Numerai deep learning

I have used the python for coding the convolutional neural network. The code has been taken from [6] and was modified to work for this dataset. The convolutional neural network was built using the Theano library in Python [1]. The model is simplified by this 23 implementation because it does not implement location-specific gain and bias parameters and also it implements pooling by maximum and not by average. The LeNet5 model uses logistic regression for image classification. The convolutional neural network was trained by passing the compressed train, test and validation datasets. There is one bias per output feature map. The feature maps are convolved with filters and each feature map is individually downsampled using max-pooling. The compressed dataset is divided into small batch sizes so as to reduce the overhead of computing and copying data for each individual image. The batch size for this model is set to 500. We keep the learning rate which is the factor for the stochastic gradient as 0.1. The maximum number of epochs for running the optimizer is kept as 200 which means the learning for each label goes on for 200 epochs so as to optimize the network. When the first convolutional pooling layer is constructed, filtering reduces the image size to 24×24, which is further reduced to 12×12 by max-pooling. During the construction of the second convolutional pooling layer the image size is reduced to 8×8 by filtering and max-pooling reduces it further to 4×4. Since the hidden layer is fully-connected it operates on 2D matrices of rasterized images. This generates a matrix of shape (500, 800) with default values. The values of the fully-connected hidden layer are classified using Logistic Regression. The cost which is minimized during training is the negative log likelihood of the model. A Theano function [2] test model is constructed to compute the incorrect calculations that are made by the model. We create two lists, one of all model parameters that have to be fit by the gradient descent and the other of gradients of all model parameter. The updating of the model parameters by Stochastic Gradient Descent(SGD) is done by the Train Model which is a Theano function. Manually creating update rules for each model parameters results in being tedious because of many parameters present in this model. The updates list is thus created by looping over all pairs automatically. We keep a improvement threshold which means that a relative improvement of this much value is considered as significant. Once the training of the convolutional neural network is done, it is the train model that is returned.

Deep learning refers to a class of machine learning techniques, where many layers of information processing stages in hierarchical architectures are exploited for pattern classifi- cation and for feature or representation learning [10]. It lies in the intersections of several research areas, including neural networks, graphical modeling, optimization, pattern recognition, and signal processing, etc. [5] Yann LeCun adopted the deep supervised backpropagation convolutional network for digit recognition. In the recent past, it has become a valuable research topic in the fields of both computer vision and machine learning where deep learning achieves state-of-the art results for a variety of tasks. The deep convolutional neural networks (CNNs) proposed by Hinton came out first in the image classification task of Imagenet classification with deep convolutional neural networks. The model was trained on more than one million images, and has achieved a winning top-5 test error rate of 15.3% over 1, 000 classes. After that, some recent works got better results by improving CNN models. The top-5 test error rate decreased to 13.24% in by training the model to simultaneously classify, locate and detect objects. Besides image classification, the object detection task can also benefit from the CNN model, as reported in. Generally speaking, three important reasons for the popularity of deep learning today are drastically increased chip processing abilities (e.g., GPU units), the significantly lower cost of computing hardware, and recent advances in machine learning and signal/information processing research. Over the past several years, a rich family of deep learning techniques has been proposed and extensively studied, e.g., Deep Belief Network (DBN), Boltzmann Machines (BM), Restricted Boltzmann Machines (RBM), Deep Boltzmann Machine (DBM), Deep Neural 6 Networks (DNN), etc. Among various techniques, the deep convolutional neural networks, which is a discriminative deep architecture and belongs to the DNN category, has found state-of-the-art performance on various tasks and competitions in computer vision and image recognition. Specifically, the CNN model consists of several convolutional layers and pooling layers, which are stacked up with one on top of another. The convolutional layer shares many weights, and the pooling layer sub-samples the output of the convolutional layer and reduces the data rate from the layer below. The weight sharing in the convolutional layer, together with appropriately chosen pooling schemes, endows the CNN with some invariance properties (e.g., translation invariance). My work is similar to the work of Ji Wan et al.[10] but differs from them in the sense that the dataset I am using is different from the ones they have used in their study. Also my approach of image matching will be completely novel which has not been used in any study similar to mine.

Numerai deep learning example

The research in the past decade related to CBIR touched many aspects of the problem and it was seen that deep learning gave the best results. The problem of annotated images was also touched upon but it was not used with the deep learning method. In my thesis I propose to show better results for annotated images using not only the images but also the annotations provided with each image. I will be using convolutional neural network

Numerai deep learning example

I have worked in the past on CBIR using Bag-of-Words model with the same dataset. The results I get in my study have been evaluated against the results I achieved in my previous study and are discussed in chapter 5. The work has also been compared against the results shown in Ji Wan et al’s work [10] where they used deep learning for CBIR with various different datasets but they differ in the sense that the datasets used by them were just plain images without any annotations.

