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Miscellaneous Aspects of Machine Learning/Transfer, Multitask and Meta-learning

Junguang Jiang, Baixu Chen, Junwei Pan, Ximei Wang, Dapeng Liu, Jie Jiang, Mingsheng Long

Auxiliary-Task Learning (ATL) aims to improve the performance of the target task by leveraging the knowledge obtained from related tasks. Occasionally, learning multiple tasks simultaneously results in lower accuracy than learning only the target task, which is known as negative transfer. This problem is often attributed to the gradient conflicts among tasks, and is frequently tackled by coordinating the task gradients in previous works. However, these optimization-based methods largely overlook the auxiliary-target generalization capability. To better understand the root cause of negative transfer, we experimentally investigate it from both optimization and generalization perspectives. Based on our findings, we introduce ForkMerge, a novel approach that periodically forks the model into multiple branches, automatically searches the varying task weights by minimizing target validation errors, and dynamically merges all branches to filter out detrimental task-parameter updates. On a series of auxiliary-task learning benchmarks, ForkMerge outperforms existing methods and effectively mitigates negative transfer.

Social Aspects/Privacy-preserving Statistics and Machine Learning

Jimmy Di, Jack Douglas, Jayadev Acharya, Gautam Kamath, Ayush Sekhari

We introduce camouflaged data poisoning attacks, a new attack vector that arises in the context of machine unlearning and other settings when model retraining may be induced. An adversary first adds a few carefully crafted points to the training dataset such that the impact on the model's predictions is minimal. The adversary subsequently triggers a request to remove a subset of the introduced points at which point the attack is unleashed and the model's predictions are negatively affected. In particular, we consider clean-label targeted attacks (in which the goal is to cause the model to misclassify a specific test point) on datasets including CIFAR-10, Imagenette, and Imagewoof. This attack is realized by constructing camouflage datapoints that mask the effect of a poisoned dataset. We demonstrate efficacy of our attack when unlearning is performed via retraining from scratch, the idealized setting of machine unlearning which other efficient methods attempt to emulate, as well as against the approximate unlearning approach of Graves et al. (2021).

Miscellaneous Aspects of Machine Learning/Everything Else

Jia-Qi Yang, De-Chuan Zhan, Le Gan

Research has shown that deep networks tend to be overly optimistic about their predictions, leading to an underestimation of prediction errors. Due to the limited nature of data, existing studies have proposed various methods based on model prediction probabilities to bin the data and evaluate calibration error. We propose a more generalized definition of calibration error called Partitioned Calibration Error (PCE), revealing that the key difference among these calibration error metrics lies in how the data space is partitioned. We put forth an intuitive proposition that an accurate model should be calibrated across any partition, suggesting that the input space partitioning can extend beyond just the partitioning of prediction probabilities, and include partitions directly related to the input. Through semantic-related partitioning functions, we demonstrate that the relationship between model accuracy and calibration lies in the granularity of the partitioning function. This highlights the importance of partitioning criteria for training a calibrated and accurate model. To validate the aforementioned analysis, we propose a method that involves jointly learning a semantic aware grouping function based on deep model features and logits to partition the data space into subsets. Subsequently, a separate calibration function is learned for each subset. Experimental results demonstrate that our approach achieves significant performance improvements across multiple datasets and network architectures, thus highlighting the importance of the partitioning function for calibration.

Miscellaneous Aspects of Machine Learning/Scalable Algorithms

Aditya Bhaskara, Sepideh Mahabadi, Ali Vakilian

Given a set of points of interest, a volumetric spanner is a subset of the points using which all the points can be expressed using "small" coefficients (measured in an appropriate norm). Formally, given a set of vectors $X = [v_1, v_2, \dots, v_n]$, the goal is to find $T \subseteq [n]$ such that every $v \in X$ can be expressed as $\sum_{i\in T} \alpha_i v_i$, with $\Vert \alpha \Vert$ being small. This notion, which has also been referred to as a well-conditioned basis, has found several applications, including bandit linear optimization, determinant maximization, and matrix low rank approximation. In this paper, we give almost optimal bounds on the size of volumetric spanners for all $\ell_p$ norms, and show that they can be constructed using a simple local search procedure. We then show the applications of our result to other tasks and in particular the problem of finding coresets for the Minimum Volume Enclosing Ellipsoid (MVEE) problem.

