Archive for neural network

Nature snapshots [and snide shots]

Posted in Books, pictures, Statistics, Travel, University life with tags , , , , , , , , , , , on October 12, 2017 by xi'an

A very rich issue of Nature I received [late] just before leaving for Warwick with a series of reviews on quantum computing, presenting machine learning as the most like immediate application of this new type of computing. Also including irate letters and an embarassed correction of an editorial published the week before reflecting on the need (or lack thereof) to remove or augment statues of scientists whose methods were unethical, even when eventually producing long lasting advances. (Like the 19th Century gynecologist J. Marion Sims experimenting on female slaves.) And a review of a book on the fascinating topic of Chinese typewriters. And this picture above of a flooded playground that looks like a piece of abstract art thanks to the muddy background.

“Quantum mechanics is well known to produce atypical patterns in data. Classical machine learning methods such as deep neural networks frequently have the feature that they can both recognize statistical patterns in data and produce data that possess the same statistical patterns: they recognize the patterns that they produce. This observation suggests the following hope. If small quantum information processors can produce statistical patterns that are computationally difficult for a classical computer to produce, then perhaps they can also recognize patterns that are equally difficult to recognize classically.” Jacob Biamonte et al., Nature, 14 Sept 2017

One of the review papers on quantum computing is about quantum machine learning. Although like Jon Snow I know nothing about this, I find it rather dull as it spends most of its space on explaining existing methods like PCA and support vector machines. Rather than exploring potential paradigm shifts offered by the exotic nature of quantum computing. Like moving to Bayesian logic that mimics a whole posterior rather than produces estimates or model probabilities. And away from linear representations. (The paper mentions a O(√N) speedup for Bayesian inference in a table, but does not tell more, which may thus be only about MAP estimators for all I know.) I also disagree with the brave new World tone of the above quote or misunderstand its meaning. Since atypical and statistical cannot but clash, “universal deep quantum learners may recognize and classify patterns that classical computers cannot” does not have a proper meaning. The paper contains a vignette about quantum Boltzman machines that finds a minimum entropy approximation to a four state distribution, with comments that seem to indicate an ability to simulate from this system.

fast ε-free ABC

Posted in Books, Mountains, pictures, Running, Statistics, Travel, University life with tags , , , , , , , , , on June 8, 2017 by xi'an

Last Fall, George Papamakarios and Iain Murray from Edinburgh arXived an ABC paper on fast ε-free inference on simulation models with Bayesian conditional density estimation, paper that I missed. The idea there is to approximate the posterior density by maximising the likelihood associated with a parameterised family of distributions on θ, conditional on the associated x. The data being then the ABC reference table. The family chosen there is a mixture of K Gaussian components, which parameters are then estimated by a (Bayesian) neural network using x as input and θ as output. The parameter values are simulated from an adaptive proposal that aims at approximating the posterior better and better. As in population Monte Carlo, actually. Except for the neural network part, which I fail to understand why it makes a significant improvement when compared with EM solutions. The overall difficulty with this approach is that I do not see a way out of the curse of dimensionality: when the dimension of θ increases, the approximation to the posterior distribution of θ does deteriorate, even in the best of cases, as any other non-parametric resolution. It would have been of (further) interest to see a comparison with a most rudimentary approach, namely the one we proposed based on empirical likelihoods.

machine learning and the future of realism

Posted in Books, Kids, Statistics, University life with tags , , , , , , , , on May 4, 2017 by xi'an

Giles and Cliff Hooker arXived a paper last week with this intriguing title. (Giles Hooker is an associate professor of statistics and biology at Cornell U, with an interesting blog on the notion of models, while Cliff Hooker is a professor of philosophy at Newcastle U, Australia.)

“Our conclusion is that simplicity is too complex”

The debate in this short paper is whether or not machine learning relates to a model. Or is it concerned with sheer (“naked”) prediction? And then does it pertain to science any longer?! While it sounds obvious at first, defining why science is more than prediction of effects given causes is much less obvious, although prediction sounds more pragmatic and engineer-like than scientific. (Furthermore, prediction has a somewhat negative flavour in French, being used as a synonym to divination and opposed to prévision.) In more philosophical terms, prediction offers no ontological feature. As for a machine learning structure like a neural network being scientific or a-scientific, its black box nature makes it much more the later than the former, in that it brings no explanation for the connection between input and output, between regressed and regressors. It further lacks the potential for universality of scientific models. For instance, as mentioned in the paper, Newton’s law of gravitation applies to any pair of weighted bodies, while a neural network built on a series of observations could not be assessed or guaranteed outside the domain where those observations are taken. Plus, would miss the simple square law established by Newton. Most fascinating questions, undoubtedly! Putting the stress on models from a totally different perspective from last week at the RSS.

