We study the problem of PAC learning halfspaces on $\mathbb{R}^d$ with Massart noise under Gaussian marginals. In the Massart noise model, an adversary is allowed to flip the label of each point $\mathbf{x}$ with probability $\eta(\mathbf{x}) \leq \eta$, for some parameter $\eta \in [0,1/2]$. The goal of the learner is to output a hypothesis with missclassification error $\mathrm{opt} + \epsilon$, where $\mathrm{opt}$ is the error of the target halfspace. Prior work studied this problem assuming that the target halfspace is homogeneous and that the parameter $\eta$ is strictly smaller than $1/2$. We explore how the complexity of the problem changes when either of these assumptions is removed, establishing the following threshold phenomena: For $\eta = 1/2$, we prove a lower bound of $d^{\Omega (\log(1/\epsilon))}$ on the complexity of any Statistical Query (SQ) algorithm for the problem, which holds even for homogeneous halfspaces. On the positive side, we give a new learning algorithm for arbitrary halfspaces in this regime with sample complexity and running time $O_\epsilon(1) \, d^{O(\log(1/\epsilon))}$. For $\eta <1/2$, we establish a lower bound of $d^{\Omega(\log(1/\gamma))}$ on the SQ complexity of the problem, where $\gamma = \max\{\epsilon, \min\{\mathbf{Pr}[f(\mathbf{x}) = 1], \mathbf{Pr}[f(\mathbf{x}) = -1]\} \}$ and $f$ is the target halfspace. In particular, this implies an SQ lower bound of $d^{\Omega (\log(1/\epsilon) )}$ for learning arbitrary Massart halfspaces (even for small constant $\eta$). We complement this lower bound with a new learning algorithm for this regime with sample complexity and runtime $d^{O_{\eta}(\log(1/\gamma))} \mathrm{poly}(1/\epsilon)$. Taken together, our results qualitatively characterize the complexity of learning halfspaces in the Massart model.

Kernels ensuing from tree ensembles such as random forest (RF) or gradient boosted trees (GBT), when used for kernel learning, have been shown to be competitive to their respective tree ensembles (particularly in higher dimensional scenarios). On the other hand, it has been also shown that performance of the kernel algorithms depends on the degree of the kernel-target alignment. However, the kernel-target alignment for kernel learning based on the tree ensembles has not been investigated and filling this gap is the main goal of our work. Using the eigenanalysis of the kernel matrix, we demonstrate that for continuous targets good performance of the tree-based kernel learning is associated with strong kernel-target alignment. Moreover, we show that well performing tree ensemble based kernels are characterized by strong target aligned components that are expressed through scalar products between the eigenvectors of the kernel matrix and the target. This suggests that when tree ensemble based kernel learning is successful, relevant information for the supervised problem is concentrated near lower dimensional manifold spanned by the target aligned components. Persistence of the strong target aligned components in tree ensemble based kernels is further supported by sensitivity analysis via landmark learning. In addition to a comprehensive simulation study, we also provide experimental results from several real life data sets that are in line with the simulations.

Modern evolvements of the technologies have been leading to a profound influence on the financial market. The introduction of constituents like Exchange-Traded Funds, and the wide-use of advanced technologies such as algorithmic trading, results in a boom of the data which provides more opportunities to reveal deeper insights. However, traditional statistical methods always suffer from the high-dimensional, high-correlation, and time-varying instinct of the financial data. In this dissertation, we focus on developing techniques to stress these difficulties. With the proposed methodologies, we can have more interpretable models, clearer explanations, and better predictions.

Graph neural networks (GNNs), has been widely used for supervised learning tasks in graphs reaching state-of-the-art results. However, little work was dedicated to creating unbiased GNNs, i.e., where the classification is uncorrelated with sensitive attributes, such as race or gender. Some ignore the sensitive attributes or optimize for the criteria of statistical parity for fairness. However, it has been shown that neither approaches ensure fairness, but rather cripple the utility of the prediction task. In this work, we present a GNN framework that allows optimizing representations for the notion of Equalized Odds fairness criteria. The architecture is composed of three components: (1) a GNN classifier predicting the utility class, (2) a sampler learning the distribution of the sensitive attributes of the nodes given their labels. It generates samples fed into a (3) discriminator that discriminates between true and sampled sensitive attributes using a novel "permutation loss" function. Using these components, we train a model to neglect information regarding the sensitive attribute only with respect to its label. To the best of our knowledge, we are the first to optimize GNNs for the equalized odds criteria. We evaluate our classifier over several graph datasets and sensitive attributes and show our algorithm reaches state-of-the-art results.