Numerai deep learning example

”Convolutional neural network (CNN) is a type of feed-forward artificial neural network where the individual neurons are tiled in such a way that they respond to overlapping regions in the visual field” [11]. They are biologically-inspired invariant of Multilayer Perceptrons (MLP) which are designed for the purpose of minimal preprocessing. These models are widely used in image and video recognition. When CNNs are used for image recognition, they look at small portions of the input image called receptive fields with the help of multiple layers of small neuron collections which the model contains [11]. The results we get from this collection are tiled in order for them to overlap such that a better representation of the original image is obtained; every such layer repeats this process. This is the reason they are able if the input image is translated in any way. The outputs of neuron clusters are combined by local or global pooling layers which may be included in convolutional networks. Inspired by biological process, convolutional networks also contain various combinations of fully connected layers and convolutional layers, with point-wise nonlinearity applied at the end of or after each layer [11]. The convolution operation is used on small regions so as to avoid the situation when if all the layers are fully connected billions of parameters will exist. Convolutional networks use shared weights in the convolutional layers i.e. for each pixel in the layer same filter (weights bank) is used which is advantageous because it reduces the required memory size and improves performance. CNNs use relatively less amount of pre-processing as compared to other image classification algorithms,

Numerai deep learning example

CNNs enforce a local connectivity pattern between neurons of adjacent layers to exploit spatially-local correlation [6]. We have illustrated in fig.4.1 that in layer m the inputs of hidden units are from a subset of units in layer m-1, units containing spatially adjoining receptive fields.

Numerai deep learning example

Every filter hi in CNNs is duplicated across the complete visual field. The duplicated filters consists of the same parameters i.e. weights and bias that form a feature map. We can see in fig.4.2 that same feature map contains 3 hidden units. The weights of same color are shared that are constrained to be identical [6]. We can still use gradient descent to learn such shared parameters by altering the original algorithm by a very small margin. When the gradients of the shared parameters are summed, then it gives the gradient of a shared weight. We can detect the features regardless of their location in the visual field by duplicating the units. The huge reduction of the number of free parameters being learnt can lead to weight sharing increasing the learning efficiency. CNNs achieve better generalization on vision problems due to the constraints on these models.

Numerai deep learning example

We obtain a feature map by repeatedly applying a function across sub-regions of the entire image, mainly by convolution of the input image with a linear filter, adding a bias term and 19 then applying a non-linear function [6]. The k-th feature map can be denoted as h k at a given layer, whose filters we can determine by the bias b k and weights Wk , then we can obtain the feature map by the given equation:

Numerai deep learning example

depicts 2 layers of CNN. There are 4 feature maps in layer m-1 and 2 feature maps in hidden layer m (h 0 and h 1 ). The pixels of layer (m-1) that lie within their 2×2 receptive field in the layer below (colored squares) are used for the computation of the pixels in the feature maps h 0 and h 1 (blue and red squares). It can be observed that how all 4 input feature maps are spanned by the receptive field. As a result the 3D weight tensors are the weights and of and . The input feature maps is indexed by the leading dimensions, whereas the pixel coordinates is referred by the other two. When we combine it all as shown in fig.4.3, at layer m the weight that connects each pixel of the k-th feature map with the pixel of the l-th layer at layer (m-1) and at coordinates (i,j) is denoted [6] .

Numerai deep learning example

Max-pooling a form of non-linear down-sampling is an important concept of CNNs. The input image is partitioned into a group of non-overlapping rectangles and a maximum value is given for each such sub-region. We use max-pooling in vision for the following reasonsThe computation of upper layers is reduced by the removal of non-maximal values. Suppose a max-pooling layer is cascaded with a convolutional layer. The input image can be translated by a single pixel in 8 directions. 3 out of 8 possible configurations produce exactly the same output at the convolutional layer if max-pooling is done over a 2×2 region. This jumps to 5/8 for max-pooling over a 3×3 region [6]. A form of translation invariance is provided by this. The dimensionality of intermediate representations is reduced by max-pooling because it provides additional robustness to position.

Numerai deep learning example

The dataset I chose for this thesis is from the SUN database [12]. The major reason for choosing this dataset was that the images in it were pre-annotated and had annotations as XML files for each image. The SUN database is huge so I had to choose a small subset of it for this study. In this study I am trying to classify images based on 8 classes namely: water, car, mountain, ground, tree, building, snow, sky and unknown which contains all the rest of the classes. I chose only those sets of images which I felt were more relevant to these classes. I collected a database of 3000 images from 41 categories. Each image has its annotations in an XML file. I randomly divided the dataset into 80% training set and 20% testing. There are 1900 training images, 600 testing images and 500 validation images. The training set was further divided into 80% training set and 20% validation set. The major drawback of this dataset is that the images are annotated by humans and the annotations are not perfect thus it may have some effect on the results. I try to handle this problem by getting as many synonyms as I can for each class label. A few examples of the synonyms are lake, lake water, sea water, river water, wave, ripple, river, sea, river water among others which all belong to the class label water. I mapped these synonyms to their respective class labels which are being used. Not all images in every categories were annotated. I filtered out the annotated images from the dataset and used only them for this study. Fig.4.5 shows an example of an image from the dataset and its annotation file where it can be seen how a river is annotated by the user