As for machine learning being a challenge to realism, I am none the wiser after reading the paper. Utilising machine learning tools to produce predictions of causes given effects does not seem to modify the structure of the World and very little our understanding of it, since they do not bring explanation per se. What would lead to anti-realism is the adoption of those tools as substitutes for scientific theories and models.

Bayesian program synthesis

Posted in Books, pictures, Statistics, University life with tags , , , , , , , , on April 7, 2017 by xi'an

Last week, I—along with Jean-Michel Marin—got an email from a journalist working for Science & Vie, a French sciences journal that published a few years ago a special issue on Bayes’ theorem. (With the insane title of “the formula that deciphers the World!”) The reason for this call was the preparation of a paper on Gamalon, a new AI company that relies on (Bayesian) probabilistic programming to devise predictive tools. And spent an hour skyping with him about Bayesian inference, probabilistic programming and machine-learning, at the general level since we had not heard previously of this company or of its central tool.

“the Gamalon BPS system learns from only a few examples, not millions. It can learn using a tablet processor, not hundreds of servers. It learns right away while we play with it, not over weeks or months. And it learns from just one person, not from thousands.”

Gamalon claims to do much better than deep learning at those tasks. Not that I have reasons to doubt that claim, quite the opposite, an obvious reason being that incorporating rules and probabilistic models in the predictor is going to help if these rule and models are even moderately realistic, another major one being that handling uncertainty and learning by Bayesian tools is usually a good idea (!), and yet another significant one being that David Blei is a member of their advisory committee. But it is hard to get a feeling for such claims when the only element in the open is the use of probabilistic programming, which is an advanced and efficient manner of conducting model building and updating and handling (posterior) distributions as objects, but which does not enjoy higher predictives abilities by default. Unless I live with a restricted definition of what probabilistic programming stands for! In any case, the video provided by Gamalon and the presentation given by its CEO do not help in my understanding of the principles behind this massive gain in efficiency. Which makes sense given that the company would not want to give up their edge on the competition.

Incidentally, the video in this presentation comparing the predictive abilities of the four major astronomical explanations of the solar system is great. If not particularly connected with the difference between deep learning and Bayesian probabilistic programming.

machines learning but not teaching…

Posted in Books, pictures with tags , , , , , , , on October 28, 2016 by xi'an

A few weeks after the editorial “Algorithms and Blues“, Nature offers another (general public) entry on AIs and their impact on society, entitled “The Black Box of AI“. The call is less on open source AIs and more on accountability, namely the fact that decisions produced by AIS and impacting people one way or another should be accountable. Rather than excused by the way out “the computer said so”. What the article exposes is how (close to) impossible this is when the algorithms are based on black-box structures like neural networks and other deep-learning algorithms. While optimised to predict as accurately as possible one outcome given a vector of inputs, hence learning in that way how the inputs impact this output [in the same range of values], these methods do not learn in a more profound way in that they very rarely explain why the output occurs given the inputs. Hence, given a neural network that predicts go moves or operates a self-driving car, there is a priori no knowledge to be gathered from this network about the general rules of how humans play go or drive cars. This rather obvious feature means that algorithms that determine the severity of a sentence cannot be argued as being rational and hence should not be used per se (or that the judicial system exploiting them should be sued). The article is not particularly deep (learning), but it mentions a few machine-learning players like Pierre Baldi, Zoubin Ghahramani and Stéphane Mallat, who comments on the distance existing between those networks and true (and transparent) explanations. And on the fact that the human brain itself goes mostly unexplained. [I did not know I could include such dynamic images on WordPress!]

go, go, go…deeper!

