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Low dimensional models like PCA are often used to simplify complex datasets by learning a single approximating subspace. This paradigm has expanded to union of subspaces models, like those learned by subspace clustering. In this paper, we present Principle Component Trees (PCTs), a graph structure that generalizes these ideas to identify mixtures of components that together describe the subspace structure of high-dimensional datasets. Each node in a PCT corresponds to a principle component of the data, and the edges between nodes indicate the components that must be mixed to produce a subspace that approximates a portion of the data. In order to construct PCTs, we propose two angle-distribution hypothesis tests to detect subspace clusters in the data. To analyze, compare, and select the best PCT model, we define two persistent homology measures that describe their shape. We show our construction yields two key properties of PCTs, namely ancestral orthogonality and non-decreasing singular values. Our main theoretical results show that learning PCTs reduces to PCA under multivariate normality, and that PCTs are efficient parameterizations of intersecting union of subspaces. Finally, we use PCTs to analyze neural network latent space, word embeddings, and reference image datasets.

AAAI 2024

Principle Component Trees and Their Persistent Homology

topological data analysis

feature extraction

dimensionality reduction

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To better understand the output of deep neural networks (DNN), attribution based methods have been an important approach for model interpretability, which assign a score for each input dimension to indicate its importance towards the model outcome. Notably, the attribution methods use the ax- ioms of sensitivity and implementation invariance to ensure the validity and reliability of attribution results. Yet, the ex- isting attribution methods present challenges for effective in- terpretation and efficient computation. In this work, we in- troduce MFABA, an attribution algorithm that adheres to ax- ioms, as a novel method for interpreting DNN. Addition- ally, we provide the theoretical proof and in-depth analy- sis for MFABA algorithm, and conduct a large scale exper- iment. The results demonstrate its superiority by achieving over 101.5142 times faster speed than the state-of-the-art at- tribution algorithms. The effectiveness of MFABA is thor- oughly evaluated through the statistical analysis in compar- ison to other methods, and the full implementation package is open-source at: https://github.com/LMBTough/MFABA.

MFABA: A More Faithful and Accelerated Boundary-Based Attribution Method for Deep Neural Networks

We characterize offline data poisoning attacks on Multi-Agent Reinforcement Learning (MARL), where an attacker may change a data set in an attempt to install a (potentially fictitious) unique Markov-perfect Nash equilibrium for a two-player zero-sum Markov game. We propose the unique Nash set, namely the set of games, specified by their Q functions, with a specific joint policy being the unique Nash equilibrium. The unique Nash set is central to poisoning attacks because the attack is successful if and only if data poisoning pushes all plausible games inside it. The unique Nash set generalizes the reward polytope commonly used in inverse reinforcement learning to MARL. For zero-sum Markov games, both the inverse Nash set and the set of plausible games induced by data are polytopes in the Q function space. We exhibit a linear program to efficiently compute the optimal poisoning attack. Our work sheds light on the structure of data poisoning attacks on offline MARL, a necessary step before one can design more robust MARL algorithms.

Data Poisoning to Fake a Nash Equilibria for Markov Games

Knowledge-grounded dialogue (KGD) learns to generate an informative response based on a given dialogue context and external knowledge (e.g., knowledge graphs; KGs). Recently, the emergence of large language models (LLMs) and pre-training techniques has brought great success to knowledge-grounded dialogue. However, when building KGD systems in real applications, there are various real-world noises that are inevitable to face. For example, the dialogue context might involve perturbations such as misspellings and abbreviations. In addition, KGs typically suffer from incompletion and also might contain erroneous and outdated facts. Such real-world noises pose a challenge to the robustness of KGD systems and hinder their applications in the real world. In this paper, we propose an entity-based contrastive learning framework for improving the robustness of KGD. Specifically, we make use of the entity information in a KGD sample to create both its positive and negative samples which involve semantic-irrelevant and semantic-relevant perturbations, respectively. The contrastive learning framework ensures the KGD model is aware of these two types of perturbations, thus could generate informative responses with the potentially noisy inputs in real applications. Experimental results on three widely-used benchmark datasets show that our method achieves new state-of-the-art performance in terms of automatic evaluation scores, verifying its effectiveness and potentiality. Furthermore, we show that our method is able to generate better responses than comparison models in both the noisy and the few-shot settings.