Data Science Courses

During the last decade, a great scientific effort has been invested in the development of methods that could provide efficient and effective detection of botnets. As a result, various detection methods based on diverse technical principles and various aspects of botnet phenomena have been defined. Due to promise of non-invasive and resilient detection, botnet detection based on network traffic analysis has drawn a special attention of the research community. Furthermore, many authors have turned their attention to the use of machine learning algorithms as the mean of inferring botnet-related knowledge from the monitored traffic. This paper presents a review of contemporary botnet detection methods that use machine learning as a tool of identifying botnet-related traffic. The main goal of the paper is to provide a comprehensive overview on the field by summarizing current scientific efforts. The contribution of the paper is threefold. First, the paper provides a detailed insight on the existing detection methods by investigating which bot-related heuristic were assumed by the detection systems and how different machine learning techniques were adapted in order to capture botnetrelated knowledge. Second, the paper compares the existing detection methods by outlining their characteristics, performances, and limitations. Special attention is placed on the practice of experimenting with the methods and the methodologies of performance evaluation. Third, the study indicates limitations and challenges of using machine learning for identifying botnet traffic and outlines possibilities for the future development of machine learning-based botnet detection systems.

 

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Machine Learning.

Supervised versus unsupervised learning Machine learning is a branch of artificial intelligence that uses algorithms, for example, to find patterns in data and make predictions about future events. In machine learning a dataset of observations called instances is comprised of a number of variables called attributes. Supervised learning is the modeling of these datasets 46 Table 3.1: An example of a supervised learning dataset Time x1 x2 x3 x4 x5 x6 x7 y 09:30 b n -0.06 -116.9 -21.7 28.6 0.209 up 09:31 b b 0.06 -85.2 -61 -21.7 0.261 unchanged 09:32 b b 0.26 -4.4 -114.7 -61 0.17 down 09:33 n b 0.11 -112.7 -132.5 -114.7 0.089 unchanged 09:34 n n 0.08 -128.5 -101.3 -132.5 0.328 down containing labeled instances. In supervised learning, each instance can be represented as (x, y), where x is a set of independent attributes (these can be discrete or continuous) and y is the dependent target attribute.

Machine Learning

The target attribute y can also be either continuous or discrete; however the category of modeling is regression if it contains a continuous target, but classification if it contains a discrete target (which is also called a class label). Table 3.1 demonstrates a dataset for supervised learning with seven independent attributes x1, x2, . . . , x7, and one dependent target attribute y. More specifically, x1, x2 ∈ {b, n} and x3, . . . , x7 ∈ R and the target attribute y ∈ {up,unchanged,down}. The attribute time is used to identify an instance and is not used in the model. Also the training and test datasets are represented in the same way however, where the training set contains a set of vectors of known label (y) values, the labels for the test set is unknown. In unsupervised learning the dataset does not include a target attribute, or a known outcome. Since the class values are not determined a priori, the purpose of this learning technique is to find similarity among the groups or some intrinsic clusters within the data. A very simple two-dimensional (two attributes) demonstration is 47 Figure 3.1: An example of an unsupervised learning technique – clustering shown in Figure 3.1 with the data partitioned into five clusters.

Machine Learning

A case could be made however that the data should be partitioned into two clusters or three, etc.; the “correct” answer depends on prior knowledge or biases associated with the dataset to determine the level of similarity required for the underlying problem. Theoretically we can have as many clusters as data instances, although that would defeat the purpose of clustering. Depending on the problem and the data available, the algorithm required can be either a supervised or unsupervised technique. In this thesis, the goal is to predict future price direction of the streaming stock dataset. Since the future direction becomes known after each instance, the training set is constantly expanding 48 with labeled data as time passes. This requires a supervised learning technique. Additionally, we explore the use of different algorithms since some may be better depending on the underlying data. Care should be taken to avoid, “when all you have is a hammer, everything becomes a nail.” 3.3 Supervised learning algorithms 3.3.1 k Nearest-neightbor The k nearest neighbor (kNN) is one of the simplest machine learning methods and is often referred to as a lazy learner because learning is not implemented until actual classification or prediction is required. It takes the most frequent class as measured by the weighted euclidean distance (or some other distance measure) among the k closest training examples in the feature space. In specific problems such as text classification, kNN has been shown to work as well as more complicated models [240]. When nominal attributes are present, it is generally advised to arrive with a “distance” between the different values of the attributes [236]. For our dataset, this could apply to the different trading days, Monday, Tuesday, Wednesday, Thursday, and Friday.