Miscellaneous Aspects of Machine Learning/Representation Learning

Yiyou Sun, Zhenmei Shi, Yixuan Li

Open-world semi-supervised learning aims at inferring both known and novel classes in unlabeled data, by harnessing prior knowledge from a labeled set with known classes. Despite its importance, there is a lack of theoretical foundations for this problem. This paper bridges the gap by formalizing a graph-theoretic framework tailored for the open-world setting, where the clustering can be theoretically characterized by graph factorization. Our graph-theoretic framework illuminates practical algorithms and provides guarantees. In particular, based on our graph formulation, we apply the algorithm called Spectral Open-world Representation Learning (SORL), and show that minimizing our loss is equivalent to performing spectral decomposition on the graph. Such equivalence allows us to derive a provable error bound on the clustering performance for both known and novel classes, and analyze rigorously when labeled data helps. Empirically, SORL can match or outperform several strong baselines on common benchmark datasets, which is appealing for practical usage while enjoying theoretical guarantees.

Miscellaneous Aspects of Machine Learning/General Machine Learning Techniques

Alexandre Blain, Bertrand Thirion, Olivier Grisel, Pierre Neuvial

Controlled variable selection is an important analytical step in various scientific fields, such as brain imaging or genomics. In these high-dimensional data settings, considering too many variables leads to poor models and high costs, hence the need for statistical guarantees on false positives. Knockoffs are a popular statistical tool for conditional variable selection in high dimension. However, they control for the expected proportion of false discoveries (FDR) and not the actual proportion of false discoveries (FDP). We present a new method, KOPI, that controls the proportion of false discoveries for Knockoff-based inference. The proposed method also relies on a new type of aggregation to address the undesirable randomness associated with classical Knockoff inference. We demonstrate FDP control and substantial power gains over existing Knockoff-based methods in various simulation settings and achieve good sensitivity/specificity tradeoffs on brain imaging data.

Miscellaneous Aspects of Machine Learning/Transfer, Multitask and Meta-learning

Mark D. McDonnell, Dong Gong, Amin Parvaneh, Ehsan Abbasnejad, Anton van den Hengel

Continual learning (CL) aims to incrementally learn different tasks (such as classification) in a non-stationary data stream without forgetting old ones. Most CL works focus on tackling catastrophic forgetting under a learning-from-scratch paradigm. However, with the increasing prominence of foundation models, pre-trained models equipped with informative representations have become available for various downstream requirements. Several CL methods based on pre-trained models have been explored, either utilizing pre-extracted features directly (which makes bridging distribution gaps challenging) or incorporating adaptors (which may be subject to forgetting). In this paper, we propose a concise and effective approach for CL with pre-trained models. Given that forgetting occurs during parameter updating, we contemplate an alternative approach that exploits training-free random projectors and class-prototype accumulation, which thus bypasses the issue. Specifically, we inject a frozen Random Projection layer with nonlinear activation between the pre-trained model's feature representations and output head, which captures interactions between features with expanded dimensionality, providing enhanced linear separability for class-prototype-based CL. We also demonstrate the importance of decorrelating the class-prototypes to reduce the distribution disparity when using pre-trained representations. These techniques prove to be effective and circumvent the problem of forgetting for both class- and domain-incremental continual learning. Compared to previous methods applied to pre-trained ViT-B/16 models, we reduce final error rates by between 20% and 62% on seven class-incremental benchmark datasets, despite not using any rehearsal memory. We conclude that the full potential of pre-trained models for simple, effective, and fast continual learning has not hitherto been fully tapped. Code is available at https://github.com/RanPAC/RanPAC.

