I am currently trying to find optimal portfolio weights by optimizing a utility function that depends on those weights. I have a dataframe of containing the time series of returns, named rets_optns. rets_optns has 100 groups of 8 assets (800 columns - 1st group column 1 to 8, 2nd group column 9 to 16). I also have a dataframe named rf_options with 100 columns that present the corresponding risk free rate for each group of returns. I want to create a new dataframe composed by the portfolio's returns, using this formula: p. returns= rf_optns+sum(weights*rets_optns). It should have 100 columns and each columns should represent the returns of a portfolio composed by 8 assets belonging to the same group. I currently have:
def pret(rf,weights,rets):
return rf+np.sum(weights*(rets-rf))
It does not work
PS: I am a student of Data Science, I was wondering the impact of correlation on categorical data.
Let say I have 2 features such as Ticket Class with 1,2,3 (class 3 is lower than class 1) as a category and Seat Numbers as A,B,C,D,E,F & N (where N represents missing data) another category.
It looks like this :
Tclass Seat
1 A
2 C
3 E
2 D
3 N
1 A
1 N
Steps I perform is :
I one hot encode the seat no
Then I check the correlation of resultant data frame by using df.corr()
The result of Correlation is :
Tclass 1.000000
Seat_N 0.713857
Seat_F 0.013122
Seat_C -0.042750
Seat_A -0.202143
Seat_E -0.225649
Seat_D -0.265341
Seat_B -0.353414
My questions are :
In this case the conclusion drawn is that missing data (N) is highly correlated to lower class. WHY was this conclusion made from the correlation data?
Conclusion made was Seat_B related to higher class while seat_N related to lower class tickets.
Is this the answer : Since, Seat_N have a +ve correlation it should mean it yields higher value of Tclass, which is numeric value of 3. In other terms Lower class
If we correlate categorical data, how can we get -ve results? (can someone share some reading material on this?)
How to interpret the result of correlation of one categorical data on another categorical data? (this question leads on question 2)
Would it be possible for me to perform correlation if the Tclass was non-numerical/label encoded ?
Reference : https://www.kaggle.com/ccastleberry/titanic-cabin-features/comments
let's say i have a dataframe of 80 columns and 1 target column,
for example a bank account table with 80 attributes for each record (account) and 1 target column which decides if the client stays or leaves.
what steps and algorithms should i follow to select the most effective columns with the higher impact on the target column ?
There are a number of steps you can take, I'll give some examples to get you started:
A correlation coefficient, such as Pearson's Rho (for parametric data) or Spearman's R (for ordinate data).
Feature importances. I like XGBoost for this, as it includes the handy xgb.ggplot.importance / xgb.plot_importance methods.
One of the many feature selection options, such as python's sklearn.feature_selection methods.
This one way to do it using the Pearson correlation coefficient in Rstudio, I used it once when exploring the red_wine dataset my targeted variable or column was the quality and I wanted to know the effect of the rest of the columns on it.
see below figure shows the output of the code as you can see the blue color represents positive relation and red represents negative relations and the closer the value to 1 or -1 the darker the color
c <- cor(
red_wine %>%
# first we remove unwanted columns
dplyr::select(-X) %>%
dplyr::select(-rating) %>%
mutate(
# now we translate quality to a number
quality = as.numeric(quality)
)
)
corrplot(c, method = "color", type = "lower", addCoef.col = "gray", title = "Red Wine Variables Correlations", mar=c(0,0,1,0), tl.cex = 0.7, tl.col = "black", number.cex = 0.9)
I have this TypeError as per below, I have checked my df and it all contains numbers only, can this be caused when I converted to numpy array? After the conversion the array has items like
[Timestamp('1993-02-11 00:00:00') 28.1216 28.3374 ...]
Any suggestion how to solve this, please?
df:
Date Open High Low Close Volume
9 1993-02-11 28.1216 28.3374 28.1216 28.2197 19500
10 1993-02-12 28.1804 28.1804 28.0038 28.0038 42500
11 1993-02-16 27.9253 27.9253 27.2581 27.2974 374800
12 1993-02-17 27.2974 27.3366 27.1796 27.2777 210900
X = np.array(df.drop(['High'], 1))
X = preprocessing.scale(X)
TypeError: float() argument must be a string or a number
While you're saying that your dataframe "all contains numbers only", you also note that the first column consists of datetime objects. The error is telling you that preprocessing.scale only wants to work with float values.
The real question, however, is what you expect to happen to begin with. preprocessing.scale centers values on the mean and normalizes the variance. This is such that measured quantities are all represented on roughly the same footing. Now, your first column tells you what dates your data correspond to, while the rest of the columns are numeric data themselves. Why would you want to normalize the dates? How would you normalize the dates?
Semantically speaking, I believe you should leave your dates alone. Whatever post-processing you're planning to perform on your numerical data, the normalized data should still be parameterized by the original dates. If you want to process your dates too, you need to come up with an explicit way to handle your dates to something numeric (say, elapsed time from a given date in given units).
So I believe you should drop your dates from your processing round altogether, and start with
X = df.drop(['Date','High'], 1).as_matrix()
I basically need the answer to this SO question that provides a power-law distribution, translated to T-SQL for me.
I want to pull a last name, one at a time, from a census provided table of names. I want to get roughly the same distribution as occurs in the population. The table has 88,799 names ranked by frequency. "Smith" is rank 1 with 1.006% frequency, "Alderink" is rank 88,799 with frequency of 1.7 x 10^-6. "Sanders" is rank 75 with a frequency of 0.100%.
The curve doesn't have to fit precisely at all. Just give me about 1% "Smith" and about 1 in a million "Alderink"
Here's what I have so far.
