I'm currently writing my master's thesis (I'm using SPSS for statistical analyses). One of my calculations is a logistic regression. These are the variables:
dependent variable: occupation (dichotomous, 1=yes, person has a job, 0= person is unemployed)
independent variable 1: self-stigmatization (mean value of a questionnaire,between 1 and 4, continuous).
Now my problem is that apparently there is no linear relationship between my independent variable and the log of my dependent variable (calculated using Box-Tidwell method). Obviously it's possible that there is no relationship between the two constructs in my data, but I've been asking myself, if there's another way to calculate a regression between these two variables if the assumptions for the logistic regression are not met? I just don't want to miss a valid (well, actually better fitting) option that I didn't know of yet...
Does anyone know a method or have any literature tips? Thanks for the help!
We need more info on the distributions of each of these variables and number of cases. One thought is whether transforming your independent variable might yield better results. If the mean value is normal, could you transform it into quartiles and see if you get a different/significant result? Additionally, you could group your sample by another variable in your dataset and see if relationships arise.
I would make this a comment but still need only one more point to do so!
Related
Business case:
Forecasting fuel consumption at site.
Say fuel consumption C, is dependent on various factors x1,x2,...xn. So mathematically speaking, C = F{x1,x2,...xn}. I do not have any equation to put this.
I do have historical dataset from where I can get a correlation of C to x1,x2 .. etc. C,x1,x2,.. are all quantitative. Finding out the correlation seems tough for a person like me with limited statistical knowledge, for a n variable equation.
So, I was thinking of employing some supervised machine learning techniques for the same. I will train a classifier with the historic data to get a prediction for the next consumption.
Question: Am I thinking in the right way?
Question: If this is correct, my system should be an evolving one. So the more real data I am going to feed to the system, that would evolve my model to make a better prediction the next time. Is this a correct understanding?
If the above the statements are true, does the AdaptiveLogisticRegression algorithm, as present in Mahout, will be of help to me?
Requesting advises from the experts here!
Thanks in advance.
Ok, correlation is not a forecasting model. Correlation simply ascribes some relationship between the datasets based on covariance.
In order to develop a forecasting model, what you need to peform is regression.
The simplest form of regression is linear univariate, where C = F (x1). This can easily be done in Excel. However, you state that C is a function of several variables. For this, you can employ linear multivariate regression. There are standard packages that can perform this (within Excel for example), or you can use Matlab, etc.
Now, we are assuming that there is a "linear" relationship between C and the components of X (the input vector). If the relationship were not linear, then you would need more sophisticated methods (nonlinear regression), which may very well employ machine learning methods.
Finally, some series exhibit auto-correlation. If this is the case, then it may be possible for you to ignore the C = F(x1, x2, x3...xn) relationships, and instead directly model the C function itself using time-series techniques such as ARMA and more complex variants.
I hope this helps,
Srikant Krishna
I have very large dataset in csv file (1,700,000 raws and 300 sparse features).
- It has a lot of missing values.
- the data varies between numeric and categoral values.
- the dependant variable (the class) is binary (either 1 or 0).
- the data is highly skewed, the number of positive response is low.
Now what is required from me is to apply regression model and any other machine learning algorithm on this data.
I'm new on this and I need help..
-how to deal with categoral data in case of regression model? and does the missing values affects too much on it?
- what is the best prediction model i can try for large, sparse, skewed data like this?
- what program u advice me to work with? I tried Weka but it can't even open that much of data (memory failure). I know that matlab can open either numeric csv or categories csv not mixed, beside the missing values has to be imputed to allow it to open the file. I know a little bit of R.
I'm trying to manipulate the data using excel, access and perl script. and that's really hard with that amount of data. excel can't open more than almost 1M record and access can't open more than 255 columns. any suggestion.
Thank you for help in advance
First of all, you are talking about classification, not regression - classification allows to predict value from the fixed set (e.g. 0 or 1) while regression produces real numeric output (e.g. 0, 0.5, 10.1543, etc.). Also don't be confused with so called logistic regression - it is classifier too, and its name just shows that it is based on linear regression.
To process such a large amount of data you need inductive (updatable) model. In particular, in Weka there's a number of such algorithms under classification section (e.g. Naive Bayes Updatable, Neutral Networks Updatable and others). With inductive model you will be able to load data portion by portion and update model in appropriate way (for Weka see Knowledge Flow interface for details of how to use it easier).
Some classifiers may work with categorical data, but I can't remember any updatable from them, so most probably you still need to transform categorical data to numeric. Standard solution here is to use indicator attributes, i.e. substitute every categorical attribute with several binary indicator. E.g. if you have attribute day-of-week with 7 possible values you may substitute it with 7 binary attributes - Sunday, Monday, etc. Of course, in each particular instance only one of 7 attributes may hold value 1 and all others have to be 0.
