Suppose a data analyst working for an insurance company was asked to build a predictive model for predicting whether a customer will buy a mobile home insurance policy. S/he tried kNN classifier with different number of neighbours (k=1,2,3,4,5). S/he got the following F-scores measured on the training data: (1.0; 0.92; 0.90; 0.85; 0.82). Based on that the analyst decided to deploy kNN with k=1. Was it a good choice? How would you select an optimal number of neighbours in this case?
It is not a good idea to select a parameter of a prediction algorithm using the whole training set as the result will be biased towards this particular training set and has no information about generalization performance (i.e. performance towards unseen cases). You should apply a cross-validation technique e.g. 10-fold cross-validation to select the best K (i.e. K with largest F-value) within a range.
This involves splitting your training data in 10 equal parts retain 9 parts for training and 1 for validation. Iterate such that each part has been left out for validation. If you take enough folds this will allow you as well to obtain statistics of the F-value and then you can test whether these values for different K values are statistically significant.
See e.g. also:
http://pic.dhe.ibm.com/infocenter/spssstat/v20r0m0/index.jsp?topic=%2Fcom.ibm.spss.statistics.help%2Falg_knn_training_crossvalidation.htm
The subtlety here however is that there is likely a dependency between the number of data points for prediction and the K-value. So If you apply cross-validation you use 9/10 of the training set for training...Not sure whether any research has been performed on this and how to correct for that in the final training set. Anyway most software packages just use the abovementioned techniques e.g. see SPSS in the link.
A solution is to use leave-one-out cross-validation (each data samples is left out once for testing) in that case you have N-1 training samples(the original training set has N).
Related
I am trying to program a prediction algorithmus which predicts the distribution of marbles among 4 cups based on the prevision user input. But I have no idea where to start or which techniques can be used to solve this.
Example:
There are 4 cups numbered from 0 to 3 and the user will receive x marbles which he distributes among those cups. Each round the user receives another amount of marbles (or the same amount) and before
the user distributes them, the algorithm tries to predict the distribution based on the users previous inputs. After that the user “corrects” it. The goal is that the user does not have to correct anything hence the
algorithm predicts the correct distribution. However the pattern which the user distributes the marbles can change, and the algorithm has to adapt.
This is the simplest design of the problem which already is not trivial to solve. However it get exponential more complex when the marbles have additional properties which can be used for distribution.
For example, they could have a color and a weight.
So, for example, how does the algorithm learn that the user (most of the time) put the marbles with the same color in one cup, but cup 2 is (most of the time empty) and the rest is equally distributed?
So in my head the algorithm has to do something like this:
search for a pattern after the users distribution is done. Those patterns can be the amount of marbles per cup / weight per cup or anything else.
if a pattern is found a predefined value (weight) is added to the pattern
if a previous pattern was not found a predefined value has to be subtracted from the pattern
when the algorithm has to predict, all patterns with a predefined weight have to be applied.
I am not sure if I am missing something and how I would implement something like this or in which area I have to look for answers.
First of all, bear in mind that human behavior does not always follow a pattern. If the user distributes these marbles randomly, it will be hard to predict the next move!
But if there IS a pattern in the distributions, you might create a prediction using an algorithm such as a neural network or a decision tree.
For example:
// dataset1
// the weights and colors of 10 marbles
let dataset1 = [4,3,1,1,2,3,4,5,3,4,7,6,4,4,2,4,1,6,1,2]
// cups1
// the cups distribution of the above marbles
let labels1 = [2,1,0,2,1,1,3,1,0,1]
Now you can train an algorithm, for example a neural network or a decision tree.
This isn't real code, just an example of how it could work.
let net = new NeuralNet()
net.train(dataset1, labels1)
After training with lots of data (at least hundreds of these datasets), you can give the network a new dataset and it will give you a prediction of the cups distribution
let newMarbleSet = [...]
let prediction = net.predict(newMarbleSet)
It's up to you what you want to do with this prediction.
I am using vowpal wabbit for logistic regression. I came to know that vowpal wabbit selects a hold out set for validation from the given training data. Is this set chosen randomly. I have a very unbalanced dataset with 100 +ve examples and 1000 -ve examples. I want to know given this training data, how vowpal wabbit selects the hold out examples?