Miscellaneous Aspects of Machine Learning/Transfer, Multitask and Meta-learning

Haizhou Shi, Hao Wang

Domain incremental learning aims to adapt to a sequence of domains with access to only a small subset of data (i.e., memory) from previous domains. Various methods have been proposed for this problem, but it is still unclear how they are related and when practitioners should choose one method over another. In response, we propose a unified framework, dubbed Unified Domain Incremental Learning (UDIL), for domain incremental learning with memory. Our UDIL **unifies** various existing methods, and our theoretical analysis shows that UDIL always achieves a tighter generalization error bound compared to these methods. The key insight is that different existing methods correspond to our bound with different **fixed** coefficients; based on insights from this unification, our UDIL allows **adaptive** coefficients during training, thereby always achieving the tightest bound. Empirical results show that our UDIL outperforms the state-of-the-art domain incremental learning methods on both synthetic and real-world datasets. Code will be available at https://github.com/Wang-ML-Lab/unified-continual-learning.

Miscellaneous Aspects of Machine Learning/Representation Learning

Yi Ren, Samuel Lavoie, Michael Galkin, Danica J. Sutherland, Aaron Courville

Compositional generalization, the ability of an agent to generalize to unseen combinations of latent factors, is easy for humans but hard for deep neural networks. A line of research in cognitive science has hypothesized a process, "iterated learning," to help explain how human language developed this ability; the theory rests on simultaneous pressures towards compressibility (when an ignorant agent learns from an informed one) and expressivity (when it uses the representation for downstream tasks). Inspired by this process, we propose to improve the compositional generalization of deep networks by using iterated learning on models with simplicial embeddings, which can approximately discretize representations. This approach is further motivated by an analysis of compositionality based on Kolmogorov complexity. We show that this combination of changes improves compositional generalization over other approaches, demonstrating these improvements both on vision tasks with well-understood latent factors and on real molecular graph prediction tasks where the latent structure is unknown.

Miscellaneous Aspects of Machine Learning/Unsupervised and Semi-supervised Learning

Maximilien Dreveton, Felipe Fernandes, Daniel Figueiredo

Classic network clustering tackles the problem of identifying sets of nodes (communities) that have similar connection patterns. However, in many scenarios nodes also have attributes that are correlated and can also be used to identify node clusters. Thus, network information (edges) and node information (attributes) can be jointly leveraged to design high-performance clustering algorithms. Under a general model for the network and node attributes, this work establishes an information-theoretic criteria for the exact recovery of community labels and characterizes a phase transition determined by the Chernoff-Hellinger divergence of the model. The criteria shows how network and attribute information can be exchanged in order to have exact recovery (e.g., more reliable network information requires less reliable attribute information). This work also presents an iterative clustering algorithm that maximizes the joint likelihood, assuming that the probability distribution of network interactions and node attributes belong to exponential families. This covers a broad range of possible interactions (e.g., edges with weights) and attributes (e.g., non-Gaussian models) while also exploring the connection between exponential families and Bregman divergences. Extensive numerical experiments using synthetic and real data indicate that the proposed algorithm outperforms algorithms that leverage only network or only attribute information as well as recently proposed algorithms that perform clustering using both sources of information. The contributions of this work provide insights into the fundamental limits and practical techniques for inferring community labels on node-attributed networks.

