The parameters of support vector machines (SVMs) such as the penalty parameter and the kernel parameters have a great impact on the classification accuracy and the complexity of the SVM model. Therefore, the model selection in SVM involves the tuning of these parameters. However, these parameters are usually tuned and used as a black box, without understanding the mathematical background or internal details. In this paper, the behavior of the SVM classification model is analyzed when these parameters take different values with balanced and imbalanced data. This analysis including visualization, mathematical and geometrical interpretations and illustrative numerical examples with the aim of providing the basics of the Gaussian and linear kernel functions with SVM. From this analysis, we proposed a novel search algorithm. In this algorithm, we search for the optimal SVM parameters into two one-dimensional spaces instead of searching into one two-dimensional space. This reduces the computational time significantly. Moreover, in our algorithm, from the analysis of the data, the range of kernel function can be expected. This also reduces the search space and hence reduces the required computational time. Different experiments were conducted to evaluate our search algorithm using different balanced and imbalanced datasets. The results demonstrated how the proposed strategy is fast and effective than other searching strategies.

We establish a family of subspace-based learning method for multi-view learning using the least squares as the fundamental basis. Specifically, we investigate orthonormalized partial least squares (OPLS) and study its important properties for both multivariate regression and classification. Building on the least squares reformulation of OPLS, we propose a unified multi-view learning framework to learn a classifier over a common latent space shared by all views. The regularization technique is further leveraged to unleash the power of the proposed framework by providing three generic types of regularizers on its inherent ingredients including model parameters, decision values and latent projected points. We instantiate a set of regularizers in terms of various priors. The proposed framework with proper choices of regularizers not only can recast existing methods, but also inspire new models. To further improve the performance of the proposed framework on complex real problems, we propose to learn nonlinear transformations parameterized by deep networks. Extensive experiments are conducted to compare various methods on nine data sets with different numbers of views in terms of both feature extraction and cross-modal retrieval.

Node classification in attributed graphs is an important task in multiple practical settings, but it can often be difficult or expensive to obtain labels. Active learning can improve the achieved classification performance for a given budget on the number of queried labels. The best existing methods are based on graph neural networks, but they often perform poorly unless a sizeable validation set of labelled nodes is available in order to choose good hyperparameters. We propose a novel graph-based active learning algorithm for the task of node classification in attributed graphs; our algorithm uses graph cognizant logistic regression, equivalent to a linearized graph convolutional neural network (GCN), for the prediction phase and maximizes the expected error reduction in the query phase. To reduce the delay experienced by a labeller interacting with the system, we derive a preemptive querying system that calculates a new query during the labelling process, and to address the setting where learning starts with almost no labelled data, we also develop a hybrid algorithm that performs adaptive model averaging of label propagation and linearized GCN inference. We conduct experiments on five public benchmark datasets, demonstrating a significant improvement over state-of-the-art approaches and illustrate the practical value of the method by applying it to a private microwave link network dataset.

There is a growing amount of clinical, anatomical and functional evidence for the heterogeneous presentation of neuropsychiatric and neurodegenerative diseases such as schizophrenia and Alzheimers Disease (AD). Elucidating distinct subtypes of diseases allows a better understanding of neuropathogenesis and enables the possibility of developing targeted treatment programs. Recent semi-supervised clustering techniques have provided a data-driven way to understand disease heterogeneity. However, existing methods do not take into account that subtypes of the disease might present themselves at different spatial scales across the brain. Here, we introduce a novel method, MAGIC, to uncover disease heterogeneity by leveraging multi-scale clustering. We first extract multi-scale patterns of structural covariance (PSCs) followed by a semi-supervised clustering with double cyclic block-wise optimization across different scales of PSCs. We validate MAGIC using simulated heterogeneous neuroanatomical data and demonstrate its clinical potential by exploring the heterogeneity of AD using T1 MRI scans of 228 cognitively normal (CN) and 191 patients. Our results indicate two main subtypes of AD with distinct atrophy patterns that consist of both fine-scale atrophy in the hippocampus as well as large-scale atrophy in cortical regions. The evidence for the heterogeneity is further corroborated by the clinical evaluation of two subtypes, which indicates that there is a subpopulation of AD patients that tend to be younger and decline faster in cognitive performance relative to the other subpopulation, which tends to be older and maintains a relatively steady decline in cognitive abilities.

