While significant advancements have been made in the field of fair machine learning, the majority of studies focus on scenarios where the decision model operates on a static population. In this paper, we study fairness in dynamic systems where sequential decisions are made. Each decision may shift the underlying distribution of features or user behavior. We model the dynamic system through a Markov Decision Process (MDP). By acknowledging that traditional fairness notions and long-term fairness are distinct requirements that may not necessarily align with one another, we propose an algorithmic framework to integrate various fairness considerations with reinforcement learning using both pre-processing and in-processing approaches. Three case studies show that our method can strike a balance between traditional fairness notions, long-term fairness, and utility.
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In statistics and machine learning, logistic regression is a widely-used supervised learning technique primarily employed for binary classification tasks. When the number of observations greatly exceeds the number of predictor variables, we present a simple, randomized sampling-based algorithm for logistic regression problem that guarantees high-quality approximations to both the estimated probabilities and the overall discrepancy of the model. Our analysis builds upon two simple structural conditions that boil down to randomized matrix multiplication, a fundamental and well-understood primitive of randomized numerical linear algebra. We analyze the properties of estimated probabilities of logistic regression when leverage scores are used to sample observations, and prove that accurate approximations can be achieved with a sample whose size is much smaller than the total number of observations. To further validate our theoretical findings, we conduct comprehensive empirical evaluations. Overall, our work sheds light on the potential of using randomized sampling approaches to efficiently approximate the estimated probabilities in logistic regression, offering a practical and computationally efficient solution for large-scale datasets.
The rapid progress in machine learning in recent years has been based on a highly productive connection to gradient-based optimization. Further progress hinges in part on a shift in focus from pattern recognition to decision-making and multi-agent problems. In these broader settings, new mathematical challenges emerge that involve equilibria and game theory instead of optima. Gradient-based methods remain essential -- given the high dimensionality and large scale of machine-learning problems -- but simple gradient descent is no longer the point of departure for algorithm design. We provide a gentle introduction to a broader framework for gradient-based algorithms in machine learning, beginning with saddle points and monotone games, and proceeding to general variational inequalities. While we provide convergence proofs for several of the algorithms that we present, our main focus is that of providing motivation and intuition.
Statistical heterogeneity of clients' local data is an important characteristic in federated learning, motivating personalized algorithms tailored to the local data statistics. Though there has been a plethora of algorithms proposed for personalized supervised learning, discovering the structure of local data through personalized unsupervised learning is less explored. We initiate a systematic study of such personalized unsupervised learning by developing algorithms based on optimization criteria inspired by a hierarchical Bayesian statistical framework. We develop adaptive algorithms that discover the balance between using limited local data and collaborative information. We do this in the context of two unsupervised learning tasks: personalized dimensionality reduction and personalized diffusion models. We develop convergence analyses for our adaptive algorithms which illustrate the dependence on problem parameters (e.g., heterogeneity, local sample size). We also develop a theoretical framework for personalized diffusion models, which shows the benefits of collaboration even under heterogeneity. We finally evaluate our proposed algorithms using synthetic and real data, demonstrating the effective sample amplification for personalized tasks, induced through collaboration, despite data heterogeneity.
In machine learning, generalization against distribution shifts -- where deployment conditions diverge from the training scenarios -- is crucial, particularly in fields like climate modeling, biomedicine, and autonomous driving. The emergence of foundation models, distinguished by their extensive pretraining and task versatility, has led to an increased interest in their adaptability to distribution shifts. GPT-4V(ision) acts as the most advanced publicly accessible multimodal foundation model, with extensive applications across various domains, including anomaly detection, video understanding, image generation, and medical diagnosis. However, its robustness against data distributions remains largely underexplored. Addressing this gap, this study rigorously evaluates GPT-4V's adaptability and generalization capabilities in dynamic environments, benchmarking against prominent models like CLIP, LLaVA, and Gemini. We delve into GPT-4V's zero-shot generalization across 13 diverse datasets spanning natural, medical, and molecular domains. We further investigate its adaptability to controlled data perturbations and examine the efficacy of in-context learning as a tool to enhance its adaptation. Our findings delineate GPT-4V's capability boundaries in distribution shifts, shedding light on its strengths and limitations across various scenarios. Importantly, this investigation contributes to our understanding of how AI foundation models generalize to distribution shifts, offering pivotal insights into their adaptability and robustness. The code is publicly available at //github.com/jameszhou-gl/gpt-4v-distribution-shift.
Knowledge graph embeddings (KGE) have been validated as powerful methods for inferring missing links in knowledge graphs (KGs) that they typically map entities into Euclidean space and treat relations as transformations of entities. Recently, some Euclidean KGE methods have been enhanced to model semantic hierarchies commonly found in KGs, improving the performance of link prediction. To embed hierarchical data, hyperbolic space has emerged as a promising alternative to traditional Euclidean space, offering high fidelity and lower memory consumption. Unlike Euclidean, hyperbolic space provides countless curvatures to choose from. However, it is difficult for existing hyperbolic KGE methods to obtain the optimal curvature settings manually, thereby limiting their ability to effectively model semantic hierarchies. To address this limitation, we propose a novel KGE model called $\textbf{Hyp}$erbolic $\textbf{H}$ierarchical $\textbf{KGE}$ (HypHKGE). This model introduces attention-based learnable curvatures for hyperbolic space, which helps preserve rich semantic hierarchies. Furthermore, to utilize the preserved hierarchies for inferring missing links, we define hyperbolic hierarchical transformations based on the theory of hyperbolic geometry, including both inter-level and intra-level modeling. Experiments demonstrate the effectiveness of the proposed HypHKGE model on the three benchmark datasets (WN18RR, FB15K-237, and YAGO3-10). The source code will be publicly released at //github.com/wjzheng96/HypHKGE.
