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

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
Data minig
Binary hipotesis test
Null hypotesis (H0)
Alternative Hypotesis (H1)
Statistical Power
Type I error
Type II error
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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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.