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Probabilistic Methods · Variational Inference

Alessandro Mastrototaro, Jimmy Olsson

Being the most classical generative model for serial data, state-space models (SSM) are fundamental in AI and statistical machine learning. In SSM, any form of parameter learning or latent state inference typically involves the computation of complex latent-state posteriors. In this work, we build upon the variational sequential Monte Carlo (VSMC) method, which provides computationally efficient and accurate model parameter estimation and Bayesian latent-state inference by combining particle methods and variational inference. While standard VSMC operates in the offline mode, by re-processing repeatedly a given batch of data, we distribute the approximation of the gradient of the VSMC surrogate ELBO in time using stochastic approximation, allowing for online learning in the presence of streams of data. This results in an algorithm, online VSMC, that is capable of performing efficiently, entirely on-the-fly, both parameter estimation and particle proposal adaptation. In addition, we provide rigorous theoretical results describing the algorithm's convergence properties as the number of data tends to infinity as well as numerical illustrations of its excellent convergence properties and usefulness also in batch-processing settings.

Social Aspects · Privacy-preserving Statistics and Machine Learning

Xueyang Tang, Song Guo, Jingcai Guo, Jie ZHANG, Yue Yu

Exploiting invariant relations and mitigating spurious correlation (a.k.a., shortcut) between representation and target across varied data distributions can tackle the challenging out-of-distribution (OOD) generalization problem. In personalized federated learning (PFL), heterogeneous data distribution across local clients offers the inherent prerequisites to extract the invariant features that maintain invariant relation with target. Nevertheless, personalized features are closely entangled with spurious features in PFL since they exhibit similar variability across different clients, which makes preserving personalization knowledge and eliminating shortcuts two conflicting objectives in PFL. To address the above challenge, we analyse the heterogeneous data generation on local clients through the lens of structured causal model and propose a crucial causal signature which can distinguish personalized features from spurious features with global invariant features as the anchor. Then the causal signature is quantified as an information-theoretic constraint that facilitates the shortcut-averse personalized invariant learning on each client. Theoretical analysis demonstrates our method, FedPIN, can yield a tighter bound on generalization error than the prevalent PFL approaches when train-test distribution shift exists on clients. Moreover, we provide a theoretical guarantee on the convergence rate of FedPIN in this paper. The results of extensive experiments show that our method can achieve superior OOD generalization performance compared with the state-of-the-art competitors.

Deep Learning · Generative Models and Autoencoders

Zehao Dou, Minshuo Chen, Mengdi Wang, Zhuoran Yang

Diffusion models have revolutionized various application domains, including computer vision and audio generation. Despite the state-of-the-art performance, diffusion models are known for their slow sample generation due to the extensive number of steps involved. In response, consistency models have been developed to merge multiple steps in the sampling process, thereby significantly boosting the speed of sample generation without compromising quality. This paper contributes towards the first statistical theory for consistency models, formulating their training as a distribution discrepancy minimization problem. Our analysis yields statistical estimation rates based on the Wasserstein distance for consistency models, matching those of vanilla diffusion models. Additionally, our results encompass the training of consistency models through both distillation and isolation methods, demystifying their underlying advantage.

Deep Learning · Sequential Models, Time series

Yair Schiff, Zhong Yi Wan, Jeffrey Parker, Stephan Hoyer, Volodymyr Kuleshov, Fei Sha, Leonardo Zepeda-Nunez

Learning dynamics from dissipative chaotic systems is notoriously difficult due to their inherent instability, as formalized by their positive Lyapunov exponents, which exponentially amplify errors in the learned dynamics. However, many of these systems exhibit ergodicity and an attractor: a compact and highly complex manifold, to which trajectories converge in finite-time, that supports an invariant measure, i.e., a probability distribution that is invariant under the action of the dynamics, which dictates the long-term statistical behavior of the system. In this work, we leverage this structure to propose a new framework that targets learning the invariant measure as well as the dynamics, in contrast with typical methods that only target the misfit between trajectories, which often leads to divergence as the trajectories' length increases. We use our framework to propose a tractable and sample efficient objective that can be used with any existing learning objectives. Our **Dy**namics **S**table **L**earning by **I**nvariant **M**easure (DySLIM) objective enables model training that achieves better point-wise tracking and long-term statistical accuracy relative to other learning objectives. By targeting the distribution with a scalable regularization term, we hope that this approach can be extended to more complex systems exhibiting slowly-variant distributions, such as weather and climate models. Code to reproduce our experiments is available here: https://github.com/google-research/swirl-dynamics/tree/main/swirl_dynamics/projects/ergodic.

