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Learning to learn thrun and pratt pdf download

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Learning to Learn | Sebastian Thrun | Springer


Learning a Synaptic Learning Rule. Download full-text PDF. Citations (59) References (14) Thrun & Pratt, ;Schmidhuber, ) in the context of link prediction. This few shot link. Learning To Learn Sebastian Thrun and Lorien Y. Pratt Kluwer Academic Publishers. Over the past three decades, research on machine learning and data mining has led to a wide variety of algorithms that induce general functions from examples. Empirical Bayes for Learning to Learn Tom Heskes tom@blogger.com SNN, University of Nijmegen, Geert Grooteplein 21, Nijmegen, EZ, The Netherlands Abstract learn" described in, among others, Baxter () and Thrun and Pratt ().




learning to learn thrun and pratt pdf download


Learning to learn thrun and pratt pdf download


To browse Academia. Skip to main content. Log In Sign Up. Tom Heskes. Empirical Bayes for learning to learn. We present a new model for studying mul- titask learning, learning to learn thrun and pratt pdf download theoretical results to Multitask learning constitutes an ideal setting for practical simulations. In our model all tasks studying learning to learn.


In multitask learning we are combined in a single feedforward neu- are dealing with many related tasks. The hope is that ral network. In this Bayesian frame- sharing parameters, learning to learn thrun and pratt pdf download. The input-to-hidden weights, task. Other hyper- set of features can be obtained. This idea has been parameters describe error variance and cor- studied and tested on practical problems in e.


Caru- relations and priors for the model param- ana and Pratt and Jennings Whether eters. Pa- cient statistics. Information-theoretic ar- ing a relatively straightforward optimization guments show that multitask learning can be highly problem.


Simulations on real-world data sets advantageous, especially when the number of hyper- on single-copy newspaper and magazine sales parameters is much larger than the number of model illustrate properties of multitask learning.


In this article, we aim at a practical implementation of Baxter's framework. The essence is the ability to com- 1. Introduction pute the probability of the hyperparameters given the Machine learning is the art of building machines that data.


In a full hierarchical Bayesian procedure, one learn from data. Whereas the learning part is auto- should sample the hyperparameters from this distri- matic, an expert has to take care of the building part.


The empirical Bayesian ap- on. In many cases the expert's capabilities are crucial proach is the frequentist shortcut: rather than sam- for the success or failure of an application: he or she pling the distribution of hyperparameters, we will only has to provide the right bias that makes the machine consider their most likely values, learning to learn thrun and pratt pdf download.


The feature learning to learn thrun and pratt pdf download B is shared by all tails. These details are necessary for building a robust tasks and will thus play the role of a hyperparameter, learning to learn thrun and pratt pdf download.


In this article and thus treated as model parameters. Assuming independently and identically retically but still applicable on real-world problems, learning to learn thrun and pratt pdf download. This sis that follows. Going through this analysis it can assumption is introduced to simplify the mathematical be seen that we do not need to require that all tasks exposition, but will be relaxed later on.


This distinction With the constraint 3 the maximum likelihood solu- between an individual noise term and a common noise tion Aml takes the simple form term becomes relevant when the individual predictions are translated to an aggregate level. Furthermore, substantial ance matrix. Note that the data likelihood 2 can correlations might indicate that some important infor- be rewritten as the exponent of a term quadratic in mation is lacking.


Aml times a term independent of A. The standard case, maximum likelihood covariance matrix. How similar is determined by the quire sampling over hyperparameters see e. The exchangeability assumption is rather strong. An example of such a ages, e. This speed- and z a vector of all ones. In the case of newspaper up enables extensive testing of all kinds of ideas and sales, task characteristics are properties of the partic- options.


An example is a useful representation of titask learning on real-world databases, leaving precise the outlet's geographical location. Empirical Bayes 3. In empirical Bayes the idea is to learning to learn thrun and pratt pdf download and for analyzing nested data sets see e. Robert, levels of noise.


Using Bayes' formula we obtain multilevel analysis are the inference of the feature ma- Z Z trix B and the incorporation of correlated errors. The original input vectors are trans- set. The second stages of learn- over patterns. ATmp Bml x 2 : volved. Apparently the loss function is dominated by Here the average is over all combinations of inputs and the dependency of the standard mean-squared error outputs belonging to data set Dtested.


