In machine learning or statistics, it is often desirable to reduce the dimensionality of a sample of data points in a high dimensional space $\mathbb{R}^d$. This paper introduces a dimensionality reduction method where the embedding coordinates are the eigenvectors of a positive semi-definite kernel obtained as the solution of an infinite dimensional analogue of a semi-definite program. This embedding is adaptive and non-linear. A main feature of our approach is the existence of a non-linear out-of-sample extension formula of the embedding coordinates, called a projected Nystr\"om approximation. This extrapolation formula yields an extension of the kernel matrix to a data-dependent Mercer kernel function. Our empirical results indicate that this embedding method is more robust with respect to the influence of outliers, compared with a spectral embedding method.

Automatic charge prediction task aims to determine the final charges based on fact descriptions of criminal cases, which is a vital application of legal assistant systems. Conventional works usually depend on fact descriptions to predict charges while ignoring the legal schematic knowledge, which makes it difficult to distinguish confusing charges. In this paper, we propose a knowledge-attentive neural network model, which introduces legal schematic knowledge about charges and exploit the knowledge hierarchical representation as the discriminative features to differentiate confusing charges. Our model takes the textual fact description as the input and learns fact representation through a graph convolutional network. A legal schematic knowledge transformer is utilized to generate crucial knowledge representations oriented to the legal schematic knowledge at both the schema and charge levels. We apply a knowledge matching network for effectively incorporating charge information into the fact to learn knowledge-aware fact representation. Finally, we use the knowledge-aware fact representation for charge prediction. We create two real-world datasets and experimental results show that our proposed model can outperform other state-of-the-art baselines on accuracy and F1 score, especially on dealing with confusing charges.

Machine learning techniques have been widely used in natural language processing (NLP). However, as revealed by many recent studies, machine learning models often inherit and amplify the societal biases in data. Various metrics have been proposed to quantify biases in model predictions. In particular, several of them evaluate disparity in model performance between protected groups and advantaged groups in the test corpus. However, we argue that evaluating bias at the corpus level is not enough for understanding how biases are embedded in a model. In fact, a model with similar aggregated performance between different groups on the entire data may behave differently on instances in a local region. To analyze and detect such local bias, we propose LOGAN, a new bias detection technique based on clustering. Experiments on toxicity classification and object classification tasks show that LOGAN identifies bias in a local region and allows us to better analyze the biases in model predictions.

Understanding customer behavior is fundamental for many use-cases in industry, especially in accelerated growth areas such as fin-tech and e-commerce. Structured data are often expensive, time-consuming and inadequate to analyze and study complex customer behaviors. In this paper, we propose a multi-graph embedding approach for creating a non-linear representation of customers in order to have a better knowledge of their characteristics without having any prior information about their financial status or their interests. By applying the current method we are able to predict users' future behavior with a reasonably high accuracy only by having the information of their friendship network. Potential applications include recommendation systems and credit risk forecasting.

With the increasing deployment of machine learning systems in practice, transparency and explainability have become serious issues. Contrastive explanations are considered to be useful and intuitive, in particular when it comes to explaining decisions to lay people, since they mimic the way in which humans explain. Yet, so far, comparably little research has addressed computationally feasible technologies, which allow guarantees on uniqueness and optimality of the explanation and which enable an easy incorporation of additional constraints. Here, we will focus on specific types of models rather than black-box technologies. We study the relation of contrastive and counterfactual explanations and propose mathematical formalizations as well as a 2-phase algorithm for efficiently computing pertinent positives of many standard machine learning models.

We propose a method for improving adversarial robustness by addition of a new bounded function just before softmax. Recent studies hypothesize that small logits (inputs of softmax) by logit regularization can improve adversarial robustness of deep learning. Following this hypothesis, we analyze norms of logit vectors at the optimal point under the assumption of universal approximation and explore new methods for constraining logits by addition of a bounded function before softmax. We theoretically and empirically reveal that small logits by addition of a common activation function, e.g., hyperbolic tangent, do not improve adversarial robustness since input vectors of the function (pre-logit vectors) can have large norms. From the theoretical findings, we develop the new bounded function. The addition of our function improves adversarial robustness because it makes logit and pre-logit vectors have small norms. Since our method only adds one activation function before softmax, it is easy to combine our method with adversarial training. Our experiments demonstrate that our method is comparable to logit regularization methods in terms of accuracies on adversarially perturbed datasets without adversarial training. Furthermore, it is superior or comparable to logit regularization methods and a recent defense method (TRADES) when using adversarial training.

We study derivative-free optimization for convex functions where we further assume that function evaluations are unavailable. Instead, one only has access to a comparison oracle, which, given two points $x$ and $y$, and returns a single bit of information indicating which point has larger function value, $f(x)$ or $f(y)$, with some probability of being incorrect. This probability may be constant or it may depend on $|f(x)-f(y)|$. Previous algorithms for this problem have been hampered by a query complexity which is polynomially dependent on the problem dimension, $d$. We propose a novel algorithm that breaks this dependence: it has query complexity only logarithmically dependent on $d$ if the function in addition has low dimensional structure that can be exploited. Numerical experiments on synthetic data and the MuJoCo dataset show that our algorithm outperforms state-of-the-art methods for comparison based optimization, and is even competitive with other derivative-free algorithms that require explicit function evaluations.

This includes causal models, regression models, factor models and so on. The sample programs are in R.

Gaussian processes offer a flexible kernel method for regression. While Gaussian processes have many useful theoretical properties and have proven practically useful, they suffer from poor scaling in the number of observations. In particular, the cubic time complexity of updating standard Gaussian process models make them generally unsuitable for application to streaming data. We propose an algorithm for sequentially partitioning the input space and fitting a localized Gaussian process to each disjoint region. The algorithm is shown to have superior time and space complexity to existing methods, and its sequential nature permits application to streaming data. The algorithm constructs a model for which the time complexity of updating is tightly bounded above by a pre-specified parameter. To the best of our knowledge, the model is the first local Gaussian process regression model to achieve linear memory complexity. Theoretical continuity properties of the model are proven. We demonstrate the efficacy of the resulting model on multi-dimensional regression tasks for streaming data.

Terror attacks have been linked in part to online extremist content. Although tens of thousands of Islamist extremism supporters consume such content, they are a small fraction relative to peaceful Muslims. The efforts to contain the ever-evolving extremism on social media platforms have remained inadequate and mostly ineffective. Divergent extremist and mainstream contexts challenge machine interpretation, with a particular threat to the precision of classification algorithms. Our context-aware computational approach to the analysis of extremist content on Twitter breaks down this persuasion process into building blocks that acknowledge inherent ambiguity and sparsity that likely challenge both manual and automated classification. We model this process using a combination of three contextual dimensions -- religion, ideology, and hate -- each elucidating a degree of radicalization and highlighting independent features to render them computationally accessible. We utilize domain-specific knowledge resources for each of these contextual dimensions such as Qur'an for religion, the books of extremist ideologues and preachers for political ideology and a social media hate speech corpus for hate. Our study makes three contributions to reliable analysis: (i) Development of a computational approach rooted in the contextual dimensions of religion, ideology, and hate that reflects strategies employed by online Islamist extremist groups, (ii) An in-depth analysis of relevant tweet datasets with respect to these dimensions to exclude likely mislabeled users, and (iii) A framework for understanding online radicalization as a process to assist counter-programming. Given the potentially significant social impact, we evaluate the performance of our algorithms to minimize mislabeling, where our approach outperforms a competitive baseline by 10.2% in precision.