Deep Learning

Bonan Zhang, Chia-Yu Chen, Naveen Verma

In-memory computing (IMC) has emerged as a promising solution to address both computation and data-movement challenges, by performing computation on data in-place directly in the memory array. IMC typically relies on analog operation, which makes analog-to-digital converters (ADCs) necessary, for converting results back to the digital domain. However, ADCs maintain computational efficiency by having limited precision, leading to substantial quantization errors in compute outputs. This work proposes RAOQ (Reshape and Adapt for Output Quantization) to overcome this issue, which comprises two classes of mechanisms including: 1) mitigating ADC quantization error by adjusting the statistics of activations and weights, through an activation-shifting approach (A-shift) and a weight reshaping technique (W-reshape); 2) adapting AI models to better tolerate ADC quantization through a bit augmentation method (BitAug), complemented by the introduction of ADC-LoRA, a low-rank approximation technique, to reduce the training overhead. RAOQ demonstrates consistently high performance across different scales and domains of neural network models for computer vision and natural language processing (NLP) tasks at various bit precisions, achieving state-of-the-art results with practical IMC implementations.

Applications

Yuhao Wang, Qiang Zhang, Ming Qin, Xiang Zhuang, Xiaotong Li, Zhichen Gong, Zeyuan Wang, Yu Zhao, Jianhua Yao, Keyan Ding 等

Directed evolution, a cornerstone of protein optimization, is to harness natural mutational processes to enhance protein functionality. Existing Machine Learning-assisted Directed Evolution (MLDE) methodologies typically rely on data-driven strategies and often overlook the profound domain knowledge in biochemical fields. In this paper, we introduce a novel Knowledge-aware Reinforced Language Model (KnowRLM) for MLDE. An Amino Acid Knowledge Graph (AAKG) is constructed to represent the intricate biochemical relationships among amino acids. We further propose a Protein Language Model (PLM)-based policy network that iteratively samples mutants through preferential random walks on the AAKG using a dynamic sliding window mechanism. The novel mutants are actively sampled to fine-tune a fitness predictor as the reward model, providing feedback to the knowledge-aware policy. Finally, we optimize the whole system in an active learning approach that mimics biological settings in practice.KnowRLM stands out for its ability to utilize contextual amino acid information from knowledge graphs, thus attaining advantages from both statistical patterns of protein sequences and biochemical properties of amino acids.Extensive experiments demonstrate the superior performance of KnowRLM in more efficiently identifying high-fitness mutants compared to existing methods.

Social Aspects · Privacy-preserving Statistics and Machine Learning

Xenia Heilmann, Mattia Cerrato, Ernst Althaus

Differentially private ML approaches seek to learn models which may be publicly released while guaranteeing that the input data is kept private. One issue with this construction is that further model releases based on the same training data (e.g. for a new task) incur a further privacy budget cost. Privacy-preserving synthetic data generation is one possible solution to this conundrum. However, models trained on synthetic private data struggle to approach the performance of private, ad-hoc models. In this paper, we present a novel method based on sum-product networks that is able to perform both privacy-preserving classification and privacy-preserving data generation with a single model. To the best of our knowledge, ours is the first approach that provides both discriminative and generative capabilities to differentially private ML. We show that our approach outperforms the state of the art in terms of stability (i.e. number of training runs required for convergence) and utility of the generated data.

Social Aspects · Trustworthy Machine Learning

David W. Hogg, Soledad Villar

Machine learning (ML) methods are having a huge impact across all of the sciences. However, ML has a strong ontology — in which only the data exist — and a strong epistemology — in which a model is considered good if it performs well on held-out training data. These philosophies are in strong conflict with both standard practices and key philosophies in the natural sciences. Here we identify some locations for ML in the natural sciences at which the ontology and epistemology are valuable. For example, when an expressive machine learning model is used in a causal inference to represent the effects of confounders, such as foregrounds, backgrounds, or instrument calibration parameters, the model capacity and loose philosophy of ML can make the results more trustworthy. We also show that there are contexts in which the introduction of ML introduces strong, unwanted statistical biases. For one, when ML models are used to emulate physical (or first-principles) simulations, they amplify confirmation biases. For another, when expressive regressions are used to label datasets, those labels cannot be used in downstream joint or ensemble analyses without taking on uncontrolled biases. The question in the title is being asked of all of the natural sciences; that is, we are calling on the scientific communities to take a step back and consider the role and value of ML in their fields; the (partial) answers we give here come from the particular perspective of physics.