Miscellaneous Aspects of Machine Learning/Causality

Kirankumar Shiragur, Jiaqi Zhang, Caroline Uhler

Learning causal structures from interventional data is a fundamental problem with broad applications across various fields. While many previous works have focused on recovering the entire causal graph, in practice, there are scenarios where learning only part of the causal graph suffices. This is called \emph{targeted} causal discovery. In our work, we focus on two such well-motivated problems: subset search and causal matching. We aim to minimize the number of interventions in both cases.Towards this, we introduce the \emph{Meek separator}, which is a subset of vertices that, when intervened, decomposes the remaining unoriented edges into smaller connected components. We then present an efficient algorithm to find Meek separators that are of small sizes. Such a procedure is helpful in designing various divide-and-conquer-based approaches. In particular, we propose two randomized algorithms that achieve logarithmic approximation for subset search and causal matching, respectively. Our results provide the first known average-case provable guarantees for both problems. We believe that this opens up possibilities to design near-optimal methods for many other targeted causal structure learning problems arising from various applications.

Miscellaneous Aspects of Machine Learning/Representation Learning

Sudhanshu Chanpuriya, Ryan Rossi, Anup B. Rao, Tung Mai, Nedim Lipka, Zhao Song, Cameron Musco

Graph models based on factorization of the adjacency matrix often fail to capture network structures related to links between dissimilar nodes (heterophily). We introduce a novel graph factorization model that leverages two nonnegative vectors per node to interpretably account for links between both similar and dissimilar nodes. We prove that our model can exactly represent any graph with low *arboricity*, a property that many real-world networks satisfy; our proof also applies to related models but has much greater scope than the closest prior bound, which is based on low *max degree*. Our factorization also has compelling properties besides expressiveness: due to its symmetric structure and nonnegativity, fitting the model inherently finds node communities, and the model's link predictions can be interpreted in terms of these communities. In experiments on real-world networks, we demonstrate our factorization's effectiveness on a variety of tasks, including community detection and link prediction.

Miscellaneous Aspects of Machine Learning/Causality

Gecia Bravo-Hermsdorff, David Watson, Jialin Yu, Jakob Zeitler, Ricardo Silva

One of the goals of causal inference is to generalize from past experiments and observational data to novel conditions. While it is in principle possible to eventually learn a mapping from a novel experimental condition to an outcome of interest, provided a sufficient variety of experiments is available in the training data, coping with a large combinatorial space of possible interventions is hard. Under a typical sparse experimental design, this mapping is ill-posed without relying on heavy regularization or prior distributions. Such assumptions may or may not be reliable, and can be hard to defend or test. In this paper, we take a close look at how to warrant a leap from past experiments to novel conditions based on minimal assumptions about the factorization of the distribution of the manipulated system, communicated in the well-understood language of factor graph models. A postulated interventional factor model (IFM) may not always be informative, but it conveniently abstracts away a need for explicitly modeling unmeasured confounding and feedback mechanisms, leading to directly testable claims. Given an IFM and datasets from a collection of experimental regimes, we derive conditions for identifiability of the expected outcomes of new regimes never observed in these training data. We implement our framework using several efficient algorithms, and apply them on a range of semi-synthetic experiments.

Theory/Miscellaneous Aspects of Machine Learning

Ryan Theisen, Hyunsuk Kim, Yaoqing Yang, Liam Hodgkinson, Michael Mahoney

Ensembling has a long history in statistical data analysis, with many impactful applications. However, in many modern machine learning settings, the benefits of ensembling are less ubiquitous and less obvious. We study, both theoretically and empirically, the fundamental question of when ensembling yields significant performance improvements in classification tasks. Theoretically, we prove new results relating the \emph{ensemble improvement rate} (a measure of how much ensembling decreases the error rate versus a single model, on a relative scale) to the \emph{disagreement-error ratio}. We show that ensembling improves performance significantly whenever the disagreement rate is large relative to the average error rate; and that, conversely, one classifier is often enough whenever the disagreement rate is low relative to the average error rate. On the way to proving these results, we derive, under a mild condition called \emph{competence}, improved upper and lower bounds on the average test error rate of the majority vote classifier.To complement this theory, we study ensembling empirically in a variety of settings, verifying the predictions made by our theory, and identifying practical scenarios where ensembling does and does not result in large performance improvements. Perhaps most notably, we demonstrate a distinct difference in behavior between interpolating models (popular in current practice) and non-interpolating models (such as tree-based methods, where ensembling is popular), demonstrating that ensembling helps considerably more in the latter case than in the former.

