ABONAMENTE VIDEO REDACȚIA
RO
EN
NOU
Numărul 144
Numărul 143 Numărul 142 Numărul 141 Numărul 140 Numărul 139 Numărul 138 Numărul 137 Numărul 136 Numărul 135 Numărul 134 Numărul 133 Numărul 132 Numărul 131 Numărul 130 Numărul 129 Numărul 128 Numărul 127 Numărul 126 Numărul 125 Numărul 124 Numărul 123 Numărul 122 Numărul 121 Numărul 120 Numărul 119 Numărul 118 Numărul 117 Numărul 116 Numărul 115 Numărul 114 Numărul 113 Numărul 112 Numărul 111 Numărul 110 Numărul 109 Numărul 108 Numărul 107 Numărul 106 Numărul 105 Numărul 104 Numărul 103 Numărul 102 Numărul 101 Numărul 100 Numărul 99 Numărul 98 Numărul 97 Numărul 96 Numărul 95 Numărul 94 Numărul 93 Numărul 92 Numărul 91 Numărul 90 Numărul 89 Numărul 88 Numărul 87 Numărul 86 Numărul 85 Numărul 84 Numărul 83 Numărul 82 Numărul 81 Numărul 80 Numărul 79 Numărul 78 Numărul 77 Numărul 76 Numărul 75 Numărul 74 Numărul 73 Numărul 72 Numărul 71 Numărul 70 Numărul 69 Numărul 68 Numărul 67 Numărul 66 Numărul 65 Numărul 64 Numărul 63 Numărul 62 Numărul 61 Numărul 60 Numărul 59 Numărul 58 Numărul 57 Numărul 56 Numărul 55 Numărul 54 Numărul 53 Numărul 52 Numărul 51 Numărul 50 Numărul 49 Numărul 48 Numărul 47 Numărul 46 Numărul 45 Numărul 44 Numărul 43 Numărul 42 Numărul 41 Numărul 40 Numărul 39 Numărul 38 Numărul 37 Numărul 36 Numărul 35 Numărul 34 Numărul 33 Numărul 32 Numărul 31 Numărul 30 Numărul 29 Numărul 28 Numărul 27 Numărul 26 Numărul 25 Numărul 24 Numărul 23 Numărul 22 Numărul 21 Numărul 20 Numărul 19 Numărul 18 Numărul 17 Numărul 16 Numărul 15 Numărul 14 Numărul 13 Numărul 12 Numărul 11 Numărul 10 Numărul 9 Numărul 8 Numărul 7 Numărul 6 Numărul 5 Numărul 4 Numărul 3 Numărul 2 Numărul 1
×
▼ LISTĂ EDIȚII ▼
Numărul 17
Abonament PDF

Cât de toxic este codul tău?

Cezar Coca
Senior Design Lead
@Endava



PROGRAMARE

In the last article I presented a short history of deep learning and I listed some of the main techniques that are used. Now I"m going to present the components of a deep learning system.

Deep learning had its first major success in 2006, when Geoffrey Hinton and Ruslan Salakhutdinov published the paper "Reducing the Dimensionality of Data with Neural Networks", which was the first efficient and fast application of Restricted Boltzmann Machines (or RBMs).

As the name suggests, RBMs are a type of Boltzmann machines, with some constraints. These have been proposed by Geoffrey Hinton and Terry Sejnowski in 1985 and they were the first neural networks that could learn internal representations (models) of the input data and then use this representation to solve different problems (such as completing images with missing parts). They weren"t used for a long time because, without any constraints, the learning algorithm for the internal representation was very inefficient.

According to the definition, Boltzmann machines are generative stochastic recurrent neural networks. The stochastic part means that they have a probabilistic element to them and that the neurons that make up the network are not fired deterministically, but with a certain probability, determined by their inputs. The fact that they are generative means that they learn the joint probability of input data, which can then be used to generate new data, similar to the original one.

But there is an alternative way to interpret Boltzmann machines, as being energy based graphical models. This means that for each possible input we associate a number, called the energy of the model, and for the combinations that we have in our data we want this energy to be as low as possible, while for other, unlikely data, it should be high.

The graphical model for an RBM with 4 input units and 3 hidden units

The constraint imposed by RBMs is that neurons must form a bipartite graph, which in practice is done by organizing them into two separate layers, a visible one and a hidden one, and the neurons from each layer have connections to the neurons in the other layer and not to any neuron in the same layer. In the above figure, you can see that there are no connections between any of the h"s, nor any of the v"s, only between every v with every h.