As shown in Baldi and Hornikthis feature matrix Bmlare used to derive the most prob- term has no local minima, only saddle points.


The obtained feature matrices B make a lot of sense, learning to learn thrun and pratt pdf download. An example is news content such inter-task test error is the most interesting one: it mea- as sports results. By inter- sions have been made. In general, the higher erage over the two options. For example, we consider this number, the higher the signal-to-noise ratio. With higher numbers of hidden units, more few training patterns.


Prior means de- 4. Mean-squared errors as a function of the number of hidden units. The lines serve to guide the eye.


Error bars give the standard deviation of the mean. Averages over 20 runs. See the text for further details. Loosely speaking, the maximumlikelihood eas. The results are shown in Figure 1. In curate priors really start to pay o. In our model we have both a bottleneck of hidden Looking at the inter-task test error on the lefthand units, reducing the inputs to a smaller set of fea- side, it can be seen that both the feature matrix and tures, and, on top of that, hyperparameters specify- the priors for the model parameters improve perfor- ing a prior for the model parameters.


Do we really mance. The test error based on the maximum likeli- need both? To check this we applied the simulation hood solutions neglecting the prior rapidly grows with paradigm sketched above to data set III, varying the increasing number of features, yielding learning to learn thrun and pratt pdf download far the worst number of features and computing error measures not performance with all tasks treated separately.


The op- only for the most probable solutions Ampbut also for timum for the most probable solutions is obtained for the maximumlikelihood solutions Aml. In short, the main aspects of the prior information following e. Caruana and model, feature reduction and exchangeability of model Pratt and Jennings Averages over 75 runs. But now we varied the ber of features, for the maximum likelihood solutions number of training tasks used for optimizing the hy- a little faster than for the most probable solutions.


Roughly speaking, they measure the of the number of tasks used to optimize the hyper- impact of a single task on the hyperparameters opti- parameters. On the right are the learning curves for mized on a set of n tasks. The intra-task training error is consistently lower than the inter-task training ear relationship between these errors and the inverse error, as could be expected.


In other words, when to be worked out more precisely in a separate article. Call consideration. We have observed similar behavior in E1 the training error that would be obtained with an other simulations, but do not yet fully understand it. Assuming that the train- In another set of simulations on data set I, we derived ing error is the dominant term in the loss function the learning curves of Figure 2.


Based on this expression, we would predict an algorithm. Furthermore, the intra- and inter-task learning hyperparameters. From a technical point of training error indeed seem to have the same intercept.


At this higher level, we test error. They are measured based on the same set can apply many of the algorithms originally designed of hyperparameters, obtained on an independent set for model parameters, such as e. Another alternative is to ap- proximate their distribution using a standard Laplace with jAj the dimension of model parameters.


This approximation see e. Robert, Furthermore, closer to the framework of Baxter Discussion and Outlook with E0 some base-line error, a related to the number of model parameters per task, b related to the num- In this article we have presented a new model ber of hyperparameters, N the number of patterns per for multitask learning, analyzed within an empirical task, and n the number of tasks.


Compared with the multitask learning ap- test error are puzzling and not yet understood. This might be done in a student-teacher level, the Bayesian approach has several advantages. This turns the maximum likelihood fying assumptions and extend the model.


Secondly, ronment of newspaper and magazine sales. More im- the Bayesian approach naturally takes into account the portant is an integration with Bayesian methodology variability of the model parameters A around their for time series prediction. But even without these im- most probable values Amp. In the model considered provements, the current model allows for rapid testing in this article, the model parameters can be inte- of architectures and all kinds of other options, which grated out explicitely, yielding a nonlinear optimiza- would otherwise be infeasible.


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Learning to learn thrun and pratt pdf download


learning to learn thrun and pratt pdf download

in Project Iris (glucose-sensing contact lenses), Wing (drones for food delivery), Loon (stratospheric balloons for telecommunication), Google Brain (deep learning for most Google services), Chauffeur. However, if the learning machine is embedded within an {\em environment} of related tasks, then it can {\em learn} its own bias by learning sufficiently many tasks from the environment. In this paper two models of bias learning (or equivalently, learning to learn) are introduced and the main theoretical results presented. Learning to Learn is an exciting new research direction within machine learning. Similar to traditional machine-learning algorithms, the methods described in Learning to Learn induce general functions from experience. However, the book investigates algorithms that can change the way they generalize, i.e., practice the task of learning itself.






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