I am working on a Information Retrieval model called DPR which is a basically a neural network (2 BERTs) that ranks document, given a query. Currently, This model is trained in binary manners (documents are whether related or not related) and uses Negative Log Likelihood (NLL) loss. I want to change this binary behavior and create a model that can handle graded relevance (like 3 grades: relevant, somehow relevant, not relevant). I have to change the loss function because currently, I can only assign 1 positive target for each query (DPR uses pytorch NLLLoss) and this is not what I need.
I was wondering if I could use a evaluation metric like NDCG (Normalized Discounted Cumulative Gain) to calculate the loss. I mean, the whole point of a loss function is to tell how off our prediction is and NDCG is doing the same.
So, can I use such metrics in place of loss function with some modifications? In case of NDCG, I think something like subtracting the result from 1 (1 - NDCG_score) might be a good loss function. Is that true?
With best regards, Ali.
Yes, this is possible. You would want to apply a listwise learning to rank approach instead of the more standard pairwise loss function.
In pairwise loss, the network is provided with example pairs (rel, non-rel) and the ground-truth label is a binary one (say 1 if the first among the pair is relevant, and 0 otherwise).
In the listwise learning approach, however, during training you would provide a list instead of a pair and the ground-truth value (still a binary) would indicate if this permutation is indeed the optimal one, e.g. the one which maximizes nDCG. In a listwise approach, the ranking objective is thus transformed into a classification of the permutations.
For more details, refer to this paper.
Obviously, the network instead of taking features as input may take BERT vectors of queries and the documents within a list, similar to ColBERT. Unlike ColBERT, where you feed in vectors from 2 docs (pairwise training), for listwise training u need to feed in vectors from say 5 documents.
Related
Is it better to have:
1 output neuron that outputs a value between 0 and 15 which would be my ultimate value
or
16 output neurons that output a value between 0 and 1 which represents the propability for this value?
Example: We want to find out the grade (ranging from 0 to 15) a student gets by inputing the number of hours he learned and his IQ.
TL;DR: I think your problem would be better framed as a regression task, so use one ouptut neuron, but it is worth to try both.
I don't quite like the broadness of your question in contrast to the very specific answers, so I am going to go a little deeper and explain what exactly should be the proper formulation.
Before we start, we should clarify the two big tasks that classical Artificial Neural Networks perform:
Classification
Regression
They are inherently very different from one another; in short, Classification tries to put a label on your input (e.g., the input image shows a dog), whereas regression tries to predict a numerical value (e.g., the input data corresponds to a house that has an estimated worth of 1.5 million $US).
Obviously, you can see that predicting the numerical value requires (trivially) only one output value. Also note that this is only true for this specific example. There could be other regression usecases, in which you want your output to have more than 0 dimensions (i.e. a single point), but instead be 1D, or 2D.
A common example would for example be Image Colorization, which we can interestingly enough also frame as a classification problem. The provided link shows examples for both. In this case you would obviously have to regress (or classify) every pixel, which leads to more than one output neuron.
Now, to get to your actual question, I want to elaborate a little more on the reasoning why one-hot encoded outputs (i.e. output with as many channels as classes) are preferred for classification tasks over a single neuron.
Since we could argue that a single neuron is enough to predict the class value, we have to understand why it is problematic to get to a specific class that way.
Categorical vs Ordinal vs Interval Variables
One of the main problems is the type of your variable. In your case, there exists a clear order (15 is better than 14 is better than 13, etc.), and even an interval ordering (at least on paper), since the difference between a 15 and 13 is the same as between 14 and 12, although some scholars might argue against that ;-)
Thus, your target is an interval variable, and could thus be in theory used to regress on it. More on that later. But consider for example a variable that describes whether the image depicts a cat (0), dog (1), or car (2). Now, arguably, we cannot even order the variables (is a car > dog, or car < dog?), nor can we say that there exists an "equal distance" between a cat and a dog (similar, since both are animals?) or a cat and a car (arguably more different from each other). Thus, it becomes really hard to interpret a single output value of the network. Say an input image results in the output of, say, 1.4.