Recent advancements in deep learning have revolutionized technology and security measures, necessitating robust identification methods. Biometric approaches, leveraging personalized characteristics, offer a promising solution. However, Face Recognition Systems are vulnerable to sophisticated attacks, notably face morphing techniques, enabling the creation of fraudulent documents. In this study, we introduce a novel quadruplet loss function for increasing the robustness of face recognition systems against morphing attacks. Our approach involves specific sampling of face image quadruplets, combined with face morphs, for network training. Experimental results demonstrate the efficiency of our strategy in improving the robustness of face recognition networks against morphing attacks.
Student modeling is central to many educational technologies as it enables predicting future learning outcomes and designing targeted instructional strategies. However, open-ended learning domains pose challenges for accurately modeling students due to the diverse behaviors and a large space of possible misconceptions. To approach these challenges, we explore the application of large language models (LLMs) for in-context student modeling in open-ended learning domains. More concretely, given a particular student's attempt on a reference task as observation, the objective is to synthesize the student's attempt on a target task. We introduce a novel framework, LLM for Student Synthesis (LLM-SS), that leverages LLMs for synthesizing a student's behavior. Our framework can be combined with different LLMs; moreover, we fine-tune LLMs to boost their student modeling capabilities. We instantiate several methods based on LLM-SS framework and evaluate them using an existing benchmark, StudentSyn, for student attempt synthesis in a visual programming domain. Experimental results show that our methods perform significantly better than the baseline method NeurSS provided in the StudentSyn benchmark. Furthermore, our method using a fine-tuned version of the GPT-3.5 model is significantly better than using the base GPT-3.5 model and gets close to human tutors' performance.
We study computational-statistical gaps for improper learning in sparse linear regression. More specifically, given $n$ samples from a $k$-sparse linear model in dimension $d$, we ask what is the minimum sample complexity to efficiently (in time polynomial in $d$, $k$, and $n$) find a potentially dense estimate for the regression vector that achieves non-trivial prediction error on the $n$ samples. Information-theoretically this can be achieved using $\Theta(k \log (d/k))$ samples. Yet, despite its prominence in the literature, there is no polynomial-time algorithm known to achieve the same guarantees using less than $\Theta(d)$ samples without additional restrictions on the model. Similarly, existing hardness results are either restricted to the proper setting, in which the estimate must be sparse as well, or only apply to specific algorithms. We give evidence that efficient algorithms for this task require at least (roughly) $\Omega(k^2)$ samples. In particular, we show that an improper learning algorithm for sparse linear regression can be used to solve sparse PCA problems (with a negative spike) in their Wishart form, in regimes in which efficient algorithms are widely believed to require at least $\Omega(k^2)$ samples. We complement our reduction with low-degree and statistical query lower bounds for the sparse PCA problems from which we reduce. Our hardness results apply to the (correlated) random design setting in which the covariates are drawn i.i.d. from a mean-zero Gaussian distribution with unknown covariance.
Data augmentation, the artificial creation of training data for machine learning by transformations, is a widely studied research field across machine learning disciplines. While it is useful for increasing the generalization capabilities of a model, it can also address many other challenges and problems, from overcoming a limited amount of training data over regularizing the objective to limiting the amount data used to protect privacy. Based on a precise description of the goals and applications of data augmentation (C1) and a taxonomy for existing works (C2), this survey is concerned with data augmentation methods for textual classification and aims to achieve a concise and comprehensive overview for researchers and practitioners (C3). Derived from the taxonomy, we divided more than 100 methods into 12 different groupings and provide state-of-the-art references expounding which methods are highly promising (C4). Finally, research perspectives that may constitute a building block for future work are given (C5).
Recent contrastive representation learning methods rely on estimating mutual information (MI) between multiple views of an underlying context. E.g., we can derive multiple views of a given image by applying data augmentation, or we can split a sequence into views comprising the past and future of some step in the sequence. Contrastive lower bounds on MI are easy to optimize, but have a strong underestimation bias when estimating large amounts of MI. We propose decomposing the full MI estimation problem into a sum of smaller estimation problems by splitting one of the views into progressively more informed subviews and by applying the chain rule on MI between the decomposed views. This expression contains a sum of unconditional and conditional MI terms, each measuring modest chunks of the total MI, which facilitates approximation via contrastive bounds. To maximize the sum, we formulate a contrastive lower bound on the conditional MI which can be approximated efficiently. We refer to our general approach as Decomposed Estimation of Mutual Information (DEMI). We show that DEMI can capture a larger amount of MI than standard non-decomposed contrastive bounds in a synthetic setting, and learns better representations in a vision domain and for dialogue generation.
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