This note shares a final recap of my series of notes on the different topics from Andrew Ng's Machine Learning course. I hope that these notes help to make machine learning more accessible and create greater collective intuition around machine learning. What are the types of Machine Learning? ML is when a computer program is able to learn without being programmed explicitly, which is often illustrated as getting better at a task as it gains more experience according to a measure of performance. ML can be bucketed as either (1) "supervised learning" where it learns from the "right answers" (e.g., regression or classification), or (2) "unsupervised learning" where there are no "right answers" given, but the model finds structure or patterns in the data (e.g., clustering).

With recent advances in artificial intelligence, machine learning (ML) approaches have become an attractive tool in petroleum engineering, particularly for reservoir characterizations. A key reservoir property is hydrocarbon recovery factor (RF) whose accurate estimation would provide decisive insights to drilling and production strategies. Therefore, this study aims to estimate the hydrocarbon RF for exploration from various reservoir characteristics, such as porosity, permeability, pressure, and water saturation via the ML. We applied three regression-based models including the extreme gradient boosting (XGBoost), support vector machine (SVM), and stepwise multiple linear regression (MLR) and various combinations of three databases to construct ML models and estimate the oil and/or gas RF. Using two databases and the cross-validation method, we evaluated the performance of the ML models. In each iteration 90 and 10% of the data were respectively used to train and test the models. The third independent database was then used to further assess the constructed models. For both oil and gas RFs, we found that the XGBoost model estimated the RF for the train and test datasets more accurately than the SVM and MLR models. However, the performance of all the models were unsatisfactory for the independent databases. Results demonstrated that the ML algorithms were highly dependent and sensitive to the databases based on which they were trained. Statistical tests revealed that such unsatisfactory performances were because the distributions of input features and target variables in the train datasets were significantly different from those in the independent databases (p-value < 0.05).

Recent studies have shown that gradient descent (GD) can achieve improved generalization when its dynamics exhibits a chaotic behavior. However, to obtain the desired effect, the step-size should be chosen sufficiently large, a task which is problem dependent and can be difficult in practice. In this study, we incorporate a chaotic component to GD in a controlled manner, and introduce multiscale perturbed GD (MPGD), a novel optimization framework where the GD recursion is augmented with chaotic perturbations that evolve via an independent dynamical system. We analyze MPGD from three different angles: (i) By building up on recent advances in rough paths theory, we show that, under appropriate assumptions, as the step-size decreases, the MPGD recursion converges weakly to a stochastic differential equation (SDE) driven by a heavy-tailed L\'evy-stable process. (ii) By making connections to recently developed generalization bounds for heavy-tailed processes, we derive a generalization bound for the limiting SDE and relate the worst-case generalization error over the trajectories of the process to the parameters of MPGD. (iii) We analyze the implicit regularization effect brought by the dynamical regularization and show that, in the weak perturbation regime, MPGD introduces terms that penalize the Hessian of the loss function. Empirical results are provided to demonstrate the advantages of MPGD.

We propose cooperative edge-assisted dynamic federated learning (CE-FL). CE-FL introduces a distributed machine learning (ML) architecture, where data collection is carried out at the end devices, while the model training is conducted cooperatively at the end devices and the edge servers, enabled via data offloading from the end devices to the edge servers through base stations. CE-FL also introduces floating aggregation point, where the local models generated at the devices and the servers are aggregated at an edge server, which varies from one model training round to another to cope with the network evolution in terms of data distribution and users' mobility. CE-FL considers the heterogeneity of network elements in terms of communication/computation models and the proximity to one another. CE-FL further presumes a dynamic environment with online variation of data at the network devices which causes a drift at the ML model performance. We model the processes taken during CE-FL, and conduct analytical convergence analysis of its ML model training. We then formulate network-aware CE-FL which aims to adaptively optimize all the network elements via tuning their contribution to the learning process, which turns out to be a non-convex mixed integer problem. Motivated by the large scale of the system, we propose a distributed optimization solver to break down the computation of the solution across the network elements. We finally demonstrate the effectiveness of our framework with the data collected from a real-world testbed.

We propose a symbolic representation for support vector machines (SVMs) by means of abstract interpretation, a well-known and successful technique for designing and implementing static program analyses. We leverage this abstraction in two ways: (1) to enhance the interpretability of SVMs by deriving a novel feature importance measure, called abstract feature importance (AFI), that does not depend in any way on a given dataset of the accuracy of the SVM and is very fast to compute, and (2) for verifying stability, notably individual fairness, of SVMs and producing concrete counterexamples when the verification fails. We implemented our approach and we empirically demonstrated its effectiveness on SVMs based on linear and non-linear (polynomial and radial basis function) kernels. Our experimental results show that, independently of the accuracy of the SVM, our AFI measure correlates much more strongly with the stability of the SVM to feature perturbations than feature importance measures widely available in machine learning software such as permutation feature importance. It thus gives better insight into the trustworthiness of SVMs.

