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 Statistical Learning


Algorithmic Trading Using Logistic Regression - Hands-Off Investing

#artificialintelligence

With the increasing popularity of machine learning, many traders are looking for ways in which they can "teach" a computer to trade for them. This process is called algorithmic trading (sometimes called algo-trading). Algorithmic trading is a hands off strategy for buying and selling stocks that leverages technical indicators instead of human intuition. In order to implement an algorithmic trading strategy though, you have to first narrow down a list of stocks that you want to analyze. This walk-through provides an automated process (using python and logistic regression) for determining the best stocks to algo-trade.


Learning to Satisfy Unknown Constraints in Iterative MPC

arXiv.org Machine Learning

We propose a control design method for linear time-invariant systems that iteratively learns to satisfy unknown polyhedral state constraints. At each iteration of a repetitive task, the method constructs an estimate of the unknown environment constraints using collected closed-loop trajectory data. This estimated constraint set is improved iteratively upon collection of additional data. An MPC controller is then designed to robustly satisfy the estimated constraint set. This paper presents the details of the proposed approach, and provides robust and probabilistic guarantees of constraint satisfaction as a function of the number of executed task iterations. We demonstrate the safety of the proposed framework and explore the safety vs. performance trade-off in a detailed numerical example.


Kernel-based parameter estimation of dynamical systems with unknown observation functions

arXiv.org Machine Learning

A low-dimensional dynamical system is observed in an experiment as a high-dimensional signal; For example, a video of a chaotic pendulums system. Assuming that we know the dynamical model up to some unknown parameters, can we estimate the underlying system's parameters by measuring its time-evolution only once? The key information for performing this estimation lies in the temporal inter-dependencies between the signal and the model. We propose a kernel-based score to compare these dependencies. Our score generalizes a maximum likelihood estimator for a linear model to a general nonlinear setting in an unknown feature space. We estimate the system's underlying parameters by maximizing the proposed score. We demonstrate the accuracy and efficiency of the method using two chaotic dynamical systems - the double pendulum and the Lorenz '63 model.


From Two-Class Linear Discriminant Analysis to Interpretable Multilayer Perceptron Design

arXiv.org Machine Learning

A closed-form solution exists in two-class linear discriminant analysis (LDA), which discriminates two Gaussian-distributed classes in a multi-dimensional feature space. In this work, we interpret the multilayer perceptron (MLP) as a generalization of a two-class LDA system so that it can handle an input composed by multiple Gaussian modalities belonging to multiple classes. Besides input layer $l_{in}$ and output layer $l_{out}$, the MLP of interest consists of two intermediate layers, $l_1$ and $l_2$. We propose a feedforward design that has three stages: 1) from $l_{in}$ to $l_1$: half-space partitionings accomplished by multiple parallel LDAs, 2) from $l_1$ to $l_2$: subspace isolation where one Gaussian modality is represented by one neuron, 3) from $l_2$ to $l_{out}$: class-wise subspace mergence, where each Gaussian modality is connected to its target class. Through this process, we present an automatic MLP design that can specify the network architecture (i.e., the layer number and the neuron number at a layer) and all filter weights in a feedforward one-pass fashion. This design can be generalized to an arbitrary distribution by leveraging the Gaussian mixture model (GMM). Experiments are conducted to compare the performance of the traditional backpropagation-based MLP (BP-MLP) and the new feedforward MLP (FF-MLP).


Generalization Bounds via Information Density and Conditional Information Density

arXiv.org Machine Learning

We present a general approach, based on an exponential inequality, to derive bounds on the generalization error of randomized learning algorithms. Using this approach, we provide bounds on the average generalization error as well as bounds on its tail probability, for both the PAC-Bayesian and single-draw scenarios. Specifically, for the case of subgaussian loss functions, we obtain novel bounds that depend on the information density between the training data and the output hypothesis. When suitably weakened, these bounds recover many of the information-theoretic available bounds in the literature. We also extend the proposed exponential-inequality approach to the setting recently introduced by Steinke and Zakynthinou (2020), where the learning algorithm depends on a randomly selected subset of the available training data. For this setup, we present bounds for bounded loss functions in terms of the conditional information density between the output hypothesis and the random variable determining the subset choice, given all training data. Through our approach, we recover the average generalization bound presented by Steinke and Zakynthinou (2020) and extend it to the PAC-Bayesian and single-draw scenarios. For the single-draw scenario, we also obtain novel bounds in terms of the conditional $\alpha$-mutual information and the conditional maximal leakage.