Social Aspects · Privacy-preserving Statistics and Machine Learning

Itamar Zimerman, Moran Baruch, Nir Drucker, Gilad Ezov, Omri Soceanu, Lior Wolf

Designing privacy-preserving DL solutions is a major challenge within the AI community. Homomorphic Encryption (HE) has emerged as one of the most promising approaches in this realm, enabling the decoupling of knowledge between a model owner and a data owner. Despite extensive research and application of this technology, primarily in CNNs, applying HE on transformer models has been challenging because of the difficulties in converting these models into a polynomial form. We break new ground by introducing the first polynomial transformer, providing the first demonstration of secure inference over HE with full transformers. This includes a transformer architecture tailored for HE, alongside a novel method for converting operators to their polynomial equivalent. This innovation enables us to perform secure inference on LMs and ViTs with several datasts and tasks. Our techniques yield results comparable to traditional models, bridging the performance gap with transformers of similar scale and underscoring the viability of HE for state-of-the-art applications. Finally, we assess the stability of our models and conduct a series of ablations to quantify the contribution of each model component. Our code is publicly available.

Zhengyu Zhou, Weiwei Liu

Goodness-of-fit testing, a classical statistical tool, has been extensively explored in the batch setting, where the sample size is predetermined. However, practitioners often prefer methods that adapt to the complexity of a problem rather than fixing the sample size beforehand. Classical batch tests are generally unsuitable for streaming data, as valid inference after data peeking requires multiple testing corrections, resulting in reduced statistical power. To address this issue, we delve into the design of consistent sequential goodness-of-fit tests. Following the principle of *testing by betting*, we reframe this task as selecting a sequence of payoff functions that maximize the wealth of a fictitious bettor, betting against the null in a repeated game. We conduct experiments to demonstrate the adaptability of our sequential test across varying difficulty levels of problems while maintaining control over type-I errors.

Miscellaneous Aspects of Machine Learning · Causality

Tom Yan, Ziyu Xu, Zachary Lipton

Discovery of causal relationships is a fundamental goal of science and vital for sound decision making. As such, there has been considerable interest in causal discovery methods with provable guarantees. Existing works have thus far largely focused on discovery under hard intervention and infinite-samples, in which intervening on a node readily reveals the orientation of every edge incident to the node. This setup however overlooks the stochasticity inherent in real-world, finite-sample settings. Our work takes a step towards studying finite-sample causal discovery, wherein multiple interventions on a node are now needed for edge orientation. In this work, we study the canonical setup in theoretical causal discovery literature, where one assumes causal sufficiency and access to the graph skeleton. Our key observation is that discovery may be viewed as structured, multiple testing, and we develop a novel testing framework to this end. Crucially, our framework allows for anytime valid testing as multiple tests are needed to conclude an edge orientation. It also allows for flexible combination of structured test-statistics (enabling one to use Meek rules to propagate edge orientation) as well as robust testing. Through empirical simulations, we confirm the usefulness of our framework. In closing, using this testing framework, we show how one may efficiently verify graph structure by drawing a connection to multi-constraint bandits and designing a novel algorithm to this end.

Social Aspects · Privacy-preserving Statistics and Machine Learning

Kunda Yan, Sen Cui, Abudukelimu Wuerkaixi, Jingfeng ZHANG, Bo Han, Gang Niu, Masashi Sugiyama, Changshui Zhang

In mobile and IoT systems, Federated Learning (FL) is increasingly important for effectively using data while maintaining user privacy. One key challenge in FL is managing statistical heterogeneity, such as non-i.i.d. data, arising from numerous clients and diverse data sources. This requires strategic cooperation, often with clients having similar characteristics. However, we are interested in a fundamental question: does achieving optimal cooperation necessarily entail cooperating with the most similar clients? Typically, significant model performance improvements are often realized not by partnering with the most similar models, but through leveraging complementary data. Our theoretical and empirical analyses suggest that optimal cooperation is achieved by enhancing complementarity in feature distribution while restricting the disparity in the correlation between features and targets. Accordingly, we introduce a novel framework, FedSaC, which balances similarity and complementarity in FL cooperation. Our framework aims to approximate an optimal cooperation network for each client by optimizing a weighted sum of model similarity and feature complementarity. The strength of FedSaC lies in its adaptability to various levels of data heterogeneity and multimodal scenarios. Our comprehensive unimodal and multimodal experiments demonstrate that FedSaC markedly surpasses other state-of-the-art FL methods.