Improving the Robustness of Knowledge-Grounded Dialogue via Contrastive Learning

We formulate the problem of eliciting agents' preferences with the goal of finding a Kemeny ranking as a Dueling Bandits problem.
Here the bandits' arms correspond to alternatives that need to be ranked and the feedback corresponds to a pairwise comparison between alternatives by a randomly sampled agent.
We consider both sampling with and without replacement, i.e., the possibility to ask the same agent about some comparison multiple times or not.

We find approximation bounds for Kemeny rankings dependant on confidence intervals over estimated winning probabilities of arms. 
Based on these we state algorithms to find Probably Approximately Correct (PAC) solutions and elaborate on their sample complexity for sampling with or without replacement.
Furthermore, if all agents' preferences are strict rankings over the alternatives, we provide means to prune confidence intervals and thereby guide a more efficient elicitation. We formulate several adaptive sampling methods that use look-aheads to estimate how much confidence intervals (and thus approximation guarantees) might be tightened. 
All described methods are compared on synthetic data.

Eliciting Kemeny Rankings

In the standard use case of Algorithmic Fairness, the goal is to eliminate the relationship between a sensitive variable and a corresponding score. Throughout recent years, the scientific community has developed a host of definitions and tools to solve this task, which work well in many practical applications. However, the applicability and effectivity of these tools and definitions becomes less straightfoward in the case of multiple sensitive attributes. To tackle this issue, we propose a sequential framework, which allows to progressively achieve fairness across a set of sensitive features. We accomplish this by leveraging multi-marginal Wasserstein barycenters, which extends the standard notion of Strong Demographic Parity to the case with multiple sensitive characteristics. This method also provides a closed-form solution for the optimal, sequentially fair predictor, permitting a clear interpretation of inter-sensitive feature correlations. Our approach seamlessly extends to approximate fairness, enveloping a framework accommodating the trade-off between risk and unfairness. This extension permits a targeted prioritization of fairness improvements for a specific attribute within a set of sensitive attributes, allowing for a case specific adaptation. A data-driven estimation procedure for the derived solution is developed, and comprehensive numerical experiments are conducted on both synthetic and real datasets. Our empirical findings decisively underscore the practical efficacy of our post-processing approach in fostering fair decision-making.

A Sequentially Fair Mechanism for Multiple Sensitive Attributes | VIDEO

Volatility, as a measure of uncertainty, plays a crucial role in numerous financial activities such as risk management. The Econometrics and Machine Learning communities have developed two distinct approaches for financial volatility forecasting: the stochastic approach and the neural network (NN) approach. Despite their individual strengths, these methodologies have conventionally evolved in separate research trajectories with little interaction between them. This study endeavors to bridge this gap by establishing an equivalence relationship between models of the GARCH family and their corresponding NN counterparts. With the equivalence relationship established, we introduce an innovative approach, named GARCH-NN, for constructing NN-based volatility models. It obtains the NN counterparts of GARCH models and integrates them as components into an established NN architecture, thereby seamlessly infusing volatility stylized facts (SFs) inherent in the GARCH models into the neural network. We develop the GARCH-LSTM model to showcase the power of GARCH-NN approach. Experiment results validate that amalgamating the NN counterparts of the GARCH family models into established NN models leads to enhanced outcomes compared to employing the stochastic and NN models in isolation.

From GARCH to Neural Network for Volatility Forecast | VIDEO

Learning from open-world noisy data, where both closed-set and open-set noise co-exist in the dataset, is a realistic but underexplored setting. Only recently, several efforts have been initialized to tackle this problem. However, these works assume the classes are balanced when dealing with open-world noisy data. This assumption often violates the nature of real-world large-scale datasets, where the label distributions are generally long-tailed, i.e. class-imbalanced. In this paper, we study the problem of robust visual recognition with class-imbalanced open-world noisy data. We propose a probabilistic graphical model-based approach: iMRF to achieve label noise correction that is robust to class imbalance via an efficient iterative inference of a Markov Random Field (MRF) in each training mini-batch. Furthermore, we design an agreement-based thresholding strategy to adaptively collect clean samples from all classes that includes corrected closed-set noisy samples while rejecting open-set noisy samples. We also introduce a noise-aware balanced cross-entropy loss to explicitly eliminate the bias caused by class-imbalanced data. Extensive experiments on several benchmark datasets including synthetic and real-world noisy datasets demonstrate the superior performance robustness of our method over existing methods. Our code is available at https://github.com/Na-Z/LIOND.

