Scaling methods have long been utilized to simplify and cluster high-dimensional data. However, the general latent spaces across all predefined groups derived from these methods sometimes do not fall into researchers' interest regarding specific patterns within groups. To tackle this issue, we adopt an emerging analysis approach called contrastive learning. We contribute to this growing field by extending its ideas to multiple correspondence analysis (MCA) in order to enable an analysis of data often encountered by social scientists -- containing binary, ordinal, and nominal variables. We demonstrate the utility of contrastive MCA (cMCA) by analyzing two different surveys of voters in the U.S. and U.K. Our results suggest that, first, cMCA can identify substantively important dimensions and divisions among subgroups that are overlooked by traditional methods; second, for other cases, cMCA can derive latent traits that emphasize subgroups seen moderately in those derived by traditional methods.
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Gaussian Partial Information Decomposition: Bias Correction and Application to High-dimensional Data
Recent advances in neuroscientific experimental techniques have enabled us to simultaneously record the activity of thousands of neurons across multiple brain regions. This has led to a growing need for computational tools capable of analyzing how task-relevant information is represented and communicated between several brain regions. Partial information decompositions (PIDs) have emerged as one such tool, quantifying how much unique, redundant and synergistic information two or more brain regions carry about a task-relevant message. However, computing PIDs is computationally challenging in practice, and statistical issues such as the bias and variance of estimates remain largely unexplored. In this paper, we propose a new method for efficiently computing and estimating a PID definition on multivariate Gaussian distributions. We show empirically that our method satisfies an intuitive additivity property, and recovers the ground truth in a battery of canonical examples, even at high dimensionality. We also propose and evaluate, for the first time, a method to correct the bias in PID estimates at finite sample sizes. Finally, we demonstrate that our Gaussian PID effectively characterizes inter-areal interactions in the mouse brain, revealing higher redundancy between visual areas when a stimulus is behaviorally relevant.
In this work, we propose a geometric framework for analyzing mechanical manipulation, for example, by a robotic agent. Under the assumption of conservative forces and quasi-static manipulation, we use energy methods to derive a metric. We first review and show that the natural geometric setting is represented by the cotangent bundle and its Lagrangian submanifolds. These are standard concepts in geometric mechanics but usually presented within dynamical frameworks. We review the basic definitions from a static mechanics perspective and show how Lagrangian submanifolds are naturally derived from a first order analysis. Then, via a second order analysis, we derive the Hessian of total energy. As this is not necessarily positive-definite from a control perspective, we propose the use of the squared-Hessian for optimality measures, motivated by insights {derived from both mechanics (Gauss's Principle) and biology (Separation Principle)}. We conclude by showing how such methods can be applied, for example, to the simple case of an elastically driven pendulum. The example is simple enough to allow for analytical solution. However, an extension is further derived and numerically solved, which is more realistically connected with actual robotic manipulation problems.
Social media platforms are often blamed for exacerbating political polarization and worsening public dialogue. Many claim hyperpartisan users post pernicious content, slanted to their political views, inciting contentious and toxic conversations. However, what factors, actually contribute to increased online toxicity and negative interactions? In this work, we explore the role that political ideology plays in contributing to toxicity both on an individual user level and a topic level on Twitter. To do this, we train and open-source a DeBERTa-based toxicity detector with a contrastive objective that outperforms the Google Jigsaw Persective Toxicity detector on the Civil Comments test dataset. Then, after collecting 187 million tweets from 55,415 Twitter users, we determine how several account-level characteristics, including political ideology and account age, predict how often each user posts toxic content. Running a linear regression, we find that the diversity of views and the toxicity of the other accounts with which that user engages has a more marked effect on their own toxicity. Namely, toxic comments are correlated with users who engage with a wider array of political views. Performing topic analysis on the toxic content posted by these accounts using the large language model MPNet and a version of the DP-Means clustering algorithm, we find similar behavior across 6,592 individual topics, with conversations on each topic becoming more toxic as a wider diversity of users become involved.
In this paper, we study a priori error estimates for the finite element approximation of the nonlinear Schr\"{o}dinger-Poisson model. The electron density is defined by an infinite series over all eigenvalues of the Hamiltonian operator. To establish the error estimate, we present a unified theory of error estimates for a class of nonlinear problems. The theory is based on three conditions: 1) the original problem has a solution $u$ which is the fixed point of a compact operator $\Ca$, 2) $\Ca$ is Fr\'{e}chet-differentiable at $u$ and $\Ci-\Ca'[u]$ has a bounded inverse in a neighborhood of $u$, and 3) there exists an operator $\Ca_h$ which converges to $\Ca$ in the neighborhood of $u$. The theory states that $\Ca_h$ has a fixed point $u_h$ which solves the approximate problem. It also gives the error estimate between $u$ and $u_h$, without assumptions on the well-posedness of the approximate problem. We apply the unified theory to the finite element approximation of the Schr\"{o}dinger-Poisson model and obtain optimal error estimate between the numerical solution and the exact solution. Numerical experiments are presented to verify the convergence rates of numerical solutions.