Importance of missing values depend on the nature of your data. Sometimes it worth to replace them with some neutral value beforehand, sometimes classifier implementation does it itself (check manuals for an algorithm for details).
And, finally, for highly skewed data use F1 (or just Precision / Recall) measure instead of accuracy.
I'm wondering how people test artificial intelligence algorithms in an automated fashion.
One example would be for the Turing Test - say there were a number of submissions for a contest. Is there any conceivable way to score candidates in an automated fashion - other than just having humans test them out.
I've also seen some data sets (obscured images of numbers/letters, groups of photos, etc) that can be fed in and learned over time. What good resources are out there for this.
One challenge I see: you don't want an algorithm that tailors itself to the test data over time, since you are trying to see how well it does in the general case. Are there any techniques to ensure it doesn't do this? Such as giving it a random test each time, or averaging its results over a bunch of random tests.
Basically, given a bunch of algorithms, I want some automated process to feed it data and see how well it "learned" it or can predict new stuff it hasn't seen yet.
This is a complex topic - good AI algorithms are generally the ones which can generalize well to "unseen" data. The simplest method is to have two datasets: a training set and an evaluation set used for measuring the performances. But generally, you want to "tune" your algorithm so you may want 3 datasets, one for learning, one for tuning, and one for evaluation. What defines tuning depends on your algorithm, but a typical example is a model where you have a few hyper-parameters (for example parameters in your Bayesian prior under the Bayesian view of learning) that you would like to tune on a separate dataset. The learning procedure would already have set a value for it (or maybe you hardcoded their value), but having enough data may help so that you can tune them separately.
As for making those separate datasets, there are many ways to do so, for example by dividing the data you have available into subsets used for different purposes. There is a tradeoff to be made because you want as much data as possible for training, but you want enough data for evaluation too (assuming you are in the design phase of your new algorithm/product).
A standard method to do so in a systematic way from a known dataset is cross validation.
Generally when it comes to this sort of thing you have two datasets - one large "training set" which you use to build and tune the algorithm, and a separate smaller "probe set" that you use to evaluate its performance.
#Anon has the right of things - training and what I'll call validation sets. That noted, the bits and pieces I see about developments in this field point at two things:
Bayesian Classifiers: there's something like this probably filtering your email. In short you train the algorithm to make a probabilistic decision if a particular item is part of a group or not (e.g. spam and ham).
Multiple Classifiers: this is the approach that the winning group involved in the Netflix challenge took, whereby it's not about optimizing one particular algorithm (e.g. Bayesian, Genetic Programming, Neural Networks, etc..) by combining several to get a better result.
As for data sets Weka has several available. I haven't explored other libraries for data sets, but mloss.org appears to be a good resource. Finally data.gov offers a lot of sets that provide some interesting opportunities.
Training data sets and test sets are very common for K-means and other clustering algorithms, but to have something that's artificially intelligent without supervised learning (which means having a training set) you are building a "brain" so-to-speak based on:
In chess: all possible future states possible from the current gameState.
In most AI-learning (reinforcement learning) you have a problem where the "agent" is trained by doing the game over and over. Basically you ascribe a value to every state. Then you assign an expected value of each possible action at a state.
So say you have S states and a actions per state (although you might have more possible moves in one state, and not as many in another), then you want to figure out the most-valuable states from s to be in, and the most valuable actions to take.
In order to figure out the value of states and their corresponding actions, you have to iterate the game through. Probabilistically, a certain sequence of states will lead to victory or defeat, and basically you learn which states lead to failure and are "bad states". You also learn which ones are more likely to lead to victory, and these are subsequently "good" states. They each get a mathematical value associated, usually as an expected reward.
Reward from second-last state to a winning state: +10
Reward if entering a losing state: -10
So the states that give negative rewards then give negative rewards backwards, to the state that called the second-last state, and then the state that called the third-last state and so-on.
Eventually, you have a mapping of expected reward based on which state you're in, and based on which action you take. You eventually find the "optimal" sequence of steps to take. This is often referred to as an optimal policy.
It is true of the converse that normal courses of actions that you are stepping-through while deriving the optimal policy are called simply policies and you are always implementing a certain "policy" with respect to Q-Learning.
Usually the way of determining the reward is the interesting part. Suppose I reward you for each state-transition that does not lead to failure. Then the value of walking all the states until I terminated is however many increments I made, however many state transitions I had.