Miscellaneous Aspects of Machine Learning/General Machine Learning Techniques

Litu Rout, Negin Raoof, Giannis Daras, Constantine Caramanis, Alex Dimakis, Sanjay Shakkottai

We present the first framework to solve linear inverse problems leveraging pre-trained \textit{latent} diffusion models. Previously proposed algorithms (such as DPS and DDRM) only apply to \textit{pixel-space} diffusion models. We theoretically analyze our algorithm showing provable sample recovery in a linear model setting. The algorithmic insight obtained from our analysis extends to more general settings often considered in practice. Experimentally, we outperform previously proposed posterior sampling algorithms in a wide variety of problems including random inpainting, block inpainting, denoising, deblurring, destriping, and super-resolution.

Miscellaneous Aspects of Machine Learning/Transfer, Multitask and Meta-learning

Matthew Wallingford, Vivek Ramanujan, Alex Fang, Aditya Kusupati, Roozbeh Mottaghi, Aniruddha Kembhavi, Ludwig Schmidt, Ali Farhadi

We propose Neural Priming, a technique for adapting large pretrained models to distribution shifts and downstream tasks given few or no labeled examples. Presented with class names or unlabeled test samples, Neural Priming enables the model to recall and conditions its parameters on relevant data seen throughout pretraining, thereby priming it for the test distribution. Neural Priming can be performed at test time in even for pretraining datasets as large as LAION-2B. Performing lightweight updates on the recalled data significantly improves accuracy across a variety of distribution shift and transfer learning benchmarks. Concretely, in the zero-shot setting, we see a 2.45% improvement in accuracy on ImageNet and 3.81% accuracy improvement on average across standard transfer learning benchmarks. Further, using our test time inference scheme, we see a 1.41% accuracy improvement on ImageNetV2. These results demonstrate the effectiveness of Neural Priming in addressing the common challenge of limited labeled data and changing distributions. Code and models are open-sourced at [https://www.github.com/RAIVNLab/neural-priming](https://www.github.com/RAIVNLab/neural-priming).

Miscellaneous Aspects of Machine Learning/Representation Learning

Xiangchen Song, Weiran Yao, Yewen Fan, Xinshuai Dong, Guangyi Chen, Juan Carlos Niebles, Eric Xing, Kun Zhang

In unsupervised causal representation learning for sequential data with time-delayed latent causal influences, strong identifiability results for the disentanglement of causally-related latent variables have been established in stationary settings by leveraging temporal structure.However, in nonstationary setting, existing work only partially addressed the problem by either utilizing observed auxiliary variables (e.g., class labels and/or domain indexes) as side information or assuming simplified latent causal dynamics. Both constrain the method to a limited range of scenarios.In this study, we further explored the Markov Assumption under time-delayed causally related process in nonstationary setting and showed that under mild conditions, the independent latent components can be recovered from their nonlinear mixture up to a permutation and a component-wise transformation, without the observation of auxiliary variables. We then introduce NCTRL, a principled estimation framework, to reconstruct time-delayed latent causal variables and identify their relations from measured sequential data only.Empirical evaluations demonstrated the reliable identification of time-delayed latent causal influences, with our methodology substantially outperforming existing baselines that fail to exploit the nonstationarity adequately and then, consequently, cannot distinguish distribution shifts.