Machine Learning

A downside of using this model is the slow classification times, however we can increase speed by using dimensionality reduction algorithms; for example, reducing the number of attributes from 200 to 20. Since the learning is not implemented until the classification phase though, this is an unsuitable algorithm to use when decisions are needed quickly. 49 3.3.2 Na¨ıve Bayes The na¨ıve Bayes classifier is an efficient probabilistic model based on the Bayes Theorem that examines the likelihood of features appearing in the predicted classes. Given a set of attributes X = {x1, x2, . . . , xn}, the objective is to construct the posterior probability for the event Ck among a set of possible class outcomes C = {c1, c2, . . . , ck}. Therefore, with Bayes’ rule P(Ck|x1, . . . , xn) ∝ P(Ck)P(x1, . . . , xn|Ck), where P(x1, . . . , xn|Ck) is the probability that attribute X belongs to Cj , and assuming independence1 we can rewrite as P(Cj |X) ∝ P(Cj ) �n i=1 P(xi|Cj ). A new instance with a set of attributes X is labeled with the class Cj that achieves the highest posterior probability. 3.3.3 Decision table A decision table classifier is built on the conceptual idea of a lookup table. The classifier returns the majority class of the training set if the decision table (lookup table) cell matching the new instance is empty. In certain datasets, classification performance has been found to be higher when using decision tables than with more complicated models. A further description can be found in [124, 125, 127]. 3.3.4 Support Vector Machines Support vector machines [221] have long been recognized as being able to efficiently handle high-dimensional data. Originally designed as a two-class classifier, it can work with more classes by making multiple binary classifications (one-versus- 1The assumption of independence is the na¨ıve aspect of the algorithm. 50 one between every pair of classes). The algorithm works by classifying instances based on a linear function of the features. Additionally non-linear classification can be performed using a kernel. The classifier is fed with pre-labeled instances and by selecting points as support vectors the SVM searches for a hyperplane that maximizes the margin. More information can be found in [221]. 3.3.5 Artificial Neural Networks An artificial neural network (ANN) is an interconnected group of nodes intended to represent the network of neurons in the brains. They are widely used in literature, because of their ability to learn complex patterns. We present only a short overview of their structure in this section. The artificial neural network is comprised of nodes (shown as circles in Figure 3.2), an input layer represented as x1 . . . , x6, an optional hidden layer, and an output layer y. The objective of the ANN is to determine a set of weights w (between the input, hidden, and output nodes) that minimize the total sum of squared errors. During training these weights wi are adjusted according to a learning parameter λ ∈ [0, 1] until the outputs become consistent with the output. Large values of λ may make changes to the weights that are too drastic, while values that are too small may require more iterations (called epochs) before the model sufficiently learns from the training data. The difficulty of using artificial neural networks is finding parameters that learn from training data without over fitting (i.e. memorizing the training data) and 51 x1 x2 x3 x4 x5 x6 input layer hidden layer output layer y Figure 3.2: Example of a multilayer feed-forward artificial neural network therefore perform poorly on unseen data. If there are too many hidden nodes, the system may overfit the current data, while if there are too few, it can prevent the system from properly fitting the input values. Also, a choice of stopping criterion has to be chosen. This can include stopping based on when the total error of the network falls below some predetermined error level or when a certain number of epochs (iterations) has been completed [16, 25, 177]. To demonstrate this, see Figure 3.3. This plot represents a segment of our high-frequency trade data that will be used later in this thesis. As the epochs increase (by tens), the number of incorrectly identified training instances decreases, as seen by the decrease in the training error. However, the validation error decreases until 30 epochs, and after 30, starts to increase. Around roughly 80 epochs the validation error begins to decrease again, however we need to make a judgment call since an increase in epochs increases the training times dramatically. Yu et al. [245] state that with foreign exchange rate forecasting, which is similar to stocks because of the high degree of noise, volatility and complexity, it is advisable to use the sigmoidal type-transfer function (i.e. logistic or hyperbolic tangent). Tigure 3.3: Artificial neural network classification error versus number of epochs base this on the large number of papers that find predictability using this type of function in the hidden layer. 3.3.6 Decision Trees The decision tree is one of the more widely used classifiers in practice because the algorithm creates rules which are easy to understand and interpret. The version we use in this paper is also one of the most popular forms, the C4.5 [186], which extends the ID3 [185] algorithm. The improvements are: 1) it is more robust to noise, 2) it allows for the use of continuous attribute, and 3) it works with missing data. The C4.5 begins as a recursive divide-and-conquer algorithm, first by selecting an attribute from the training set to place at the root node. Each value of the attribute 53 creates a new branch, with this process repeating recursively using all the instances reaching that branch [236]. An ideal node contains all (or nearly all) of one class. To determine the best attribute to choose for a particular node in the tree, the gain in information entropy for the decision is calculated. More information can be found in [186]. 3.3.7 Ensembles An ensemble is a collection of multiple base classifiers that take a new example, pass it to each of its base classifiers, and then combines those predictions according to some method (such as through voting). The motivation is that by combining the predictions, the ensemble is less likely to misclassify. For example, Figure 3.4a demonstrates an ensemble with 25 hypothetical classifiers, each with an independent error rate of 0.45 (assuming a uniform 2 class problem). The probability of getting k incorrect classifier votes is a binomial distribution, P(k) = �n k � pk(1 − p)n−k. The probability that 13 or more is in error is 0.31, which is less than the error rate of the individual classifier. This is a potential advantage of using multiple models. This advantage of using multiple models (ensembles) is under the assumption that the individual classifier error rate is less than 0.50. If the independent classifier error rate is 0.55, then the probability of 13 or more in error is 0.69 – it would be better not to use an ensemble of classifiers. Figure 3.4b2 demonstrates the error rate of the ensemble for three independent error rates, 0.55, 0.50, and 0.45 for ensembles 2The idea for the visualization came from [59, 82]. 54 Error rate versus number of classifiers in the ensemble (employing majority voting) for three independent error rates Figure 3.4: Ensemble simulation containing an odd number of classifiers, from 3 to 101. From the figure it can be seen that the smaller the independent classifier error rate is, and the larger the number of classifiers in the ensemble is, the less likely a majority of the classifiers will predict incorrectly [59, 82]. The idea of classifier independence may be unreasonable, given that the classifiers may predict in a similar manner due to the training set. Obtaining a base classifier that generates errors as uncorrelated as possible is ideal. Creating a diverse set of classifiers within the ensemble is considered an important property since the likelihood that a majority of the base classifiers misclassify the instance is decreased. Two of the more popular methods used within ensemble learning is bagging [27] and boosting (e.g. the AdaBoost algorithm [78] described in Subsection 3.3.7.2 is the most common). These methods promote diversity by building base classifiers on different subsets of the training data or different weights of classifiers. 