How do I assign more weights to the +ve examples
By default each 10th example is used for holdout (you can change it with --holdout_period,
see https://github.com/JohnLangford/vowpal_wabbit/wiki/Command-line-arguments#holdout-options).
This means the model trained with holdout evaluation on is trained only on 90% of the training data.
This may result in slightly worse accuracy.
On the other hand, it allows you to use --early_terminate (which is set to 3 passes by default),
which makes it easier to reduce the risk of overtraining caused by too many training passes.
Note that by default holdout evaluation is on, only if multiple passes are used (VW uses progressive validation loss otherwise).
As for the second question, you can add importance weight to the positive examples. The default importance weight is 1. See https://github.com/JohnLangford/vowpal_wabbit/wiki/Input-format
Why would one use kmedoids algoirthm rather then kmeans? Is it only the fact that
the number of metrics that can be used in kmeans is very limited or is there something more?
Is there an example of data, for which it makes much more sense to choose the best representatives
of cluster from the data rather then from R^n?
The problem with k-means is that it is not interpretable. By interpretability i mean the model should also be able to output the reason that why it has resulted a certain output.
lets take an example.
Suppose there is food review dataset which has two posibility that there is a +ve review or a -ve review so we can say we will have k= 2 where k is the number of clusters. Now if you go with k-means where in the algorithm the third step is updation step where you update your k-centroids based on the mean distance of the points that lie in a particular cluster. The example that we have chosen is text problem, so you would also apply some kind of text-featured vector schemes like BagOfWords(BOW), word2vec. now for every review you would get the corresponding vector. Now the generated centroid c_i that you will get after running the k-means would be the mean of the vectors present in that cluster. Now with that centroid you cannot interpret much or rather i should say nothing.
But for same problem you apply k-medoids wherein you choose your k-centroids/medoids from your dataset itself. lets say you choose x_5 point from your dataset as first medoid. From this your interpretability will increase beacuse now you have the review itself which is termed as medoid/centroid. So in k-medoids you choose the centroids from your dataset itself.
This is the foremost motivation of introducing k-mediods
Coming to the metrics part you can apply all the metrics that you apply for k-means
Hope this helps.
Why would we use k-medoids instead of k-means in case of (squared) Euclidean distance?
1. Technical justification
In case of relatively small data sets (as k-medoids complexity is greater) - to obtain a clustering more robust to noise and outliers.
Example 2D data showing that:
The graph on the left shows clusters obtained with K-medoids (sklearn_extra.cluster.KMedoids method in Python with default options) and the one on the right with K-means for K=2. Blue crosses are cluster centers.
The Python code used to generate green points:
import numpy as np
import matplotlib.pyplot as plt
rng = np.random.default_rng(seed=32)
a = rng.random((6,2))*2.35 - 3*np.ones((6,2))
b = rng.random((50,2))*0.25 - 2*np.ones((50,2))
c = rng.random((100,2))*0.5 - 1.5*np.ones((100,2))
d = rng.random((7,2))*0.55
points = np.concatenate((a, b, c, d))
plt.plot(points[:,0],points[:,1],"g.", markersize=8, alpha=0.3) # green points
2. Business case justification
Here are some example business cases showing why we would prefer k-medoids. They mostly come down to the interpretability of the results and the fact that in k-medoids the resulting cluster centers are members of the original dataset.
2.1 We have a recommender engine based only on user-item preference data and want to recommend to the user those items (e.g. movies) that other similar people enjoyed. So we assign the user to his/her closest cluster and recommend top movies that the cluster representant (actual person) watched. If the cluster representant wasn't an actual person we wouldn't possess the history of actually watched movies to recommend. Each time we'd have to search additionally e.g. for the closest person from the cluster. Example data: classic MovieLens 1M Dataset
2.2 We have a database of patients and want to pick a small representative group of size K to test a new drug with them. After clustering the patients with K-medoids, cluster representants are invited to the drug trial.