Posted in pictures, Statistics with tags , , , , , , , , , , on February 19, 2016 by xi'an

While visiting Warwick, last week, I came across the very issue of Nature with the highly advertised paper of David Silver and co-authors from DeepMind detailing how they designed their Go player algorithm that bested a European Go master five games in a row last September. Which is a rather unexpected and definitely brilliant feat given the state of the art! And compares (in terms of importance, if not of approach) with the victory of IBM Deep Blue over Gary Kasparov 20 years ago… (Another deep algorithm, showing that the attraction of programmers for this label has not died off over the years!)This paper is not the easiest to read (especially over breakfast), with (obviously) missing details, but I gathered interesting titbits from this cursory read. One being the reinforced learning step where the predictor is improved by being applied against earlier versions. While this can lead to overfitting, the authors used randomisation to reduce this feature. This made me wonder if a similar step could be on predictors like random forests. E.g., by weighting the trees or the probability of including a predictor or another.Another feature of major interest is their parallel use of two neural networks in the decision-making, a first one estimating a probability distribution over moves learned from millions of human Go games and a second one returning a utility or value for each possible move. The first network is used for tree exploration with Monte Carlo steps, while the second leads to the final decision.

This is a fairly good commercial argument for machine learning techniques (and for DeepMind as well), but I do not agree with the doom-sayers predicting the rise of the machines and our soon to be annihilation! (Which is the major theme of Superintelligence.) This result shows that, with enough learning data and sufficiently high optimising power and skills, it is possible to produce an excellent predictor of the set of Go moves leading to a victory. Without the brute force strategy of Deep Blue that simply explored the tree of possible games to a much more remote future than a human player could do (along with the  perfect memory of a lot of games). I actually wonder if DeepMind has also designed a chess algorithm on the same principles: there is no reason why it should no work. However, this success does not predict the soon to come emergence of AI’s able to deal with vaguer and broader scopes: in that sense, automated drivers are much more of an advance (unless they start bumping into other cars and pedestrians on a regular basis!).

deep learning ABC summary statistics

Posted in Books, Statistics, University life with tags , , , , , , , , on October 19, 2015 by xi'an

“The main task of this article is to construct low-dimensional and informative summary statistics for ABC methods.”

The idea in the paper “Learning Summary Statistic for ABC via Deep Neural Network”, arXived a few days ago, is to start from the raw data and build a “deep neural network” (meaning a multiple layer neural network) to provide a non-linear regression of the parameters over the data. (There is a rather militant tone to the justification of the approach, not that unusual with proponents of deep learning approaches, I must add…) Whose calibration never seems an issue. The neural construct is called to produce an estimator (function) of θ, θ(x). Which is then used as the summary statistics. Meaning, if Theorem 1 is to be taken as the proposal, that a different ABC needs to be run for every function of interest. Or, in other words, that the method is not reparameterisation invariant.

The paper claims to achieve the same optimality properties as in Fearnhead and Prangle (2012). These are however moderate optimalities in that they are obtained for the tolerance ε equal to zero. And using the exact posterior expectation as a summary statistic, instead of a non-parametric estimate.  And an infinite functional basis in Theorem 2. I thus see little added value in results like Theorem 2 and no real optimality: That the ABC distribution can be arbitrarily close to the exact posterior is not an helpful statement when implementing the method.

The first example in the paper is the posterior distribution associated with the Ising model, which enjoys a sufficient statistic of dimension one. The issue of generating pseudo-data from the Ising model is evacuated by a call to a Gibbs sampler, but remains an intrinsic problem as the convergence of the Gibbs sampler depends on the value of the parameter θ and especially its location wrt the critical point. Both ABC posteriors are shown to be quite close.

The second example is the posterior distribution associated with an MA(2) model, apparently getting into a benchmark in the ABC literature. The comparison between an ABC based on the first two autocorrelations, an ABC based on the semi-automatic solution of Fearnhead and Prangle (2012) [for which collection of summaries?], and the neural network proposal, leads to the dismissal of the semi-automatic solution and the neural net being closest to the exact posterior [with the same tolerance quantile ε for all approaches].

A discussion crucially missing from the paper—from my perspective—is an accounting for size: First, what is the computing cost of fitting and calibrating and storing a neural network for the sole purpose of constructing a summary statistic? Once the neural net is constructed, I would assume most users would see little need in pursuing the experiment any further. (This was also why we stopped at our random forest output rather than using it as a summary statistic.) Second, how do cost and performances evolve as the dimension of the parameter θ grows? I would deem necessary to understand when the method fails. As for instance in latent variable models such as HMMs. Third, how does the size of the sample impact cost and performances? In many realistic cases when ABC applies, it is not possible to use the raw data, given its size, and summary statistics are a given. For such examples, neural networks should be compared with other ABC solutions, using the same reference table.