55 3.3.7.1 Bagging Bagging, also known as bootstrap aggregation, was proposed by Breiman in 1994 in an early version of [27]. It works by generating k bootstrapped training sets and building a classifier on each (where k is determined by the user). Each training set of size N is created by randomly selecting instances from the original dataset, with each receiving an equal probability of being selected and with replacement. Since every instance has an equal probability of being selected, bagging does not focus on any particular instance of the training data and therefore is less likely to over-fit [177]. Bagging is generally for unstable3 classifiers such as decision trees and neural networks. 3.3.7.2 Boosting The AdaBoost (Adaptive Boosting) algorithm of Freud and Schapire [78] in 1995 is synonymous with boosting. The idea however was proposed in 1988 by Michael Kearns [114] in a class project, where he hypothesized that a “weak” classifier, performing slightly better than average, could be “boosted” into a “strong” classifier. In boosting, instances being classified are assigned a weight; instances that were previously incorrectly classified receive larger weights, with the hope that subsequent models correct the mistake of the previous model. In the AdaBoost algorithm the original training set D has a weight w assigned to each of its N instances {(x1, y1), . . . ,(xn, yn)}, where xi is a vector of inputs and yi is the class label of that 3By unstable, it is meant that small changes in the training set can lead to large changes in the classifier outcome. 56 instance. With the weight added the instances become {(x1, y1, w1), . . . ,(xn, yn, wn)} and the sum of the wi must equal 1. The AdaBoost algorithm then builds k base classifiers with an initial weight wi = 1 N . Upon each iteration of the algorithm (which is determined by the user), the weight wi gets adjusted according to the error �i of the classifier hypothesis4. The points that were incorrectly identified receive higher weights, and the ones that were correctly identified receive less. The desire is that on the next iteration, the re-weighting will help to correctly classify the instances that were misclassified by the previous classifier. When implementing the boosting ensemble on test data, the final class is determined by a weighted vote of the classifiers [78, 149]. Boosting does more to reduce bias than variance. This reduction is due to the algorithm adjusting its weight to learn previously misclassified instances and therefore increasing the probability that these instances will be learned correctly in the future. This has had a tendency to correct biases. However, it tends to perform poorly on noisy datasets and therefore the weights become greater, which causes the model to focus on the noisy instances and over-fit the data [195]. 3.3.7.3 Combining classifiers for ensembles The last step in any ensemble-based system is the method used to combine the individual classifiers; this is often referred to as fusion rules. Classifiers within an ensemble are most commonly combined using a majority voting algorithm. There 4If the error is greater than what would be achieved by guessing the class, then the ensemble is returned to the previously generated base classifier. 57 are however, different methods of combining, which often depend on the underlying classifiers used. For example, the Naive Bayes algorithm provides continuous valued outputs, allowing a wide range of strategies for combining, while an artificial neural network provides a discrete-valued output, allowing for fewer [133, 134, 247]. A description of each follows: • Majority voting – Plurality majority voting – The class that receives the highest number of votes among classifiers (in literature, majority voting typically refers to version) – Simple majority voting – The class that receives one more than fifty percent of all votes among classifiers – Unanimous majority voting – The class that all the classifiers unanimously vote on • Weighted majority voting – If the confidence in among classifiers is not equal, we can weight certain classifiers more heavily. This method is followed in the AdaBoost algorithm. • Algebraic combiners – Mean/Minimum/Maximum/Median rules – The ensemble decision is chosen for the class according to the average/minimum/maximum/median of each classifier’s confidence. 58 Table 3.2: Confusion matrix Predicted class + – Actual + TP FN Class – FP TN While ensembles have shown success in a variety of problems, there are some associated drawbacks. This includes added memory and computation cost in keeping multiple classifiers stored and ready to process. Also the loss of interpretability may be a cause for concern depending on the needs of the problem. For example, a single decision tree can be easily interpreted, while an ensemble of 100 decision trees could be difficult [21]. 3.4 Performance metrics 3.4.1 Confusion matrix and accuracy A confusion matrix, also called a contingency table, is a visualization of the performance of a supervised learning method. A problem with n classes, requires a confusion matrix of size n × n with the rows representing the specific actual class and the columns representing the classifiers predicted class. In a confusion matrix, TP (true positive) is the number of positives correctly identified, TN (true negative) is the number of negatives correctly identified, FP (false positive) is the number of negatives incorrectly identified as positive, and FN (false negative) is the number of positives incorrectly identified as negatives. An example of a confusion matrix can be seen in Table 3.2. 59 From the confusion matrix it is relatively simple to arrive at different measures for comparing models. An example is accuracy, which is a widely used metric and is easy to interpret. From Equation 3.1, accuracy is the total number of correct predictions made over the total number of predictions made. While accuracy is a popular metric, it is also not very descriptive when used to measure the performance of a highly imbalanced dataset. A model may have high levels of accuracy, but may not obtain high levels of identification of the class that we are interested in predicting. For example, if attempting to identify large moves in a stock which is comprised of 99% small moves and 1% large moves, it is trivial to report a model has accuracy of 99% without additional information. A classifier could also have 99% accuracy by simply reporting the class with the largest number of instances (e.g. the majority class is “small moves”). In an imbalanced dataset, a model may misidentify all positive classes and still have high levels of accuracy; pure randomness is not taken into account with the accuracy metric. Accuracy’s complement is the error rate (1 − Accuracy) and can be seen in Equation 3.2. Accuracy = T P + T N T P + T N + F P + F N (3.1) Error rate = F P + F N T P + F P + T N + F N (3.2) There are several approaches to comparing models with imbalanced datasets. First is the precision and recall metrics and the accompanying harmonic mean, the F-measure. The second metric is based on Cohen’s kappa statistic, which takes into account the randomness of the class. The third metric is the receiver operating characteristic which is based on the true positive and false positives rates. The 60 fourth is a cost-based metric which gives specific “costs” to correctly and incorrectly identifying specific classes. And the last method is based not on the ability of the model to make correct decisions, but instead on the profitability of the classifier as it applies to a trading system. A more detailed description of these metrics follows. 3.4.2 Precision and recall Precision and recall are both popular metrics for evaluating classifier performance and will be used extensively in this paper. Precision is the percentage that the model correctly predicts positive when making a decision (Equation 3.3).