Difference between is that in k-means centroids(cluster centrum) are calculated as average of vectors containing in the cluster, and in k-medoids the medoid (cluster centrum) is record from dataset closest to centroid, so if you need to represent cluster centrum by record of your data you use k-medoids, otherwise i should use k-means (but concept of these algorithms are same)
The K-Means algorithm uses a Distance Function such as Euclidean Distance or Manhattan Distance, which are computed over vector-based instances. The K-Medoid algorithm instead uses a more general (and less constrained) distance function: aka pair-wise distance function.
This distinction works well in contexts like Complex Data Types or relational rows, where the instances have a high number of dimensions.
High dimensionality problem
In standard clustering libraries and the k-means algorithms, the distance computation phase can spend a lot of time scanning the entire vector of attributes that belongs to an instance; for instance, in the context of documents clustering, using the standard TF-IDF representation. During the computation of the cosine similarity, the distance function scans all the possible words that appear in the whole collection of documents. Which in many cases can be composed by millions of entries. This is why, in this domain, some authors [1] suggests to restrict the words considered to a subset of N most frequent word of that language.
Using K-Kedoids there is no need to represent and store the documents as vectors of word frequencies.
As an alternative representation for the documents is possible to use the set of words appearing at least twice in the document; and as a distance measure, there can be used Jaccard Distance.
In this case, vector representation is long as the number of words in your dictionary.
Heterogeneousity and Complex Data Types.
There are many domains where is considerably better to abstract the implementation of an instance:
Graph's nodes clustering;
Car driving behaviour, represented as GPS routes;
Complex data type allows the design of ad-hoc distance measures which can fit better with the proper data domain.
[1] Christopher D. Manning, Prabhakar Raghavan, and Hinrich Schütze. 2008. Introduction to Information Retrieval. Cambridge University Press, New York, NY, USA.
Source: https://github.com/eracle/Gap
Advice please. I have a collection of documents that all share a common attribute (e.g. The word French appears) some of these documents have been marked as not pertinent to this collection (e.g. French kiss appears) but not all documents are guaranteed to have been identified. What is the best method to use to figure out which other documents don't belong.
Assumptions
Given your example "French", I will work under the assumption that the feature is a word that appears in the document. Also, since you mention that "French kiss" is not relevant, I will further assume that in your case, a feature is a word used in a particular sense. For example, if "pool" is a feature, you may say that documents mentioning swimming pools are relevant, but those talking about pool (the sport, like snooker or billiards) are not relevant.
Note: Although word sense disambiguation (WSD) methods would work, they require too much effort, and is an overkill for this purpose.
Suggestion: localized language model + bootstrapping
Think of it this way: You don't have an incomplete training set, but a smaller training set. The idea is to use this small training data to build bigger training data. This is bootstrapping.
For each occurrence of your feature in the training data, build a language model based only on the words surrounding it. You don't need to build a model for the entire document. Ideally, just the sentences containing the feature should suffice. This is what I am calling a localized language model (LLM).
Build two such LLMs from your training data (let's call it T_0): one for pertinent documents, say M1, and another for irrelevant documents, say M0. Now, to build a bigger training data, classify documents based on M1 and M0. For every new document d, if d does not contain the feature-word, it will automatically be added as a "bad" document. If d contains the feature-word, then consider a local window around this word in d (the same window size that you used to build the LLMs), and compute the perplexity of this sequence of words with M0 and M1. Classify the document as belonging to the class which gives lower perplexity.
To formalize, the pseudo-code is:
T_0 := initial training set (consisting of relevant/irrelevant documents)
D0 := additional data to be bootstrapped
N := iterations for bootstrapping
for i = 0 to N-1
T_i+1 := empty training set
Build M0 and M1 as discussed above using a window-size w
for d in D0
if feature-word not in d
then add d to irrelevant documents of T_i+1
else
compute perplexity scores P0 and P1 corresponding to M0 and M1 using
window size w around the feature-word in d.
if P0 < P1 - delta
add d to irrelevant documents of T_i+1
else if P1 < P0 - delta
add d to relevant documents of T_i+1
else
do not use d in T_i+1
end
end
end
Select a small random sample from relevant and irrelevant documents in
T_i+1, and (re)classify them manually if required.
end
T_N is your final training set. In this above bootstrapping, the parameter delta needs to be determined with experiments on some held-out data (also called development data).