SELECT [LastName]
FROM [LastNames] as LN
WHERE LN.[Rank] = ROUND(88799 * RAND(), 0)
But this of course yields a uniform distribution.
I promise I'll still be trying to figure this out myself by the time a smarter person responds.
Why settle for the power-law distribution when you can draw from the actual distribution ?
I suggest you alter the LastNames table to include a numeric column which would contain a numeric value representing the actual number of indivuduals with a name that is more common. You'll probably want a number on a smaller but proportional scale, say, maybe 10,000 for each percent of representation.
The list would then look something like:
(other than the 3 names mentioned in the question, I'm guessing about White, Johnson et al)
Smith 0
White 10,060
Johnson 19,123
Williams 28,456
...
Sanders 200,987
..
Alderink 999,997
And the name selection would be
SELECT TOP 1 [LastName]
FROM [LastNames] as LN
WHERE LN.[number_described_above] < ROUND(100000 * RAND(), 0)
ORDER BY [number_described_above] DESC
That's picking the first name which number does not exceed the [uniform distribution] random number. Note how the query, uses less than and ordering in desc-ending order; this will guaranty that the very first entry (Smith) gets picked. The alternative would be to start the series with Smith at 10,060 rather than zero and to discard the random draws smaller than this value.
Aside from the matter of boundary management (starting at zero rather than 10,060) mentioned above, this solution, along with the two other responses so far, are the same as the one suggested in dmckee's answer to the question referenced in this question. Essentially the idea is to use the CDF (Cumulative Distribution function).
Edit:
If you insist on using a mathematical function rather than the actual distribution, the following should provide a power law function which would somehow convey the "long tail" shape of the real distribution. You may wan to tweak the #PwrCoef value (which BTW needn't be a integer), essentially the bigger the coeficient, the more skewed to the beginning of the list the function is.
DECLARE #PwrCoef INT
SET #PwrCoef = 2
SELECT 88799 - ROUND(POWER(POWER(88799.0, #PwrCoef) * RAND(), 1.0/#PwrCoef), 0)
Notes:
- the extra ".0" in the function above are important to force SQL to perform float operations rather than integer operations.
- the reason why we subtract the power calculation from 88799 is that the calculation's distribution is such that the closer a number is closer to the end of our scale, the more likely it is to be drawn. The List of family names being sorted in the reverse order (most likely names first), we need this substraction.
Assuming a power of, say, 3 the query would then look something like
SELECT [LastName]
FROM [LastNames] as LN
WHERE LN.[Rank]
= 88799 - ROUND(POWER(POWER(88799.0, 3) * RAND(), 1.0/3), 0)
Which is the query from the question except for the last line.
Re-Edit:
In looking at the actual distribution, as apparent in the Census data, the curve is extremely steep and would require a very big power coefficient, which in turn would cause overflows and/or extreme rounding errors in the naive formula shown above.
A more sensible approach may be to operate in several tiers i.e. to perform an equal number of draws in each of the, say, three thirds (or four quarters or...) of the cumulative distribution; within each of these parts list, we would draw using a power law function, possibly with the same coeficient, but with different ranges.
For example
Assuming thirds, the list divides as follow:
First third = 425 names, from Smith to Alvarado
Second third = 6,277 names, from to Gainer
Last third = 82,097 names, from Frisby to the end
If we were to need, say, 1,000 names, we'd draw 334 from the top third of the list, 333 from the second third and 333 from the last third.
For each of the thirds we'd use a similar formula, maybe with a bigger power coeficient for the first third (were were are really interested in favoring the earlier names in the list, and also where the relative frequencies are more statistically relevant). The three selection queries could look like the following:
-- Random Drawing of a single Name in top third
-- Power Coef = 12
SELECT [LastName]
FROM [LastNames] as LN
WHERE LN.[Rank]
= 425 - ROUND(POWER(POWER(425.0, 12) * RAND(), 1.0/12), 0)
-- Second third; Power Coef = 7
...
WHERE LN.[Rank]
= (425 + 6277) - ROUND(POWER(POWER(6277.0, 7) * RAND(), 1.0/7), 0)
-- Bottom third; Power Coef = 4
...
WHERE LN.[Rank]
= (425 + 6277 + 82097) - ROUND(POWER(POWER(82097.0, 4) * RAND(), 1.0/4), 0)
Instead of storing the pdf as rank, store the CDF (the sum of all frequencies until that name, starting from Aldekirk).
Then modify your select to retrieve the first LN with rank greater than your formula result.
I read the question as "I need to get a stream of names which will mirror the frequency of last names from the 1990 US Census"
I might have read the question a bit differently than the other suggestions and although an answer has been accepted, and a very through answer it is, I will contribute my experience with the Census last names.
I had downloaded the same data from the 1990 census. My goal was to produce a large number of names to be submitted for search testing during performance testing of a medical record app. I inserted the last names and the percentage of frequency into a table. I added a column and filled it with a integer which was the product of the "total names required * frequency". The frequency data from the census did not add up to exactly 100% so my total number of names was also a bit short of the requirement. I was able to correct the number by selecting random names from the list and increasing their count until I had exactly the required number, the randomly added count never ammounted to more than .05% of the total of 10 million.
I generated 10 million random numbers in the range of 1 to 88799. With each random number I would pick that name from the list and decrement the counter for that name. My approach was to simulate dealing a deck of cards except my deck had many more distinct cards and a varing number of each card.
Do you store the actual frequencies with the ranks?
Converting the algebra from that accepted answer to MySQL is no bother, if you know what values to use for n. y would be what you currently have ROUND(88799 * RAND(), 0) and x0,x1 = 1,88799 I think, though I might misunderstand it. The only non-standard maths operator involved from a T-SQL perspective is ^ which is just POWER(x,y) == x^y.