Federated Learning (FL) is a privacy-protected machine learning paradigm that allows model to be trained directly at the edge without uploading data. One of the biggest challenges faced by FL in practical applications is the heterogeneity of edge node data, which will slow down the convergence speed and degrade the performance of the model. For the above problems, a representative solution is to add additional constraints in the local training, such as FedProx, FedCurv and FedCL. However, the above algorithms still have room for improvement. We propose to use the aggregation of all models obtained in the past as new constraint target to further improve the performance of such algorithms. Experiments in various settings demonstrate that our method significantly improves the convergence speed and performance of the model.

The present paper aims at analyzing the topological content of the complex trajectories that weeder-autonomous robots follow in operation. We will prove that the topological descriptors of these trajectories are affected by the robot environment as well as by the robot state, with respect to maintenance operations. Topological Data Analysis will be used for extracting the trajectory descriptors, based on homology persistence. Then, appropriate metrics will be applied in order to compare that topological representation of the trajectories, for classifying them or for making efficient pattern recognition.

One possible approach may be to visualize training and test distributions side-by-side (i.e., juxtaposition) using Identifying covariate shift is crucial for making machine learning dimensionality reduction methods (e.g., t-SNE) [1] and show each systems robust in the real world and for detecting training data biases data point as an image thumbnail [4, 26]. However, the scale of that are not reflected in test data. However, detecting covariate shift modern image datasets makes it difficult because we cannot easily is challenging, especially when the data consists of high-dimensional show many images on the projected space [4,8]. Instead of visualizing images, and when multiple types of localized covariate shift affect the distributions of the entire training and test datasets globally, we different subspaces of the data. Although automated techniques aim to intelligently show only local regions of the space, where the can be used to detect the existence of covariate shift, our goal is to locality is informed by the detection algorithm. For example, given help human users characterize the extent of covariate shift in large a test set image highly ranked by a shift detection algorithm (i.e., image datasets with interfaces that seamlessly integrate information deviated from training set distribution), a visualization may show obtained from the detection algorithms. In this paper, we design that many of its similar test images (i.e., local neighborhood) share a and evaluate a new visual interface that facilitates the comparison characteristic (e.g., many faces with sunglasses) while the similar of the local distributions of training and test data. We conduct a training images do not (e.g., no faces with sunglasses).

We present a novel learning-based approach to graph representations of road networks employing state-of-the-art graph convolutional neural networks. Our approach is applied to realistic road networks of 17 cities from Open Street Map. While edge features are crucial to generate descriptive graph representations of road networks, graph convolutional networks usually rely on node features only. We show that the highly representative edge features can still be integrated into such networks by applying a line graph transformation. We also propose a method for neighborhood sampling based on a topological neighborhood composed of both local and global neighbors. We compare the performance of learning representations using different types of neighborhood aggregation functions in transductive and inductive tasks and in supervised and unsupervised learning. Furthermore, we propose a novel aggregation approach, Graph Attention Isomorphism Network, GAIN. Our results show that GAIN outperforms state-of-the-art methods on the road type classification problem.

In ensemble learning, it is aimed to train the model most successfully with multiple learning algorithms. In one of the ensemble learning, Bagging method, more than one model was applied to different subsamples of the same dataset in parallel. Boosting, which is another method and frequently used in practice, builds sequentially instead of parallelly and aims to train the algorithm as well as training the model. A weak algorithm trains the model, then it is re-organized according to the training results and it is made easier to learn. This modified model is then sent to the next algorithm and the second algorithm learns easier than the first one. This article contains different boosting methods that interpret this sequential method from different angles.

Feature selection is the process of reducing the number of input variables when developing a predictive model. It is desirable to reduce the number of input variables to both reduce the computational cost of modeling and, in some cases, to improve the performance of the model. Statistical-based feature selection methods involve evaluating the relationship between each input variable and the target variable using statistics and selecting those input variables that have the strongest relationship with the target variable. These methods can be fast and effective, although the choice of statistical measures depends on the data type of both the input and output variables. As such, it can be challenging for a machine learning practitioner to select an appropriate statistical measure for a dataset when performing filter-based feature selection.