The manual reclassification on a small sample is done so that the noise during this bootstrapping is not accumulated through all the N iterations.
Firstly you should take care of how to extract features of the sample docs. Counting every word is not a good way. You might need some technique like TFIDF to teach the classifier that which words are important to classify and which are not.
Build a right dictionary. In your case, the word French kiss should be a unique word, instead of a sequence of French + kiss. Use the right technique to build a right dictionary is important.
The remain errors in samples are normal, we call it "not linear separable". There're a huge amount of advanced researches on how to solve this problem. For example, SVM (support vector machine) would be what you like to use. Please note that single-layer Rosenblatt perceptron usually shows very bad performance for the dataset which are not linear separable.
Some kinds of neural networks (like Rosenblatt perceptron) can be educated on erroneus data set and can show a better performance than tranier has. Moreover in many cases you should make errors for avoid over-training.
You can mark all unlabeled documents randomly, train several nets and estimate theirs performance on the test set (of course, you should not include unlabeled documents in the test set). After that you can in cycle recalculate weights of unlabeled documents as w_i = sum of quality(j) * w_ij, and then repeate training and the recalculate weight and so on. Because procedure is equivalent to introducing new hidden layer and recalculating it weights by Hebb procedure the overall procedure should converge if your positive and negative sets are lineary separable in some network feature space.
I once wrote a Tetris AI that played Tetris quite well. The algorithm I used (described in this paper) is a two-step process.
In the first step, the programmer decides to track inputs that are "interesting" to the problem. In Tetris we might be interested in tracking how many gaps there are in a row because minimizing gaps could help place future pieces more easily. Another might be the average column height because it may be a bad idea to take risks if you're about to lose.
The second step is determining weights associated with each input. This is the part where I used a genetic algorithm. Any learning algorithm will do here, as long as the weights are adjusted over time based on the results. The idea is to let the computer decide how the input relates to the solution.
Using these inputs and their weights we can determine the value of taking any action. For example, if putting the straight line shape all the way in the right column will eliminate the gaps of 4 different rows, then this action could get a very high score if its weight is high. Likewise, laying it flat on top might actually cause gaps and so that action gets a low score.
I've always wondered if there's a way to apply a learning algorithm to the first step, where we find "interesting" potential inputs. It seems possible to write an algorithm where the computer first learns what inputs might be useful, then applies learning to weigh those inputs. Has anything been done like this before? Is it already being used in any AI applications?
In neural networks, you can select 'interesting' potential inputs by finding the ones that have the strongest correlation, positive or negative, with the classifications you're training for. I imagine you can do similarly in other contexts.
I think I might approach the problem you're describing by feeding more primitive data to a learning algorithm. For instance, a tetris game state may be described by the list of occupied cells. A string of bits describing this information would be a suitable input to that stage of the learning algorithm. actually training on that is still challenging; how do you know whether those are useful results. I suppose you could roll the whole algorithm into a single blob, where the algorithm is fed with the successive states of play and the output would just be the block placements, with higher scoring algorithms selected for future generations.
Another choice might be to use a large corpus of plays from other sources; such as recorded plays from human players or a hand-crafted ai, and select the algorithms who's outputs bear a strong correlation to some interesting fact or another from the future play, such as the score earned over the next 10 moves.
Yes, there is a way.
If you choose M selected features there are 2^M subsets, so there is a lot to look at.
I would to the following:
For each subset S
run your code to optimize the weights W
save S and the corresponding W
Then for each pair S-W, you can run G games for each pair and save the score L for each one. Now you have a table like this:
feature1 feature2 feature3 featureM subset_code game_number scoreL
1 0 1 1 S1 1 10500
1 0 1 1 S1 2 6230
...
0 1 1 0 S2 G + 1 30120
0 1 1 0 S2 G + 2 25900
Now you can run some component selection algorithm (PCA for example) and decide which features are worth to explain scoreL.
A tip: When running the code to optimize W, seed the random number generator, so that each different 'evolving brain' is tested against the same piece sequence.
I hope it helps in something!