Machine Learning

More specifically, precision is the number of correctly identified positive examples divided by the total number of examples that are classified as positive. Recall is the percentage of positives correctly identified out of all the existing positives (Equation 3.4); it is the number of correctly classified positive examples divided by the total number of true positive examples in the test set. From our imbalanced example above with the 99% small moves and 1% large moves, precision would be how often a large move was correctly identified as such, while recall would be the total number of large moves that are correctly identified out of all the large moves in the dataset. Precision = T P T P + F P (3.3) Sensitivity (Recall) = T P T P + F N (3.4) Specificity = T N T N + F P (3.5) F-measure = 2(precision)(recall) precision + recall (3.6) Precision and recall are often achieved at the expense of the other, i.e. high 61 precision is achieved at the expense of recall and high recall is achieved at the expense of precision. An ideal model would have both high recall and high precision. The F-measure5, which can be seen in Equation 3.6, is the harmonic measure of precision and recall in a single measurement. The F-measure ranges from 0 to 1, with a measure of 1 being a classifier perfectly capturing precision and recall. 3.4.3 Kappa The second approach to comparing imbalanced datasets is based on Cohen’s kappa statistic. This metric takes into consideration randomness of the class and provides an intuitive result. From [14], the metric can be observed in Equation 3.7 where P0 is the total agreement probability and Pc is the agreement probability which is due to chance. κ = P0 − Pc 1 − Pc (3.7) P0 = � I i=1 P(xii) (3.8) Pc = � I i=1 P(xi.)P(x.i) (3.9) The total agreement probability P0 (i.e. the classifier’s accuracy) can be be computed according to Equation 3.8, where I is the number of class values, P(xi.) is the row marginal probability and P(x.i) is the column marginal probability, with both obtained from the confusion matrix. The probability due to chance, Pc, can be computed according to Equation 3.9. The kappa statistic is constrained to the interval 5The F-measure, in the literature is also called the F-score and the F1-score. 62 Table 3.3: Computing the Kappa statistic from the confusion matrix (a) Confusion matrix – Numbers Predicted class up down flat Actual up 139 80 89 308 class down 10 298 13 323 flat 40 16 313 369 189 396 4157 1000 (b) Confusion matrix – Probabilities Predicted class up down flat  Actual up 0.14 0.08 0.09 0.31 class down 0.01 0.30 0.01 0.32 flat  0.04 0.02 0.31 0.37 0.19 0.40 0.42 1.00 [−1, 1], with a kappa κ = 0 meaning that agreement is equal to random chance, and a kappa κ equaling 1 and -1 meaning perfect agreement and perfect disagreement respectively. For example, in Table 3.3a the results of a three-class problem are shown, with the marginal probabilities calculated in Table 3.3b. The total agreement probability, also known as accuracy, is computed as P0 = 0.14 + 0.30 + 0.31 = 0.75, while the probability by chance is Pc = (0.19×0.31) + (0.40×0.32) + (0.42×0.37) = 0.34. The kappa statistic is therefore κ = (0.75 − 0.34)/(1 − 0.34) = 0.62. 3.4.4 ROC The third approach to comparing classifiers is the Receiver Operating Characteristic (ROC) curve. This is a plot of the true positive rate, which is also called recall or 63 Figure 3.5: ROC curve example sensitivity (Equation 3.10), against the false positive rate, which is also known as 1-specificity (3.11). T P R = T P T P + F N (3.10) F P R = F P T N + F P (3.11) The best performance is noted by a curve close to the top left corner (i.e. a small false positive rate and a large true positive rate), with a curve along the diagonal reflecting a purely random classifier. As a demonstration, in Figure 3.5 three ROC curves are displayed for three classifiers. Classifier 1 has a more ideal ROC curve than Classifier 2 or 3. Classifier 2 is slightly better than random, while Classifier 3 is worse. In Classifier 3’s case, it would be better to choose as a solution that is opposite of what the classifier predicts. 64 For single number comparison, the Area Under the ROC Curve (AUC) is calculated by integrating the ROC curve. Random would therefore have an AUC of 0.50 and a classifier better and worse than random would have an AUC greater than and less than 0.50 respectively. It is most commonly used with two-class problems although with multi-class examples the AUC can be weighted according to the class distribution. AUC is also equal to the Wilcoxon statistic. 3.4.5 Cost-based The cost-based method of evaluating classifiers is based on the “cost” associated with making incorrect decisions [61, 65, 102]. The performance metrics seen thus far do not take into consideration the possibility that not all classification errors are equal. For example, an opportunity cost can be associated with missing a large move in a stock. A cost can also be provided for initiating an incorrect trade. A model can be built with a high recall, which misses no large moves in the stock, but the precision would most likely suffer. The cost-based approach gives an associated cost to this decision which can be evaluated to determine the suitability of the model. A cost matrix is used to represent the associated cost of each decision with the goal of minimizing the total cost associated with the model. This can be formalized with a cost matrix C and the entry (i, j) with the actual cost i and the predicted class j. When i = j the prediction is correct and when i �= j the prediction is incorrect. An advantage of using a cost-based evaluation metric for trading models is the cost associated with making incorrect decisions is known by analyzing empirical 65 data.