Does this now still correspond to a dog, or is this closer to a car? But what if the image actually depicts a car that has properties of a cat?
On the other hand, having 3 separate neurons that reflect the different probabilities of each class eliminate that problem, since each one can depict a relatively "undisturbed" probability.
How to Loss Function
The other problem is the question how to backpropagate through the network in the previous example. Classically, classification tasks make use of Cross-Entropy Loss (CE), whereas regression uses Mean Squared Error (MSE) as a measure. Those two are inherently different, and especially the combination of CE and Softmax lead to very convenient (and stable) derivations.
Arguably, you could apply rounding to get from 1.4 to a concise class value (in that case, 1) and then use CE loss, but that would maybe lead to numerically instability; MSE on the other hand will never give you a "clear class value", but more a regressed estimate.
In the end, the question boils down to: Do I have a classification or regression problem. In your case, I would argue that both approaches could work reasonably well. A (classification) network might not recognize the correlation between the different output classes; i.e. a student that has a high likelihood for class 14 basically has zero probability of scoring a 3 or lower. On the other hand, regression might not be able to accurately predict the results for other reasons.
If you have the time, I would highly encourage you to try both approaches. For now, considering the interval type of your target, I would personally go with a regression task, and use rounding after you have trained your network and can make accurate predictions.
It is better to have a single neuron for each class (except binary classification). This allows for better design in terms of expanding upon an existing design. A simple example is creating a network for recognizing digits 0 through 9, but then changing the design to hex from 0 through F.
I was reading through all (or most) previously asked questions, but couldn't find an answer to my problem...
I have 13 variables measured on an ordinal scale (thy represent knowledge transfer channels), which I want to cluster (HCA) for a following binary logistic regression analysis (including all 13 variables is not possible due to sample size of N=208). A Factor Analysis seems inappropriate due to the scale level. I am using SPSS (but tried R as well).
Questions:
1: Am I right in using the Chi-Squared measure for count data instead of the (squared) euclidian distance?
2. How can I justify a choice of method? I tried single, complete, Ward and average, but all give different results and I can't find a source to base my decision on.
Thanks a lot in advance!
Answer 1: Since the variables are on ordinal scale, the chi-square test is an appropriate measurement test. Because, "A Chi-square test is designed to analyze categorical data. That means that the data has been counted and divided into categories. It will not work with parametric or continuous data (such as height in inches)." Reference.
Again, ordinal scaled data is essentially count or frequency data you can use regular parametric statistics: mean, standard deviation, etc Or non-parametric tests like ANOVA or Mann-Whitney U test to compare 2 groups or Kruskal–Wallis H test to compare three or more groups.
Answer 2: In a clustering problem, the choice of distance method solely depends upon the type of variables. I recommend you to read these detailed posts 1, 2,3
I am building a bidirectional LSTM to do multi-class sentence classification.
I have in total 13 classes to choose from and I am multiplying the output of my LSTM network to a matrix whose dimensionality is [2*num_hidden_unit,num_classes] and then apply softmax to get the probability of the sentence to fall into 1 of the 13 classes.
So if we consider output[-1] as the network output:
W_output = tf.Variable(tf.truncated_normal([2*num_hidden_unit,num_classes]))
result = tf.matmul(output[-1],W_output) + bias
and I get my [1, 13] matrix (assuming I am not working with batches for the moment).
Now, I also have information that a given sentence does not fall into a given class for sure and I want to restrict the number of classes considered for a given sentence. So let's say for instance that for a given sentence, I know it can fall only in 6 classes so the output should really be a matrix of dimensionality [1,6].
One option I was thinking of is to put a mask over the result matrix where I multiply the rows corresponding to the classes that I want to keep by 1 and the ones I want to discard by 0, by in this way I will just lose some of the information instead of redirecting it.