Miscellaneous Aspects of Machine Learning · Causality

Feng Xie, Zhengming Chen, Shanshan Luo, Wang Miao, Ruichu Cai, zhi geng

Recently, interest has grown in the use of proxy variables of unobserved confounding for inferring the causal effect in the presence of unmeasured confounders from observational data. One difficulty inhibiting the practical use is finding valid proxy variables of unobserved confounding to a target causal effect of interest. These proxy variables are typically justified by background knowledge. In this paper, we investigate the estimation of causal effects among multiple treatments and a single outcome, all of which are affected by unmeasured confounders, within a linear causal model, without prior knowledge of the validity of proxy variables. To be more specific, we first extend the existing proxy variable estimator, originally addressing a single unmeasured confounder, to accommodate scenarios where multiple unmeasured confounders exist between the treatments and the outcome. Subsequently, we present two different sets of precise identifiability conditions for selecting valid proxy variables of unmeasured confounders, based on the second-order statistics and higher-order statistics of the data, respectively. Moreover, we propose two data-driven methods for the selection of proxy variables and for the unbiased estimation of causal effects. Theoretical analysis demonstrates the correctness of our proposed algorithms. Experimental results on both synthetic and real-world data show the effectiveness of the proposed approach.

Social Aspects · Trustworthy Machine Learning

Jeremy Wayland, Corinna Coupette, Bastian Rieck

Echoing recent calls to counter reliability and robustness concerns in machine learning via *multiverse analysis*, we present PRESTO, a principled framework for *mapping the multiverse* of machine-learning models that rely on *latent representations*. Although such models enjoy widespread adoption, the variability in their embeddings remains poorly understood, resulting in unnecessary complexity and untrustworthy representations. Our framework uses *persistent homology* to characterize the latent spaces arising from different combinations of diverse machine-learning methods, (hyper)parameter configurations, and datasets, allowing us to measure their pairwise *(dis)similarity* and statistically reason about their *distributions*. As we demonstrate both theoretically and empirically, our pipeline preserves desirable properties of collections of latent representations, and it can be leveraged to perform sensitivity analysis, detect anomalous embeddings, or efficiently and effectively navigate hyperparameter search spaces.

Social Aspects · Privacy-preserving Statistics and Machine Learning

Chendi Wang, Yuqing Zhu, Weijie Su, Yu-Xiang Wang

A recent study by De et al. (2022) shows that large-scale representation learning through pre-training on a public dataset significantly enhances differentially private (DP) learning in downstream tasks. To explain this, we consider a layer-peeled model in representation learning, resulting in Neural Collapse (NC) phenomena. Within NC, we establish that the misclassification error is independent of dimension when the distance between actual and ideal features is below a threshold. We empirically evaluate feature quality in the last layer under different pre-trained models, showing that a more powerful pre-trained model improves feature representation. Moreover, we show that DP fine-tuning is less robust compared to non-DP fine-tuning, especially with perturbations. Supported by theoretical analyses and experiments, we suggest strategies like feature normalization and dimension reduction methods such as PCA to enhance DP fine-tuning robustness. Conducting PCA on last-layer features significantly improves testing accuracy.

Theory · Learning Theory

Jiayi Wang, Zhengling Qi, Raymond K. W. Wong

In this paper, we delve into the statistical analysis of the fitted Q-evaluation (FQE) method, which focuses on estimating the value of a target policy using offline data generated by some behavior policy. We provide a comprehensive theoretical understanding of FQE estimators under both parametric and non-parametric models on the Q-function. Specifically, we address three key questions related to FQE that remain largely unexplored in the current literature: (1) Is the optimal convergence rate for estimating the policy value regarding the sample size $n$ ($n^{−1/2}$) achievable for FQE under a nonparametric model with a fixed horizon ($T$ )? (2) How does the error bound depend on the horizon T ? (3) What is the role of the probability ratio function in improving the convergence of FQE estimators? Specifically, we show that under the completeness assumption of Q-functions, which is mild in the non-parametric setting, the estimation errors for policy value using both parametric and non-parametric FQE estimators can achieve an optimal rate in terms of n. The corresponding error bounds in terms of both $n$ and $T$ are also established. With an additional realizability assumption on ratio functions, the rate of estimation errors can be improved from $T^{ 1.5}/\sqrt{n}$ to $T /\sqrt{n}$, which matches the sharpest known bound in the current literature under the tabular setting.