CIPER: Combining Invariant and Equivariant Representations Using Contrastive and Predictive Learning
Self-supervised representation learning (SSRL) methods have shown great success in computer vision. In recent studies, augmentation-based contrastive learning methods have been proposed for learning representations that are invariant or equivariant to pre-defined data augmentation operations. However, invariant or equivariant features favor only specific downstream tasks depending on the augmentations chosen. They may result in poor performance when the learned representation does not match task requirements. Here, we consider an active observer that can manipulate views of an object and has knowledge of the action(s) that generated each view. We introduce Contrastive Invariant and Predictive Equivariant Representation learning (CIPER). CIPER comprises both invariant and equivariant learning objectives using one shared encoder and two different output heads on top of the encoder. One output head is a projection head with a state-of-the-art contrastive objective to encourage invariance to augmentations. The other is a prediction head estimating the augmentation parameters, capturing equivariant features. Both heads are discarded after training and only the encoder is used for downstream tasks. We evaluate our method on static image tasks and time-augmented image datasets. Our results show that CIPER outperforms a baseline contrastive method on various tasks. Interestingly, CIPER encourages the formation of hierarchically structured representations where different views of an object become systematically organized in the latent representation space.
When the input signal is correlated input signals, and the input and output signal is contaminated by Gaussian noise, the total least squares normalized subband adaptive filter (TLS-NSAF) algorithm shows good performance. However, when it is disturbed by impulse noise, the TLS-NSAF algorithm shows the rapidly deteriorating convergence performance. To solve this problem, this paper proposed the robust total minimum mean M-estimator normalized subband filter (TLMM-NSAF) algorithm. In addition, this paper also conducts a detailed theoretical performance analysis of the TLMM-NSAF algorithm and obtains the stable step size range and theoretical steady-state mean squared deviation (MSD) of the algorithm. To further improve the performance of the algorithm, we also propose a new variable step size (VSS) method of the algorithm. Finally, the robustness of our proposed algorithm and the consistency of theoretical and simulated values are verified by computer simulations of system identification and echo cancellation under different noise models.
Federated learning enables multiple parties to collaboratively train a machine learning model without communicating their local data. A key challenge in federated learning is to handle the heterogeneity of local data distribution across parties. Although many studies have been proposed to address this challenge, we find that they fail to achieve high performance in image datasets with deep learning models. In this paper, we propose MOON: model-contrastive federated learning. MOON is a simple and effective federated learning framework. The key idea of MOON is to utilize the similarity between model representations to correct the local training of individual parties, i.e., conducting contrastive learning in model-level. Our extensive experiments show that MOON significantly outperforms the other state-of-the-art federated learning algorithms on various image classification tasks.
Predictions obtained by, e.g., artificial neural networks have a high accuracy but humans often perceive the models as black boxes. Insights about the decision making are mostly opaque for humans. Particularly understanding the decision making in highly sensitive areas such as healthcare or fifinance, is of paramount importance. The decision-making behind the black boxes requires it to be more transparent, accountable, and understandable for humans. This survey paper provides essential definitions, an overview of the different principles and methodologies of explainable Supervised Machine Learning (SML). We conduct a state-of-the-art survey that reviews past and recent explainable SML approaches and classifies them according to the introduced definitions. Finally, we illustrate principles by means of an explanatory case study and discuss important future directions.
There has been appreciable progress in unsupervised network representation learning (UNRL) approaches over graphs recently with flexible random-walk approaches, new optimization objectives and deep architectures. However, there is no common ground for systematic comparison of embeddings to understand their behavior for different graphs and tasks. In this paper we theoretically group different approaches under a unifying framework and empirically investigate the effectiveness of different network representation methods. In particular, we argue that most of the UNRL approaches either explicitly or implicit model and exploit context information of a node. Consequently, we propose a framework that casts a variety of approaches -- random walk based, matrix factorization and deep learning based -- into a unified context-based optimization function. We systematically group the methods based on their similarities and differences. We study the differences among these methods in detail which we later use to explain their performance differences (on downstream tasks). We conduct a large-scale empirical study considering 9 popular and recent UNRL techniques and 11 real-world datasets with varying structural properties and two common tasks -- node classification and link prediction. We find that there is no single method that is a clear winner and that the choice of a suitable method is dictated by certain properties of the embedding methods, task and structural properties of the underlying graph. In addition we also report the common pitfalls in evaluation of UNRL methods and come up with suggestions for experimental design and interpretation of results.
Video anomaly detection under weak labels is formulated as a typical multiple-instance learning problem in previous works. In this paper, we provide a new perspective, i.e., a supervised learning task under noisy labels. In such a viewpoint, as long as cleaning away label noise, we can directly apply fully supervised action classifiers to weakly supervised anomaly detection, and take maximum advantage of these well-developed classifiers. For this purpose, we devise a graph convolutional network to correct noisy labels. Based upon feature similarity and temporal consistency, our network propagates supervisory signals from high-confidence snippets to low-confidence ones. In this manner, the network is capable of providing cleaned supervision for action classifiers. During the test phase, we only need to obtain snippet-wise predictions from the action classifier without any extra post-processing. Extensive experiments on 3 datasets at different scales with 2 types of action classifiers demonstrate the efficacy of our method. Remarkably, we obtain the frame-level AUC score of 82.12% on UCF-Crime.
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