Anyone has a clue on what to do in this case?
I think your best bet is, as you seem to have described, using a weighted cross entropy loss function where the weights for your "impossible class" are 0 and 1 for the other possible classes. Tensorflow has a weighted cross entropy loss function.
Another interesting but probably less effective method is to feed whatever information you now have about what classes your sentence can/cannot fall into the network at some point (probably towards the end).
I have a question regarding cross validation in Linear regression model.
From my understanding, in cross validation, we split the data into (say) 10 folds and train the data from 9 folds and the remaining folds we use for testing. We repeat this process until we test all of the folds, so that every folds are tested exactly once.
When we are training the model from 9 folds, should we not get a different model (may be slightly different from the model that we have created when using the whole dataset)? I know that we take an average of all the "n" performances.
But, what about the model? Shouldn't the resulting model also be taken as the average of all the "n" models? I see that the resulting model is same as the model which we created using whole of the dataset before cross-validation. If we are considering the overall model even after cross-validation (and not taking avg of all the models), then what's the point of calculating average performance from n different models (because they are trained from different folds of data and are supposed to be different, right?)
I apologize if my question is not clear or too funny.
Thanks for reading, though!
I think that there is some confusion in some of the answers proposed because of the use of the word "model" in the question asked. If I am guessing correctly, you are referring to the fact that in K-fold cross-validation we learn K-different predictors (or decision functions), which you call "model" (this is a bad idea because in machine learning we also do model selection which is choosing between families of predictors and this is something which can be done using cross-validation). Cross-validation is typically used for hyperparameter selection or to choose between different algorithms or different families of predictors. Once these chosen, the most common approach is to relearn a predictor with the selected hyperparameter and algorithm from all the data.
However, if the loss function which is optimized is convex with respect to the predictor, than it is possible to simply average the different predictors obtained from each fold.
This is because for a convex risk, the risk of the average of the predictor is always smaller than the average of the individual risks.
The PROs and CONs of averaging (vs retraining) are as follows
PROs: (1) In each fold, the evaluation that you made on the held out set gives you an unbiased estimate of the risk for those very predictors that you have obtained, and for these estimates the only source of uncertainty is due to the estimate of the empirical risk (the average of the loss function) on the held out data.
This should be contrasted with the logic which is used when you are retraining and which is that the cross-validation risk is an estimate of the "expected value of the risk of a given learning algorithm" (and not of a given predictor) so that if you relearn from data from the same distribution, you should have in average the same level of performance. But note that this is in average and when retraining from the whole data this could go up or down. In other words, there is an additional source of uncertainty due to the fact that you will retrain.
(2) The hyperparameters have been selected exactly for the number of datapoints that you used in each fold to learn. If you relearn from the whole dataset, the optimal value of the hyperparameter is in theory and in practice not the same anymore, and so in the idea of retraining, you really cross your fingers and hope that the hyperparameters that you have chosen are still fine for your larger dataset.
If you used leave-one-out, there is obviously no concern there, and if the number of data point is large with 10 fold-CV you should be fine. But if you are learning from 25 data points with 5 fold CV, the hyperparameters for 20 points are not really the same as for 25 points...
CONs: Well, intuitively you don't benefit from training with all the data at once
There are unfortunately very little thorough theory on this but the following two papers especially the second paper consider precisely the averaging or aggregation of the predictors from K-fold CV.
Jung, Y. (2016). Efficient Tuning Parameter Selection by Cross-Validated Score in High Dimensional Models. International Journal of Mathematical and Computational Sciences, 10(1), 19-25.
Maillard, G., Arlot, S., & Lerasle, M. (2019). Aggregated Hold-Out. arXiv preprint arXiv:1909.04890.
The answer is simple: you use the process of (repeated) cross validation (CV) to obtain a relatively stable performance estimate for a model instead of improving it.