If certain states are extremely unvaluable, then loss is easy to avoid because almost all bad states are avoided.
However, you don't want to discourage discovery of new, potentially more-efficient paths that don't follow just this-one-works, so you want to reward and punish the agent in such a way as to ensure "victory" or "keeping the pole balanced" or whatever as long as possible, but you don't want to be stuck at local maxima and minima for efficiency if failure is too painful, so no new, unexplored routes will be tried. (Although there are many approaches in addition to this one).
So when you ask "how do you test AI algorithms" the best part is is that the testing itself is how many "algorithms" are constructed. The algorithm is designed to test a certain course-of-action (policy). It's much more complicated than
"turn left every half mile"
it's more like
"turn left every half mile if I have turned right 3 times and then turned left 2 times and had a quarter in my left pocket to pay fare... etc etc"
It's very precise.
So the testing is usually actually how the A.I. is being programmed. Most models are just probabilistic representations of what is probably good and probably bad. Calculating every possible state is easier for computers (we thought!) because they can focus on one task for very long periods of time and how much they remember is exactly how much RAM you have. However, we learn by affecting neurons in a probabilistic manner, which is why the memristor is such a great discovery -- it's just like a neuron!
You should look at Neural Networks, it's mindblowing. The first time I read about making a "brain" out of a matrix of fake-neuron synaptic connections... A brain that can "remember" basically rocked my universe.
A.I. research is mostly probabilistic because we don't know how to make "thinking" we just know how to imitate our own inner learning process of try, try again.
What are the relevant differences, in terms of performance and use cases, between simulated annealing (with bean search) and genetic algorithms?
I know that SA can be thought as GA where the population size is only one, but I don't know the key difference between the two.
Also, I am trying to think of a situation where SA will outperform GA or GA will outperform SA. Just one simple example which will help me understand will be enough.
Well strictly speaking, these two things--simulated annealing (SA) and genetic algorithms are neither algorithms nor is their purpose 'data mining'.
Both are meta-heuristics--a couple of levels above 'algorithm' on the abstraction scale. In other words, both terms refer to high-level metaphors--one borrowed from metallurgy and the other from evolutionary biology. In the meta-heuristic taxonomy, SA is a single-state method and GA is a population method (in a sub-class along with PSO, ACO, et al, usually referred to as biologically-inspired meta-heuristics).
These two meta-heuristics are used to solve optimization problems, particularly (though not exclusively) in combinatorial optimization (aka constraint-satisfaction programming). Combinatorial optimization refers to optimization by selecting from among a set of discrete items--in other words, there is no continuous function to minimize. The knapsack problem, traveling salesman problem, cutting stock problem--are all combinatorial optimization problems.
The connection to data mining is that the core of many (most?) supervised Machine Learning (ML) algorithms is the solution of an optimization problem--(Multi-Layer Perceptron and Support Vector Machines for instance).
Any solution technique to solve cap problems, regardless of the algorithm, will consist essentially of these steps (which are typically coded as a single block within a recursive loop):
encode the domain-specific details
in a cost function (it's the
step-wise minimization of the value
returned from this function that
constitutes a 'solution' to the c/o
problem);
evaluate the cost function passing
in an initial 'guess' (to begin
iteration);
based on the value returned from the
cost function, generate a subsequent
candidate solution (or more than
one, depending on the
meta-heuristic) to the cost
function;
evaluate each candidate solution by
passing it in an argument set, to
the cost function;
repeat steps (iii) and (iv) until
either some convergence criterion is
satisfied or a maximum number of
iterations is reached.
Meta-heuristics are directed to step (iii) above; hence, SA and GA differ in how they generate candidate solutions for evaluation by the cost function. In other words, that's the place to look to understand how these two meta-heuristics differ.
Informally, the essence of an algorithm directed to solution of combinatorial optimization is how it handles a candidate solution whose value returned from the cost function is worse than the current best candidate solution (the one that returns the lowest value from the cost function). The simplest way for an optimization algorithm to handle such a candidate solution is to reject it outright--that's what the hill climbing algorithm does. But by doing this, simple hill climbing will always miss a better solution separated from the current solution by a hill. Put another way, a sophisticated optimization algorithm has to include a technique for (temporarily) accepting a candidate solution worse than (i.e., uphill from) the current best solution because an even better solution than the current one might lie along a path through that worse solution.
So how do SA and GA generate candidate solutions?
The essence of SA is usually expressed in terms of the probability that a higher-cost candidate solution will be accepted (the entire expression inside the double parenthesis is an exponent:
p = e((-highCost - lowCost)/temperature)
Or in python:
p = pow(math.e, (-hiCost - loCost) / T)
The 'temperature' term is a variable whose value decays during progress of the optimization--and therefore, the probability that SA will accept a worse solution decreases as iteration number increases.