Walk Extraction Strategies for Node Embeddings with RDF2Vec in Knowledge Graphs

arXiv.org Artificial Intelligence

As KGs are symbolic constructs, specialized techniques have to be applied in order to make them compatible with data mining techniques. RDF2Vec is an unsupervised technique that can create task-agnostic numerical representations of the nodes in a KG by extending successful language modelling techniques. The original work proposed the Weisfeiler-Lehman (WL) kernel to improve the quality of the representations. However, in this work, we show both formally and empirically that the WL kernel does little to improve walk embeddings in the context of a single KG. As an alternative to the WL kernel, we propose five different strategies to extract information complementary to basic random walks. We compare these walks on several benchmark datasets to show that the \emph{n-gram} strategy performs best on average on node classification tasks and that tuning the walk strategy can result in improved predictive performances.


Vision-Based Autonomous Drone Control using Supervised Learning in Simulation

arXiv.org Artificial Intelligence

Limited power and computational resources, absence of high-end sensor equipment and GPS-denied environments are challenges faced by autonomous micro areal vehicles (MAVs). We address these challenges in the context of autonomous navigation and landing of MAVs in indoor environments and propose a vision-based control approach using Supervised Learning. To achieve this, we collected data samples in a simulation environment which were labelled according to the optimal control command determined by a path planning algorithm. Based on these data samples, we trained a Convolutional Neural Network (CNN) that maps low resolution image and sensor input to high-level control commands. We have observed promising results in both obstructed and non-obstructed simulation environments, showing that our model is capable of successfully navigating a MAV towards a landing platform. Our approach requires shorter training times than similar Reinforcement Learning approaches and can potentially overcome the limitations of manual data collection faced by comparable Supervised Learning approaches.


Developing and Improving Risk Models using Machine-learning Based Algorithms

arXiv.org Machine Learning

The objective of this study is to develop a good risk model for classifying business delinquency by simultaneously exploring several machine learning based methods including regularization, hyper-parameter optimization, and model ensembling algorithms. The rationale under the analyses is firstly to obtain good base binary classifiers (include Logistic Regression ($LR$), K-Nearest Neighbors ($KNN$), Decision Tree ($DT$), and Artificial Neural Networks ($ANN$)) via regularization and appropriate settings of hyper-parameters. Then two model ensembling algorithms including bagging and boosting are performed on the good base classifiers for further model improvement. The models are evaluated using accuracy, Area Under the Receiver Operating Characteristic Curve (AUC of ROC), recall, and F1 score via repeating 10-fold cross-validation 10 times. The results show the optimal base classifiers along with the hyper-parameter settings are $LR$ without regularization, $KNN$ by using 9 nearest neighbors, $DT$ by setting the maximum level of the tree to be 7, and $ANN$ with three hidden layers. Bagging on $KNN$ with $K$ valued 9 is the optimal model we can get for risk classification as it reaches the average accuracy, AUC, recall, and F1 score valued 0.90, 0.93, 0.82, and 0.89, respectively.


Relative Attribute Classification with Deep Rank SVM

arXiv.org Machine Learning

Relative attributes indicate the strength of a particular attribute between image pairs. We introduce a deep Siamese network with rank SVM loss function, called Deep Rank SVM (DRSVM), in order to decide which one of a pair of images has a stronger presence of a specific attribute. The network is trained in an end-to-end fashion to jointly learn the visual features and the ranking function. We demonstrate the effectiveness of our approach against the state-of-the-art methods on four image benchmark datasets: LFW-10, PubFig, UTZap50K-lexi and UTZap50K-2 datasets. DRSVM surpasses state-of-art in terms of the average accuracy across attributes, on three of the four image benchmark datasets.


A Black-box Adversarial Attack for Poisoning Clustering

arXiv.org Machine Learning

Clustering algorithms play a fundamental role as tools in decision-making and sensible automation processes. Due to the widespread use of these applications, a robustness analysis of this family of algorithms against adversarial noise has become imperative. To the best of our knowledge, however, only a few works have currently addressed this problem. In an attempt to fill this gap, in this work, we propose a black-box adversarial attack for crafting adversarial samples to test the robustness of clustering algorithms. We formulate the problem as a constrained minimization program, general in its structure and customizable by the attacker according to her capability constraints. We do not assume any information about the internal structure of the victim clustering algorithm, and we allow the attacker to query it as a service only. In the absence of any derivative information, we perform the optimization with a custom approach inspired by the Abstract Genetic Algorithm (AGA). In the experimental part, we demonstrate the sensibility of different single and ensemble clustering algorithms against our crafted adversarial samples on different scenarios. Furthermore, we perform a comparison of our algorithm with a state-of-the-art approach showing that we are able to reach or even outperform its performance. Finally, to highlight the general nature of the generated noise, we show that our attacks are transferable even against supervised algorithms such as SVMs, random forests and neural networks.