Robust Visual Recognition with Class-Imbalanced Open-World Noisy Data

We address the challenging problem of Long-Tailed Semi-Supervised Learning (LTSSL) where labeled data exhibit imbalanced class distribution and unlabeled data follow an unknown distribution. Unlike in balanced SSL, the generated pseudo-labels are skewed towards head classes, intensifying the training bias. Such a phenomenon is even amplified as more unlabeled data will be mislabeled as head classes when the class distribution of labeled and unlabeled datasets are mismatched. To solve this problem, we propose a novel method named ComPlementary Experts (CPE). Specifically, we train multiple experts to model various class distributions, each of them yielding high-quality pseudo-labels within one form of class distribution. Besides, we introduce Classwise Batch Normalization for CPE to avoid performance degradation caused by feature distribution mismatch between head and non-head classes. CPE achieves state-of-the-art performances on CIFAR-10-LT, CIFAR-100-LT, and STL-10-LT dataset benchmarks. For instance, on CIFAR-10-LT, CPE improves test accuracy by over >2.22% compared to baselines. Code is available at https://github.com/machengcheng2016/CPE-LTSSL.

Three Heads Are Better than One: Complementary Experts for Long-Tailed Semi-supervised Learning | VIDEO

Interactive segmentation methods rely on user inputs to iteratively update the selection mask. A click specifying the object of interest is arguably the most simple and intuitive interaction type, and thereby the most common choice for interactive segmentation. However, user clicking patterns in the interactive segmentation context remain unexplored. Accordingly, interactive segmentation evaluation strategies rely more on intuition and common sense rather than empirical studies (e.g., assuming that users tend to click in the center of the area with the largest error). In this work, we conduct a real-user study to investigate real user clicking patterns. This study reveals that the intuitive assumption made in the common evaluation strategy may not hold. As a result, interactive segmentation models may show high scores in the standard benchmarks, but it does not imply that they would perform well in a real world scenario. To assess the applicability of interactive segmentation methods, we propose a novel evaluation strategy providing a more comprehensive analysis of a model's performance. To this end, we propose a methodology for finding extreme user inputs by a direct optimization in a white-box adversarial attack on the interactive segmentation model. Based on the performance with such adversarial user inputs, we assess the robustness of interactive segmentation models w.r.t click positions. Besides, we introduce a novel benchmark for measuring the robustness of interactive segmentation, and report the results of an extensive evaluation of dozens of models.

TETRIS: Towards Exploring the Robustness of Interactive Segmentation | VIDEO

In this paper, we study an underexplored, yet important and challenging problem: counting the number of distinct sounds in raw audio characterized by a high degree of polyphonicity. We do so by systematically proposing a novel end-to-end trainable neural network~(which we call DyDecNet, consisting of a dyadic decomposition front-end and backbone network), and quantifying the difficulty level of counting depending on sound polyphonicity. The dyadic decomposition front-end progressively decomposes the raw waveform dyadically along the frequency axis to obtain time-frequency representation in multi-stage, coarse-to-fine manner. Each intermediate waveform convolved by a parent filter is further processed by a pair of child filters that evenly split the parent filter's carried frequency response, with the higher-half child filter encoding the detail and lower-half child filter encoding the approximation. We further introduce an energy gain normalization to normalize sound loudness variance and spectrum overlap, and apply it to each intermediate parent waveform before feeding it to the two child filters. To better quantify sound counting difficulty level, we further design three polyphony-aware metrics: polyphony ratio, max polyphony and mean polyphony. We test DyDecNet on various datasets to show its superiority, and we further show dyadic decomposition network can be used as a general front-end to tackle other acoustic tasks.

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