Think of trying out different model types and parametrizations which are differently well suited for your problem. Using CV you obtain many different estimates on how each model type and parametrization would perform on unseen data. From those results you usually choose one well suited model type + parametrization which you will use, then train it again on all (training) data. The reason for doing this many times (different partitions with repeats, each using different partition splits) is to get a stable estimation of the performance - which will enable you to e.g. look at the mean/median performance and its spread (would give you information about how well the model usually performs and how likely it is to be lucky/unlucky and get better/worse results instead).
Two more things:
Usually, using CV will improve your results in the end - simply because you take a model that is better suited for the job.
You mentioned taking the "average" model. This actually exists as "model averaging", where you average the results of multiple, possibly differently trained models to obtain a single result. Its one way to use an ensemble of models instead of a single one. But also for those you want to use CV in the end for choosing reasonable model.
I like your thinking. I think you have just accidentally discovered Random Forest:
https://en.wikipedia.org/wiki/Random_forest
Without repeated cv your seemingly best model is likely to be only a mediocre model when you score it on new data...
I'm trying to create a sample neural network that can be used for credit scoring. Since this is a complicated structure for me, i'm trying to learn them small first.
I created a network using back propagation - input layer (2 nodes), 1 hidden layer (2 nodes +1 bias), output layer (1 node), which makes use of sigmoid as activation function for all layers. I'm trying to test it first using a^2+b2^2=c^2 which means my input would be a and b, and the target output would be c.
My problem is that my input and target output values are real numbers which can range from (-/infty, +/infty). So when I'm passing these values to my network, my error function would be something like (target- network output). Would that be correct or accurate? In the sense that I'm getting the difference between the network output (which is ranged from 0 to 1) and the target output (which is a large number).
I've read that the solution would be to normalise first, but I'm not really sure how to do this. Should i normalise both the input and target output values before feeding them to the network? What normalisation function is best to use cause I read different methods in normalising. After getting the optimized weights and use them to test some data, Im getting an output value between 0 and 1 because of the sigmoid function. Should i revert the computed values to the un-normalized/original form/value? Or should i only normalise the target output and not the input values? This really got me stuck for weeks as I'm not getting the desired outcome and not sure how to incorporate the normalisation idea in my training algorithm and testing..
Thank you very much!!
So to answer your questions :
Sigmoid function is squashing its input to interval (0, 1). It's usually useful in classification task because you can interpret its output as a probability of a certain class. Your network performes regression task (you need to approximate real valued function) - so it's better to set a linear function as an activation from your last hidden layer (in your case also first :) ).
I would advise you not to use sigmoid function as an activation function in your hidden layers. It's much better to use tanh or relu nolinearities. The detailed explaination (as well as some useful tips if you want to keep sigmoid as your activation) might be found here.
It's also important to understand that architecture of your network is not suitable for a task which you are trying to solve. You can learn a little bit of what different networks might learn here.
In case of normalization : the main reason why you should normalize your data is to not giving any spourius prior knowledge to your network. Consider two variables : age and income. First one varies from e.g. 5 to 90. Second one varies from e.g. 1000 to 100000. The mean absolute value is much bigger for income than for age so due to linear tranformations in your model - ANN is treating income as more important at the beginning of your training (because of random initialization). Now consider that you are trying to solve a task where you need to classify if a person given has grey hair :) Is income truly more important variable for this task?
There are a lot of rules of thumb on how you should normalize your input data. One is to squash all inputs to [0, 1] interval. Another is to make every variable to have mean = 0 and sd = 1. I usually use second method when the distribiution of a given variable is similiar to Normal Distribiution and first - in other cases.
When it comes to normalize the output it's usually also useful to normalize it when you are solving regression task (especially in multiple regression case) but it's not so crucial as in input case.
You should remember to keep parameters needed to restore the original size of your inputs and outputs. You should also remember to compute them only on a training set and apply it on both training, test and validation sets.