Machine Learning

For example all trades incur a cost in the form of a trade commission and money used in a trade is temporarily unavailable, thus incurring an opportunity cost. Additionally, a loss associated with an incorrect decision can be averaged over similar previous losses; gains can be computed similarly. Consider, for example, a trading firm is attempting to predict the directional price move of a stock with the objective to trade on the decision. At time t, the stock can move up, down, or have no change in price; at time t+n, the direction is unknown (this can be observed in Figure 3.6). For time t + 1, a prediction of up might result in the firm purchasing the stock. Different errors in classification however would have different associated cost. A firm expecting a move up would purchase the stock in anticipation of the move, but a subsequent move down would be more harmful than no change in price. A actual move down would immediately result in a trading loss, whereas no change in price would result in an temporary opportunity cost with the stock still having the potential to go in the desired direction. Additionally an incorrect prediction of “no change” would merely result in an opportunity lost, but no actual money being put to risk since a firm would not trade based on the anticipation of a unchanged market (no change). Table 3.4 represents a theoretical cost matrix of the problem, with three separate error amounts represented: 0.25, 0.50, and 1.25. 3.4.6 Profitability of the model While the end result of predicting stock price direction is to increase profitability, the performance metrics discussed thus far (with the exception of the cost-based 66 Predicted class Down No change Up Actual Down 0 0.25 1.25 class No change 0.50 0 0.50 Up 1.25 0.25 0 metric) evaluate classifiers based on the ability to correctly classify and not on overall profitability of a trading system. As an example, a classifier may have very high accuracy, kappa, AUC, etc. but this may not necessarily equate to a profitable trading strategy, since profitability of individual trades may be more important than being “right” a majority of times; e.g. making $0.50 on each of one hundred trades is not as profitable as losing $0.05 95 times and then making $12 on each of five trades6. Figure 3.7 represents a trading model represented in much of the academic literature, where the classifier is built on the data with a prediction of up, down, or no change in the market price with the outcome passed to a second set of rules. These 6An argument can also be made that a less volatile approach is more ideal (i.e. making small sums consistently). This depends on the overall objective of the trader – maximizing stability or overall profitability. 67 Figure 3.7: Trading algorithm process rules provide direction if a prediction of “up”, for example, should equate to buying stock, buying more stock, or buying back a position that was previously shorted. The rules also address the amount of stock to be purchased, how much to risk, etc. When considering profitability of a model, the literature generally follows the form of an automated trading model, which is “buy when the model says to buy, then sell after n number of minutes/hours/days [161]” or “buy when the model says to buy, then sell if the position is up x% or else sell after n minutes/days/hours [138, 164, 202].” Teixeira et al. [214] added another rule (called a “stop loss” within trading), which prevented losses from going past a certain dollar amount during an individual trade. The goal of this thesis is not to provide an “out of the box” trading system with proven profitability, but to instead help the user make trading decisions with the help of machine learning techniques. Additionally, there are many different rules in the trading literature relating to how much stock to buy or sell, how much money to risk in a position, how often trades should take place, and when to buy and sell; each of these questions are enough for entire dissertations. In practice, trading systems often involve many layers of controls such as forecasting and optimization methodologies 68 Table 3.5: Importance of using an unbiased estimate of its generalizability – trained using the dataset from Appendix B for January 3, 2012 January 3, 2012 (training data) January 4, 2012 (unseen data) Accuracy 94.713% 37.31% that are filtered through multiple layers of risk management. This typically involves a human supervisor (risk manager) that can make decisions such as when to override the system [69]. The focus of this paper therefore, will remain on the classifier itself; maximizing predictability when faced with different market conditions.