Hierarchical Agglomerative Clustering (HAC) algorithms are extensively utilized in modern data science and machine learning, and seek to partition the dataset into clusters while generating a hierarchical relationship between the data samples themselves. HAC algorithms are employed in a number of applications, such as biology, natural language processing, and recommender systems. Thus, it is imperative to ensure that these algorithms are fair-- even if the dataset contains biases against certain protected groups, the cluster outputs generated should not be discriminatory against samples from any of these groups. However, recent work in clustering fairness has mostly focused on center-based clustering algorithms, such as k-median and k-means clustering. Therefore, in this paper, we propose fair algorithms for performing HAC that enforce fairness constraints 1) irrespective of the distance linkage criteria used, 2) generalize to any natural measures of clustering fairness for HAC, 3) work for multiple protected groups, and 4) have competitive running times to vanilla HAC. To the best of our knowledge, this is the first work that studies fairness for HAC algorithms. We also propose an algorithm with lower asymptotic time complexity than HAC algorithms that can rectify existing HAC outputs and make them subsequently fair as a result. Moreover, we carry out extensive experiments on multiple real-world UCI datasets to demonstrate the working of our algorithms.

This article explores the use of machine learning models to build a market generator. The underlying idea is to simulate artificial multi-dimensional financial time series, whose statistical properties are the same as those observed in the financial markets. In particular, these synthetic data must preserve the probability distribution of asset returns, the stochastic dependence between the different assets and the autocorrelation across time. The article proposes then a new approach for estimating the probability distribution of backtest statistics. The final objective is to develop a framework for improving the risk management of quantitative investment strategies, in particular in the space of smart beta, factor investing and alternative risk premia.

We present a federated learning approach for learning a client adaptable, robust model when data is non-identically and non-independently distributed (non-IID) across clients. By simulating heterogeneous clients, we show that adding learned client-specific conditioning improves model performance, and the approach is shown to work on balanced and imbalanced data set from both audio and image domains. The client adaptation is implemented by a conditional gated activation unit and is particularly beneficial when there are large differences between the data distribution for each client, a common scenario in federated learning.

Machine teaching [42, 37] uses a meta/teacher model to guide the training of a student model (which will be used in real tasks) through training data selection, loss function design, etc. Previously, the teacher model only takes shallow/surface information as inputs (e.g., training iteration number, loss and accuracy from training/validation sets) while ignoring the internal states of the student model, which limits the potential of learning to teach. In this work, we propose an improved data teaching algorithm, where the teacher model deeply interacts with the student model by accessing its internal states. The teacher model is jointly trained with the student model using meta gradients propagated from a validation set. We conduct experiments on image classification with clean/noisy labels and empirically demonstrate that our algorithm makes significant improvement over previous data teaching methods.

In a reward-free environment, what is a suitable intrinsic objective for an agent to pursue so that it can learn an optimal task-agnostic exploration policy? In this paper, we argue that the entropy of the state distribution induced by limited-horizon trajectories is a sensible target. Especially, we present a novel and practical policy-search algorithm, Maximum Entropy POLicy optimization (MEPOL), to learn a policy that maximizes a non-parametric, $k$-nearest neighbors estimate of the state distribution entropy. In contrast to known methods, MEPOL is completely model-free as it requires neither to estimate the state distribution of any policy nor to model transition dynamics. Then, we empirically show that MEPOL allows learning a maximum-entropy exploration policy in high-dimensional, continuous-control domains, and how this policy facilitates learning a variety of meaningful reward-based tasks downstream.

While successful in many fields, deep neural networks (DNNs) still suffer from some open problems such as bad local minima and unsatisfactory generalization performance. In this work, we propose a novel architecture called Maximum-and-Concatenation Networks (MCN) to try eliminating bad local minima and improving generalization ability as well. Remarkably, we prove that MCN has a very nice property; that is, \emph{every local minimum of an $(l+1)$-layer MCN can be better than, at least as good as, the global minima of the network consisting of its first $l$ layers}. In other words, by increasing the network depth, MCN can autonomously improve its local minima's goodness, what is more, \emph{it is easy to plug MCN into an existing deep model to make it also have this property}. Finally, under mild conditions, we show that MCN can approximate certain continuous functions arbitrarily well with \emph{high efficiency}; that is, the covering number of MCN is much smaller than most existing DNNs such as deep ReLU. Based on this, we further provide a tight generalization bound to guarantee the inference ability of MCN when dealing with testing samples.