iterative observation of data (arrays) and problem with jagged array type specification - infer.net
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Hi Zahra,
I'm not sure that what you did is correct. In the new way you defined the model, w is no longer shared across data batches. I thought you do want to share w though. For now I'll assume this is the case, so do let me know if it's not.
My previous post showed how to do online learning when the model parameters are defined using the Random factor. If you want to do online learning in a model where the prior is hierarchical, you need to take a different approach. I’ll explain how to do this for a single model parameter to avoid boiler plate code, but I hope you can extend it to arrays of parameters.
Let’s firstly consider the simpler scenario where w is defined using the Random factor from a fixed wPrior variable. That is, the prior is not hierarchical. We’ll assume that the online learning is performed over a set of data batches, and the parameter w is shared across all of them. What you do after training on each data batch is to infer the posterior of w and plug it in as the new prior for the next batch. Thus, you can think of wPrior as the summary of what we’ve learnt “so far” (or “up to the current batch”).
Unfortunately, when the prior is hierarchical, you can no longer “store” your current knowledge in it in such a way. Look at the following model, which hopefully resembles your factor graph to a certain extend. The variable w now has a Laplace prior – the mean of the Gaussian is observed, but its variance is drawn from a Gamma. Here G.M.V. stands for GaussianFromMeanAndVariance and G.S.R. stands for GammaFromShapeAndRate.
I explicitly denoted the data batches with b<sub>1</sub>…b<sub>n</sub> to illustrate the abstract model that you have. This is important because it will differ from the model that you actually run inference in. That’s because you want to process these batches one by one (as opposed to having them all at once as shown above).
To process the batches sequentially, we need to add a new “accumulator” of our knowledge (an equivalent to what wPrior was used for in the non-hierarchical case). We’ll call this wMsg. It stores the product of all messages sent to w by the previous batches. We’ll attach this variable to w by using yet another special factor – ConstrainEqualRandom (or C.E.R.). All it does is to pass forward the message of its argument. This is shown in the following factor graph:
Initially, wMsg should be Uniform, since there are no previous batches. After each batch, you need to store there the message sent upward to w, which also happens to be the marginal of w divided by its prior. Luckily, Infer.NET allows you to obtain this by doing the following:
wMsg.ObservedValue = engine.Infer<Gaussian>(w, QueryTypes.MarginalDividedByPrior);Also, you need to give the compiler a hint that you’ll be doing this:
w.AddAttribute(QueryTypes.MarginalDividedByPrior);Here’s the complete code for online learning of a Gaussian with a Laplacian mean:
Variable<int> nItems = Variable.New<int>().Named("nItems"); Range item = new Range(nItems).Named("item"); Variable<double> variance = Variable.GammaFromShapeAndRate(1.0, 1.0).Named("variance"); Variable<double> w = Variable.GaussianFromMeanAndVariance(0.0, variance).Named("w"); VariableArray<double> x = Variable.Array<double>(item).Named("x"); x[item] = Variable.GaussianFromMeanAndPrecision(w, 1.0).ForEach(item); Variable<Gaussian> wMsg = Variable.Observed(Gaussian.Uniform()).Named("wMsg"); Variable.ConstrainEqualRandom(w, wMsg); w.AddAttribute(QueryTypes.Marginal); w.AddAttribute(QueryTypes.MarginalDividedByPrior); InferenceEngine engine = new InferenceEngine(); // inference on a single batch double[] data = { 2, 3, 4, 5 }; x.ObservedValue = data; nItems.ObservedValue = data.Length; Gaussian wExpected = engine.Infer<Gaussian>(w); // online learning in mini-batches int batchSize = 1; double[][] dataBatches = new double[data.Length / batchSize][]; for (int batch = 0; batch < dataBatches.Length; ++batch) { dataBatches[batch] = data.Skip(batch * batchSize).Take(batchSize).ToArray(); } Gaussian wMarginal = Gaussian.Uniform(); for (int batch = 0; batch < dataBatches.Length; ++batch) { nItems.ObservedValue = dataBatches[batch].Length; x.ObservedValue = dataBatches[batch]; wMarginal = engine.Infer<Gaussian>(w); Console.WriteLine("w after batch {0} = {1}", batch, wMarginal); wMsg.ObservedValue = engine.Infer<Gaussian>(w, QueryTypes.MarginalDividedByPrior); } Console.WriteLine("Expected: {0}", wExpected); Console.WriteLine("Actual: {0}", wMarginal);Note that in general you need to apply this method to all model parameters that are shared across the data batches.