Social Aspects · Accountability, Transparency and Interpretability

Wenshuo Wang, Lucas Janson, Lihua Lei, Aaditya Ramdas

Inferring variable importance is the key goal of many scientific studies, where researchers seek to learn the effect of a feature $X$ on the outcome $Y$ in the presence of confounding variables $Z$. Focusing on classification problems, we define the expected total variation (ETV), which is an intuitive and deterministic measure of variable importance that does not rely on any model assumption. We then introduce algorithms for statistical inference on the ETV under design-based/model-X assumptions. We name our method Total Variation Floodgate in reference to its shared high-level structure with the Floodgate method of Zhang & Janson (2020). The algorithms we introduce can leverage any user-specified regression function and produce asymptotic lower confidence bounds for the ETV. We show the effectiveness of our algorithms with simulations and a case study in conjoint analysis on the US general election.

Social Aspects · Privacy-preserving Statistics and Machine Learning

Marten van Dijk, Nhuong Nguyen, Toan N. Nguyen, Lam M. Nguyen, Phuong Ha Nguyen

We introduce a multiple target optimization framework for DP-SGD referred to as pro-active DP. In contrast to traditional DP accountants, which are used to track the expenditure of privacy budgets, the pro-active DP scheme allows one to *a-priori* select parameters of DP-SGD based on a fixed privacy budget (in terms of $\epsilon$ and $\delta$) in such a way to optimize the anticipated utility (test accuracy) the most. To achieve this objective, we first propose significant improvements to the moment account method, presenting a closed-form $(\epsilon,\delta)$-DP guarantee that connects all parameters in the DP-SGD setup. Generally, DP-SGD is $(\epsilon\leq 1/2,\delta=1/N)$-DP if $\sigma=\sqrt{2(\epsilon +\ln(1/\delta))/\epsilon}$ with $T$ at least $\approx 2k^2/\epsilon$ and $(2/e)^2k^2-1/2\geq \ln(N)$, where $T$ is the total number of rounds, and $K=kN$ is the total number of gradient computations where $k$ measures $K$ in number of epochs of size $N$ of the local data set. We prove that our expression is close to tight in that if $T$ is more than a constant factor $\approx 4$ smaller than the lower bound $\approx 2k^2/\epsilon$, then the $(\epsilon,\delta)$-DP guarantee is violated. Our enhanced DP theory allows us to create a utility graph and DP calculator. These tools link privacy and utility objectives and search for optimal experiment setups, efficiently taking into account both accuracy and privacy objectives, as well as implementation goals. We furnish a comprehensive implementation flow of our proactive DP, with rigorous experiments to showcase the proof-of-concept.

Applications · Physics

Yehui Tang, Nianzu Yang, Mabiao Long, Junchi Yan

The accurate classification of quantum states is crucial for advancing quantum computing, as it allows for the effective analysis and correct functioning of quantum devices by analyzing the statistics of the data from quantum measurements. Traditional supervised methods, which rely on extensive labeled measurement outcomes, are used to categorize unknown quantum states with different properties. However, the labeling process demands computational and memory resources that increase exponentially with the number of qubits. We propose SSL4Q, manage to achieve (for the first time) semi-supervised learning specifically designed for quantum state classification. SSL4Q's architecture is tailored to ensure permutation invariance for unordered quantum measurements and maintain robustness in the face of measurement uncertainties. Our empirical studies encompass simulations on two types of quantum systems: the Heisenberg Model and the Variational Quantum Circuit (VQC) Model, with system size reaching up to 50 qubits. The numerical results demonstrate SSL4Q's superiority over traditional supervised models in scenarios with limited labels, highlighting its potential in efficiently classifying quantum states with reduced computational and resource overhead.

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

Sophia Sun, Abishek Sankararaman, Balakrishnan Narayanaswamy

Selecting appropriate thresholds for anomaly detection in online, unsupervised settings is a challenging task, especially in the presence of data distribution shifts. Addressing these challenges is critical in many practical large scale systems, such as infrastructure monitoring and network intrusion detection. This paper proposes an algorithm that connects online thresholding with constructing confidence sequences achieving (1) adaptive online threshold selection robust to distribution shifts, (2) statistical guarantees on false positive and false negative rates without any distributional assumptions, and (3) improved performance when given relevant offline data to warm-start the online algorithm, while having bounded degradation if the offline data is irrelevant. We complement our theoretical results by empirical evidence that our method outperforms commonly used baselines across synthetic and real world datasets.