame.DataFrame’>

RangeIndex: 896 entries, 0 to 895

Data columns (total 11 columns):

Index                                           896 non-null int64

Country                                         896 non-null object

Year                                            896 non-null int64

DU/DG                                           896 non-null object

Population                                      896 non-null object

GDP (constant 2010 US\$)                         896 non-null object

Broad money (% of GDP)                          896 non-null object

urban population absolute                       896 non-null object

Energy use (kg of oil equivalent per capita)    896 non-null object

agricultural land km2                           896 non-null object

Cereal yield (kg per hectare)                   896 non-null object

dtypes: int64(2), object(9)

memory usage: 77.1+ KB

I think I understand. My numerical data has been imported as object, and I want it to be float values.  Once again, I have the same valuable lesson: before I do anything with my data, in Python, I need to  check and curate it. It is strangely connected to my theory of collective intelligence. Our human perception accepts empirical experience for further processing, especially for collective processing at the level of culture, only if said experience has the right form. We tend to ignore phenomena, which manifest in a form we are not used to process cognitively.

Just by sheer curiosity, I take another dataset and I repeat the whole sequence of import from CSV, and definition of data type. This time, I take a reduced version of Penn Tables 9.1. The full citation due in this case is: Feenstra, Robert C., Robert Inklaar and Marcel P. Timmer (2015), “The Next Generation of the Penn World Table” American Economic Review, 105(10), 3150-3182, available for download at www.ggdc.net/pwt. The ‘reduced’ part means that I took out of the database all the rows (i.e. country <> year observations) with at least one empty cell. I go:

>> PWT=pd.DataFrame(pd.read_csv(‘PWT 9_1 no empty cells.csv’))

…aaaaand it lands. Import successful. I test the properties of PWT data frame:

>> PWT.info()

yields:

<class ‘pandas.core.frame.DataFrame’>

RangeIndex: 3006 entries, 0 to 3005

Data columns (total 44 columns):

country      3006 non-null object

year         3006 non-null int64

rgdpe        3006 non-null float64

rgdpo        3006 non-null float64

pop          3006 non-null float64

emp          3006 non-null float64

emp / pop    3006 non-null float64

avh          3006 non-null float64

hc           3006 non-null float64

ccon         3006 non-null float64

cda          3006 non-null float64

cgdpe        3006 non-null float64

cgdpo        3006 non-null float64

cn           3006 non-null float64

ck           3006 non-null float64

ctfp         3006 non-null float64

cwtfp        3006 non-null float64

rgdpna       3006 non-null float64

rconna       3006 non-null float64

rdana        3006 non-null float64

rnna         3006 non-null float64

rkna         3006 non-null float64

rtfpna       3006 non-null float64

rwtfpna      3006 non-null float64

labsh        3006 non-null float64

irr          3006 non-null float64

delta        3006 non-null float64

xr           3006 non-null float64

pl_con       3006 non-null float64

pl_da        3006 non-null float64

pl_gdpo      3006 non-null float64

csh_c        3006 non-null float64

csh_i        3006 non-null float64

csh_g        3006 non-null float64

csh_x        3006 non-null float64

csh_m        3006 non-null float64

csh_r        3006 non-null float64

pl_c         3006 non-null float64

pl_i         3006 non-null float64

pl_g         3006 non-null float64

pl_x         3006 non-null float64

pl_m         3006 non-null float64

pl_n         3006 non-null float64

pl_k         3006 non-null float64

dtypes: float64(42), int64(1), object(1)

memory usage: 1.0+ MB

>> PWT.describe()

gives nice descriptive statistics. This dataset has been imported in the format I want. I do the same thing I attempted with the DU_DG dataset: I try to convert it into a NumPy array and to check the shape obtained. I do:

>> PWTNumeric=np.array(PWT)

>> PWTNumeric.shape

I get (3006,44), i.e. 3006 rows over 44 columns.

I try to wrap my mind around standardising values in PWT. I start gently. I slice one column out of PWT, namely the AVH variable, which stands for the average number of hours worked per person per year. I do:

>> AVH=pd.DataFrame(PWT[‘avh’])

>> stdAVH=pd.DataFrame(AVH/AVH.max())

Apparently, it worked. I check with ‘stdAVH.describe()’ and I get a nice distribution of values between 0 and 1.

I do the same thing with mean-reversion. I create the ‘mrAVH’ data frame according to the s(x) = [x – avg(x)]/std(x) drill. I do:

>> mrAVH=pd.DataFrame((AVH-AVH.mean())/AVH.std())

…and I get a nice distribution of mean reverted values.

Cool. Now, it is time to try and iterate the same standardisation over many columns in the same Data Frame. I have already rummaged a bit and apparently it is not going to as simple as in Excel. It usually isn’t.

That would be all in that update. A short summary is due. It works again. I mean, learning something and keeping a journal of how exactly I learn, that thing works. I feel that special vibe, like ‘What the hell, even if it sucks, it is interesting’. Besides the technical details of programming, I have already learnt two big things about data analysis in Python. Firstly, however comfortable it is to use libraries such as NumPy or Pandas, being really efficient requires the understanding of small details at the very basic level, e.g. conversion of data types, and, as a matter of fact, the practical workability of different data types, selection of values in a data set, by row and by column, iteration over rows and columns etc. Secondly, once again, data works well in Python when it has been properly curated prior to analysis. Learning quick algorithmic ways to curate that data, without having to do is manually in Excel, is certainly an asset, which I need to learn.