Hope this helps,
Yordan- Proposed as answer by Yordan ZaykovMicrosoft employee Wednesday, June 4, 2014 11:19 PM
- Marked as answer by RazinR Sunday, June 8, 2014 11:29 AM
All replies
-
Hi Zahra,
I'm not sure that what you did is correct. In the new way you defined the model, w is no longer shared across data batches. I thought you do want to share w though. For now I'll assume this is the case, so do let me know if it's not.
My previous post showed how to do online learning when the model parameters are defined using the Random factor. If you want to do online learning in a model where the prior is hierarchical, you need to take a different approach. I’ll explain how to do this for a single model parameter to avoid boiler plate code, but I hope you can extend it to arrays of parameters.
Let’s firstly consider the simpler scenario where w is defined using the Random factor from a fixed wPrior variable. That is, the prior is not hierarchical. We’ll assume that the online learning is performed over a set of data batches, and the parameter w is shared across all of them. What you do after training on each data batch is to infer the posterior of w and plug it in as the new prior for the next batch. Thus, you can think of wPrior as the summary of what we’ve learnt “so far” (or “up to the current batch”).
Unfortunately, when the prior is hierarchical, you can no longer “store” your current knowledge in it in such a way. Look at the following model, which hopefully resembles your factor graph to a certain extend. The variable w now has a Laplace prior – the mean of the Gaussian is observed, but its variance is drawn from a Gamma. Here G.M.V. stands for GaussianFromMeanAndVariance and G.S.R. stands for GammaFromShapeAndRate.
I explicitly denoted the data batches with b<sub>1</sub>…b<sub>n</sub> to illustrate the abstract model that you have. This is important because it will differ from the model that you actually run inference in. That’s because you want to process these batches one by one (as opposed to having them all at once as shown above).
To process the batches sequentially, we need to add a new “accumulator” of our knowledge (an equivalent to what wPrior was used for in the non-hierarchical case). We’ll call this wMsg. It stores the product of all messages sent to w by the previous batches. We’ll attach this variable to w by using yet another special factor – ConstrainEqualRandom (or C.E.R.). All it does is to pass forward the message of its argument. This is shown in the following factor graph:
Initially, wMsg should be Uniform, since there are no previous batches. After each batch, you need to store there the message sent upward to w, which also happens to be the marginal of w divided by its prior. Luckily, Infer.NET allows you to obtain this by doing the following:
wMsg.ObservedValue = engine.Infer<Gaussian>(w, QueryTypes.MarginalDividedByPrior);Also, you need to give the compiler a hint that you’ll be doing this:
w.AddAttribute(QueryTypes.MarginalDividedByPrior);Here’s the complete code for online learning of a Gaussian with a Laplacian mean:
Variable<int> nItems = Variable.New<int>().Named("nItems"); Range item = new Range(nItems).Named("item"); Variable<double> variance = Variable.GammaFromShapeAndRate(1.0, 1.0).Named("variance"); Variable<double> w = Variable.GaussianFromMeanAndVariance(0.0, variance).Named("w"); VariableArray<double> x = Variable.Array<double>(item).Named("x"); x[item] = Variable.GaussianFromMeanAndPrecision(w, 1.0).ForEach(item); Variable<Gaussian> wMsg = Variable.Observed(Gaussian.Uniform()).Named("wMsg"); Variable.ConstrainEqualRandom(w, wMsg); w.AddAttribute(QueryTypes.Marginal); w.AddAttribute(QueryTypes.MarginalDividedByPrior); InferenceEngine engine = new InferenceEngine(); // inference on a single batch double[] data = { 2, 3, 4, 5 }; x.ObservedValue = data; nItems.ObservedValue = data.Length; Gaussian wExpected = engine.Infer<Gaussian>(w); // online learning in mini-batches int batchSize = 1; double[][] dataBatches = new double[data.Length / batchSize][]; for (int batch = 0; batch < dataBatches.Length; ++batch) { dataBatches[batch] = data.Skip(batch * batchSize).Take(batchSize).ToArray(); } Gaussian wMarginal = Gaussian.Uniform(); for (int batch = 0; batch < dataBatches.Length; ++batch) { nItems.ObservedValue = dataBatches[batch].Length; x.ObservedValue = dataBatches[batch]; wMarginal = engine.Infer<Gaussian>(w); Console.WriteLine("w after batch {0} = {1}", batch, wMarginal); wMsg.ObservedValue = engine.Infer<Gaussian>(w, QueryTypes.MarginalDividedByPrior); } Console.WriteLine("Expected: {0}", wExpected); Console.WriteLine("Actual: {0}", wMarginal);Note that in general you need to apply this method to all model parameters that are shared across the data batches.
Hope this helps,
Yordan- Proposed as answer by Yordan ZaykovMicrosoft employee Wednesday, June 4, 2014 11:19 PM
- Marked as answer by RazinR Sunday, June 8, 2014 11:29 AM