Miscellaneous Aspects of Machine Learning/Representation Learning

Somnath Basu Roy Chowdhury, Nicholas Monath, Kumar Avinava Dubey, Amr Ahmed, Snigdha Chaturvedi

Distributed representations provide a vector space that captures meaningful relationships between data instances. The distributed nature of these representations, however, entangles together multiple attributes or concepts of data instances (e.g., the topic or sentiment of a text, characteristics of the author (age, gender, etc), etc). Recent work has proposed the task of concept erasure, in which rather than making a concept predictable, the goal is to remove an attribute from distributed representations while retaining other information from the original representation space as much as possible. In this paper, we propose a new distance metric learning-based objective, the Kernelized Rate-Distortion Maximizer (KRaM), for performing concept erasure. KRaM fits a transformation of representations to match a specified distance measure (defined by a labeled concept to erase) using a modified rate-distortion function. Specifically, KRaM's objective function aims to make instances with similar concept labels dissimilar in the learned representation space while retaining other information. We find that optimizing KRaM effectively erases various types of concepts—categorical, continuous, and vector-valued variables—from data representations across diverse domains. We also provide a theoretical analysis of several properties of KRaM's objective. To assess the quality of the learned representations, we propose an alignment score to evaluate their similarity with the original representation space. Additionally, we conduct experiments to showcase KRaM's efficacy in various settings, from erasing binary gender variables in word embeddings to vector-valued variables in GPT-3 representations.

Miscellaneous Aspects of Machine Learning/Transfer, Multitask and Meta-learning

Suyash Gupta, Dominik Rothenhäusler

Common statistical measures of uncertainty such as $p$-values and confidence intervals quantify the uncertainty due to sampling, that is, the uncertainty due to not observing the full population. However, sampling is not the only source of uncertainty. In practice, distributions change between locations and across time. This makes it difficult to gather knowledge that transfers across data sets. We propose a measure of instability that quantifies the distributional instability of a statistical parameter with respect to Kullback-Leibler divergence, that is, the sensitivity of the parameter under general distributional perturbations within a Kullback-Leibler divergence ball. In addition, we quantify the instability of parameters with respect to directional or variable-specific shifts. Measuring instability with respect to directional shifts can be used to detect under which kind of distribution shifts a statistical conclusion might be reversed. We discuss how such knowledge can inform data collection for transfer learning of statistical parameters under shifted distributions. We evaluate the performance of the proposed measure on real data and show that it can elucidate the distributional instability of a parameter with respect to certain shifts and can be used to improve estimation accuracy under shifted distributions.

Miscellaneous Aspects of Machine Learning/Online Learning, Active Learning and Bandits

Abishek Sankararaman, Balakrishnan Narayanaswamy

The real-time estimation of time-varying parameters from high-dimensional, heavy-tailed and corrupted data-streams is a common sub-routine in systems ranging from those for network monitoring and anomaly detection to those for traffic scheduling in data-centers. For estimation tasks that can be cast as minimizing a strongly convex loss function, we prove that an appropriately tuned version of the {\ttfamily clipped Stochastic Gradient Descent} (SGD) is simultaneously {\em(i)} adaptive to drift, {\em (ii)} robust to heavy-tailed inliers and arbitrary corruptions, {\em(iii)} requires no distributional knowledge and {\em (iv)} can be implemented in an online streaming fashion. All prior estimation algorithms have only been proven to posses a subset of these practical desiderata. A observation we make is that, neither the $\mathcal{O}\left(\frac{1}{t}\right)$ learning rate for {\ttfamily clipped SGD} known to be optimal for strongly convex loss functions of a \emph{stationary} data-stream, nor the $\mathcal{O}(1)$ learning rate known to be optimal for being adaptive to drift in a \emph{noiseless} environment can be used. Instead, a learning rate of $T^{-\alpha}$ for $ \alpha < 1$ where $T$ is the stream-length is needed to balance adaptivity to potential drift and to combat noise. We develop a new inductive argument and combine it with a martingale concentration result to derive high-probability under \emph{any learning rate} on data-streams exhibiting \emph{arbitrary distribution shift} - a proof strategy that may be of independent interest. Further, using the classical doubling-trick, we relax the knowledge of the stream length $T$. Ours is the first online estimation algorithm that is provably robust to heavy-tails, corruptions and distribution shift simultaneously. We complement our theoretical results empirically on synthetic and real data.