This study is about inducing classifiers using data that is imbalanced, with a minority class being under-represented in relation to the majority classes. The first section of this research focuses on the main characteristics of data that generate this problem. Following a study of previous, relevant research, a variety of artificial, imbalanced data sets influenced by important elements were created. These data sets were used to create decision trees and rule-based classifiers. The second section of this research looks into how to improve classifiers by pre-processing data with resampling approaches. The results of the following trials are compared to the performance of distinct pre-processing re-sampling methods: two variants of random over-sampling and focused under-sampling NCR. This paper further optimises class imbalance with a new method called Sparsity. The data is made more sparse from its class centers, hence making it more homogenous.

Adversarial Examples Detection (AED) is a crucial defense technique against adversarial attacks and has drawn increasing attention from the Natural Language Processing (NLP) community. Despite the surge of new AED methods, our studies show that existing methods heavily rely on a shortcut to achieve good performance. In other words, current search-based adversarial attacks in NLP stop once model predictions change, and thus most adversarial examples generated by those attacks are located near model decision boundaries. To surpass this shortcut and fairly evaluate AED methods, we propose to test AED methods with \textbf{F}ar \textbf{B}oundary (\textbf{FB}) adversarial examples. Existing methods show worse than random guess performance under this scenario. To overcome this limitation, we propose a new technique, \textbf{ADDMU}, \textbf{a}dversary \textbf{d}etection with \textbf{d}ata and \textbf{m}odel \textbf{u}ncertainty, which combines two types of uncertainty estimation for both regular and FB adversarial example detection. Our new method outperforms previous methods by 3.6 and 6.0 \emph{AUC} points under each scenario. Finally, our analysis shows that the two types of uncertainty provided by \textbf{ADDMU} can be leveraged to characterize adversarial examples and identify the ones that contribute most to model's robustness in adversarial training.

Efficient k-nearest neighbor search is a fundamental task, foundational for many problems in NLP. When the similarity is measured by dot-product between dual-encoder vectors or $\ell_2$-distance, there already exist many scalable and efficient search methods. But not so when similarity is measured by more accurate and expensive black-box neural similarity models, such as cross-encoders, which jointly encode the query and candidate neighbor. The cross-encoders' high computational cost typically limits their use to reranking candidates retrieved by a cheaper model, such as dual encoder or TF-IDF. However, the accuracy of such a two-stage approach is upper-bounded by the recall of the initial candidate set, and potentially requires additional training to align the auxiliary retrieval model with the cross-encoder model. In this paper, we present an approach that avoids the use of a dual-encoder for retrieval, relying solely on the cross-encoder. Retrieval is made efficient with CUR decomposition, a matrix decomposition approach that approximates all pairwise cross-encoder distances from a small subset of rows and columns of the distance matrix. Indexing items using our approach is computationally cheaper than training an auxiliary dual-encoder model through distillation. Empirically, for k > 10, our approach provides test-time recall-vs-computational cost trade-offs superior to the current widely-used methods that re-rank items retrieved using a dual-encoder or TF-IDF.

We present a method for learning 3D geometry and physics parameters of a dynamic scene from only a monocular RGB video input. To decouple the learning of underlying scene geometry from dynamic motion, we represent the scene as a time-invariant signed distance function (SDF) which serves as a reference frame, along with a time-conditioned deformation field. We further bridge this neural geometry representation with a differentiable physics simulator by designing a two-way conversion between the neural field and its corresponding hexahedral mesh, enabling us to estimate physics parameters from the source video by minimizing a cycle consistency loss. Our method also allows a user to interactively edit 3D objects from the source video by modifying the recovered hexahedral mesh, and propagating the operation back to the neural field representation. Experiments show that our method achieves superior mesh and video reconstruction of dynamic scenes compared to competing Neural Field approaches, and we provide extensive examples which demonstrate its ability to extract useful 3D representations from videos captured with consumer-grade cameras.

We introduce the Lossy Implicit Network Activation Coding (LINAC) defence, an input transformation which successfully hinders several common adversarial attacks on CIFAR-$10$ classifiers for perturbations up to $\epsilon = 8/255$ in $L_\infty$ norm and $\epsilon = 0.5$ in $L_2$ norm. Implicit neural representations are used to approximately encode pixel colour intensities in $2\text{D}$ images such that classifiers trained on transformed data appear to have robustness to small perturbations without adversarial training or large drops in performance. The seed of the random number generator used to initialise and train the implicit neural representation turns out to be necessary information for stronger generic attacks, suggesting its role as a private key. We devise a Parametric Bypass Approximation (PBA) attack strategy for key-based defences, which successfully invalidates an existing method in this category. Interestingly, our LINAC defence also hinders some transfer and adaptive attacks, including our novel PBA strategy. Our results emphasise the importance of a broad range of customised attacks despite apparent robustness according to standard evaluations. LINAC source code and parameters of defended classifier evaluated throughout this submission are available: https://github.com/deepmind/linac