Machine Learning

 

Machine Learning

 

Machine Learning

 

Machine Learning

 

 

 

 

 

 

 

 

deep learning,data mining,machine learning,artificial intelligence,kaggle,tensor flow,data scientist,neural network,what is machine learning,machine learning algorithms

Regularization
Multiple regression
Model validation
Precision
Recall
ROC curve
Predictive model
Overfitting
Loss function
L1/L2 Regularization
Response variable
Estimation
Multi-Collinearity
Resampling
Jackknife resampling/Jacknifing
MSE – mean squared error
Selection bias
Local Max/Min/Optimum
A/B Testing
Web Analytics
Root cause analysis
Big data
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Binary hipotesis test
Null hypotesis (H0)
Alternative Hypotesis (H1)
Statistical Power
Type I error
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Bootstrapping
Cross-Validation
Ridge regression
Lasso
K-means clustering
Semantic Indexing
Principal Component Analysis
Supervised learning
Unsupervised learning
False positives
Fase negatives
NLP
Feature vector
Random forrest
Support Vector Machines
Colaborative Filtering
N-grams
Cosine distance
Naive Bayes
Boosted trees
Decision tree
Stepwise regression
Intercept
Impurity measures
Maximal margin classifier
Kernel
Kernel trick
Dimensionality reduction
Dimensionality course
Newton’s method

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Data Science Definition. What is Data Science?

There is much debate on it, but the short definition of data science is:

“Data science is an interdisciplinary field of using scientific methods to get information from data in various forms.”

Data science involves using methods from fields of statistics, computer science and mathematics, to interpret data for business decisions. Amounts of data available in modern society grow with the input of technology in peoples lives. These massive sets of structured and unstructured data help to show patterns and trends for business opportunities or academic research. One can see an increasing number of traditional fields of science with adjective ‘computational’ or ‘quantitative’. In industry, data science transforms everything from healthcare to media and this trend shall pick up in future.

Machine Learning Definition

Machine learning is subfield of science, that provides computers with the ability to learn without being explicitly programmed.   The goal of machine learning is to develop learning algorithms, that do the learning automatically without human intervention or assistance, just by being exposed to new Data Science The machine learning paradigm can be viewed as “programming by example”. This subarea of artificial intelligence intersects broadly with other fields like, statistics, mathematics, physics, theoretical computer science and more.

What is Machine Learning?

Intro to Machine Learning

 

What is definition of Machine Learning?

Machine Learning subfield of science that provides computers with the ability to learn without being explicitly programmed.   The goal of Machine Learning is to develop learning algorithms that do the learning automatically without human intervention or assistance, just by being exposed to new data. The Machine Learning paradigm can be viewed as “programming by example”. This subarea of artificial intelligence intersects broadly with other fields like statistics, mathematics, physics, theoretical computer science and more.

Machine Learning can play a key role in a wide range of critical applications, such as data mining, natural language processing, image recognition, and expert systems. Machine Learning can be a game changer in all these domains and is set to be a pillar of our future civilization. If one wants a program to predict something, one can run it through a Machine Learning algorithm with historical data and “train” the model, it will then predict future patterns. Machine Learning is quite vast and is expanding rapidly, into different sub-specialties and types.

Examples of Machine Learning problems include, “Is this car?”, “How much is this house worth?”, “Will this person like this movie?”, “Who is this?”, “What did you say?”, and “How do you fly this thing?”. All of these problems are excellent targets for a Machine Learning project, and in fact, it has been applied to each of them with great success.

Among the different types of Machine Learning tasks, a crucial distinction is drawn between supervised and unsupervised learning:

Supervised machine learning: The program is “trained” on a pre-defined set of “training examples”, which then facilitate its ability to reach an accurate conclusion when given new data.

Unsupervised machine learning: The program is given a bunch of data and must find patterns and relationships between them.

Supervised Machine Learning

In the majority of supervised learning applications, the ultimate goal is to develop a finely tuned predictor function. “Learning” consists of using sophisticated mathematical algorithms to optimize this function so that, given input data about a certain domain, it will accurately predict some interesting value. The goal of Machine Learning is not to make “perfect” guesses, but to make guesses that are good enough to be useful.

Many modern Machine Learning problems take thousands or even millions of dimensions of data to build predictions using hundreds of coefficients.

The iterative approach taken by Machine Learning algorithms works very well for multiple problems, but it doesn’t mean Machine Learning can solve any arbitrary problem, it can’t, but it is very a powerful tool in our hands.

In supervised learning, there are two categories of problems:

Regression – the value being predicted is continuous, it answers questions like: “How much?” or “How many?”

Classification – yes-or-no prediction, categorical answer, Eg. “Is this cat?”, “Is this product category x?”.

The underlying theory is more or less the same, differences are the design of the predictor and the design of the cost function.

Unsupervised Machine Learning

Unsupervised learning typically is tasked with finding relationships within data. There are no training examples, the system is given a set data and tasked with finding patterns. A good example is identifying groups of friends in social network data. The algorithms used to do this are different from those used for supervised learning.

 

Machine Learning is an incredibly powerful tool, it will help to solve some of the human most burning problems, as well as open up whole new opportunities.