The hidden layer of the RBM can be thought to be made of latent factors that determine the input layer. If, for example, we analyze the grades users give to some movies, the input data will be the grades given by a certain user to the movies, and the hidden layer will correspond to the categories of movies. These categories are not predefined, but the RBM determines them while building its internal model, grouping the movies in such a way that the total energy is minimized. If the input data are pixels, then the hidden layer can be seen as features of objects that could generate those pixels (such as edges, corners, straight lines and other differentiating traits).

If we regard the RBMs as energy based models, we can use the mathematical apparatus used by statistical physics to estimate the probability distributions and then to make predictions. Actually, the Boltzmann distribution from modeling the atoms in a gas gave the name to these neural networks.

The energy of such a model, given the vector v (the input layer), the vector h (the hidden layer), the matrix W (the weights associated with the connections between each neuron from the input layer and the hidden one) and the vectors a and b (which represent the activations thresholds for each neuron, from the input layer and from the hidden layer) can be computed using the following formula:

The formula is nothing to be scared of, it"s just a couple of matrix additions and multiplications.

Once we have the energy for a state, its probability is given by:

where Z is a normalization factor.

And this is where the constraints from the RBM help us. Because the neurons from the visible layer are not connected to each other, it means that for a given value of the hidden layer neuron, the visible ones are conditionally independent of each other. Using this we can easily get the probability for some input data, given the hidden layer:

where

is the activation probability for a single neuron:

is the logistic function.

In a similar way we can define the probability for the hidden layer, having the visible layer fixed.

How does it help us if we know these probabilities?

Let"s presume that we know the correct values for the weights and the thresholds of an RBM and that we want to determine what items are in an image. We set the pixels of the image as the input of the RBM and we calculate the activation probabilities of the hidden layer. We can interpret these probabilities as filters learned by the RBM about the possible objects in the images.

We take the values of those probabilities and we enter them into another RBM as input data. This RBM will also give out some other probabilities for its hidden layer, and these probabilities are also filters for its own inputs. These filters will be of a higher level and more complex. We repeat this a couple of times, we stack the resulting RBMs and, on top of the last one, we add a classification layer (such as logistic regression) and we get ourselves a Deep Belief Network.

Greedy layerwise training of a DBN

Greedy layerwise training of a DBN

The idea that started the deep learning revolution was this: you can learn layer by layer filters that get more and more complex and at the end you don"t work directly with pixels, but with high level features, that are much better indicators of what objects are there in an image.

The learning of the parameters of a RBM is done using an algorithm called "contrastive divergence". This starts with an example from the input data, calculates the values for the hidden layer and then these values are used to simulate what input data they would produce. The weights are then adjusted with the difference between the original input data and the "dreamed" input data (with some inner products around there). This process is repeated for each example of the input data, several times, until either the error is small enough or a predetermined number of iterations have passed.

There are many implementations of RBMs in machine learning libraries. One such library is scikit-learn, a Python library used by companies such as Evernote and Spotify for their note classifications and music recommendation engines. The following code shows how easy it is to train an RBM on images that each contain one digit or one letter and then to visualize the learned filters.

from sklearn.neural_network import BernoulliRBM as RBM
import numpy as np
import matplotlib.pyplot as plt
import cPickle

X,y = cPickle.load(open("letters.pkl"))
X = (X - np.min(X, 0)) / (np.max(X, 0) + 0.0001)  # 0-1 scaling
rbm = RBM(n_components=900, learning_rate=0.05, batch_size=100, n_iter=50)
print("Init rbm")

rbm.fit(X)

plt.figure(figsize=(10.2, 10))
for i, comp in enumerate(rbm.components_):
    plt.subplot(30, 30, i + 1)
    plt.imshow(comp.reshape((20, 20)), cmap=plt.cm.gray_r,
               interpolation="nearest")
    plt.xticks(())
    plt.yticks(())
plt.suptitle("900 components extracted by RBM", fontsize=16)

plt.show()
Some of the filters learned by the RBM: you can notice filters for the letters B, R, S, for the digits 0, 8, 7 and some others

Some of the filters learned by the RBM: you can notice filters for the letters B, R, S, for the digits 0, 8, 7 and some others

Some of the filters learned by the RBM: you can notice filters for the letters B, R, S, for the digits 0, 8, 7 and some others

RBMs are an essential component from which deep learning started and are one of the few models that allow us to learn efficiently an internal representation of the problem we want to solve. In the next article, we will see another approach in learning representations, using autoencoders.

LANSAREA NUMĂRULUI 144

Modern Agile

joi, 20 iunie, ora 18:00

sediul msg systems Romania

Facebook Meetup StreamEvent YouTube

NUMĂRUL 143 - Software Craftsmanship

Sponsori

  • Accenture
  • BT Code Crafters
  • Accesa
  • Bosch
  • Betfair
  • MHP
  • BoatyardX
  • .msg systems
  • P3 group
  • Ing Hubs
  • Colors in projects