Put another way, when the algorithm begins iterating, T is very large, which as you can see, causes the algorithm to move to every newly created candidate solution, whether better or worse than the current best solution--i.e., it is doing a random walk in the solution space. As iteration number increases (i.e., as the temperature cools) the algorithm's search of the solution space becomes less permissive, until at T = 0, the behavior is identical to a simple hill-climbing algorithm (i.e., only solutions better than the current best solution are accepted).
Genetic Algorithms are very different. For one thing--and this is a big thing--it generates not a single candidate solution but an entire 'population of them'. It works like this: GA calls the cost function on each member (candidate solution) of the population. It then ranks them, from best to worse, ordered by the value returned from the cost function ('best' has the lowest value). From these ranked values (and their corresponding candidate solutions) the next population is created. New members of the population are created in essentially one of three ways. The first is usually referred to as 'elitism' and in practice usually refers to just taking the highest ranked candidate solutions and passing them straight through--unmodified--to the next generation. The other two ways that new members of the population are usually referred to as 'mutation' and 'crossover'. Mutation usually involves a change in one element in a candidate solution vector from the current population to create a solution vector in the new population, e.g., [4, 5, 1, 0, 2] => [4, 5, 2, 0, 2]. The result of the crossover operation is like what would happen if vectors could have sex--i.e., a new child vector whose elements are comprised of some from each of two parents.
So those are the algorithmic differences between GA and SA. What about the differences in performance?
In practice: (my observations are limited to combinatorial optimization problems) GA nearly always beats SA (returns a lower 'best' return value from the cost function--ie, a value close to the solution space's global minimum), but at a higher computation cost. As far as i am aware, the textbooks and technical publications recite the same conclusion on resolution.
but here's the thing: GA is inherently parallelizable; what's more, it's trivial to do so because the individual "search agents" comprising each population do not need to exchange messages--ie, they work independently of each other. Obviously that means GA computation can be distributed, which means in practice, you can get much better results (closer to the global minimum) and better performance (execution speed).
In what circumstances might SA outperform GA? The general scenario i think would be those optimization problems having a small solution space so that the result from SA and GA are practically the same, yet the execution context (e.g., hundreds of similar problems run in batch mode) favors the faster algorithm (which should always be SA).
It is really difficult to compare the two since they were inspired from different domains..
A Genetic Algorithm maintains a population of possible solutions, and at each step, selects pairs of possible solution, combines them (crossover), and applies some random changes (mutation). The algorithm is based the idea of "survival of the fittest" where the selection process is done according to a fitness criteria (usually in optimization problems it is simply the value of the objective function evaluated using the current solution). The crossover is done in hope that two good solutions, when combined, might give even better solution.
On the other hand, Simulated Annealing only tracks one solution in the space of possible solutions, and at each iteration considers whether to move to a neighboring solution or stay in the current one according to some probabilities (which decays over time). This is different from a heuristic search (say greedy search) in that it doesn't suffer from the problems of local optimum since it can get unstuck from cases where all neighboring solutions are worst the current one.
I'm far from an expert on these algorithms, but I'll try and help out.
I think the biggest difference between the two is the idea of crossover in GA and so any example of a learning task that is better suited to GA than SA is going to hinge on what crossover means in that situation and how it is implemented.
The idea of crossover is that you can meaningfully combine two solutions to produce a better one. I think this only makes sense if the solutions to a problem are structured in some way. I could imagine, for example, in multi-class classification taking two (or many) classifiers that are good at classifying a particular class and combining them by voting to make a much better classifier. Another example might be Genetic Programming, where the solution can be expressed as a tree, but I find it hard to come up with a good example where you could combine two programs to create a better one.
I think it's difficult to come up with a compelling case for one over the other because they really are quite similar algorithms, perhaps having been developed from very different starting points.
First find the minimum frequent patterns from the database.
Then divide them into various data types like interval based , binary ,ordinal variables etc and define various distance measures for all the variables.
Finally apply cluster analysis method.
Is this sequence right or am i missing something?
whether you're right or not depends on what you want to do. The general approach that you describe seems to go into the right direction, but you'll never know if your on target until you answer the following questions:
What is your data?
What are trying to find/Which cluster method do you want to use?
From what you describe it seems to me that you want to do 'preprocessing' steps like feature selection and vectorization. Unfortunately, this by itself can be quite challenging. For example, one of the biggest partical problems is the design of a distance function (there's a tremendous amount of research available).
So, please give us more information on your specific target application.