active_learning

In many applications like experimental design, group testing, and medical diagnosis, the state of a random variable $Y$ is revealed by successively observing the outcomes of binary tests about $Y$. New tests are selected adaptively based on the history of outcomes observed so far. If the number of states of $Y$ is finite, the process ends when $Y$ can be predicted with a desired level of confidence or all available tests have been used. Finding the strategy that minimizes the expected number of tests needed to predict $Y$ is virtually impossible in most real applications. Therefore, the commonly used strategy is the greedy heuristic of Information Maximization (InfoMax) that selects tests sequentially in order of information gain. Despite its widespread use, existing guarantees on its performance are often vacuous when compared to its empirical efficiency. In this paper, for the first time to the best of our knowledge, we establish tight non-vacuous bounds on InfoMax's performance. Our analysis is based on the assumption that at any iteration of the greedy strategy, there is always a binary test available whose conditional probability of being 'true', given the history, is within $\delta$ units of one-half. This assumption is motivated by practical applications where the available set of tests often satisfies this property for modest values of $\delta$, say, ${0.1 \leq \delta \leq 0.4}$. Specifically, we analyze two distinct scenarios: (i) all tests are functions of $Y$, and (ii) test outcomes are corrupted by a binary symmetric channel. For both cases, our bounds guarantee the near-optimal performance of InfoMax for modest $\delta$ values. It requires only a small multiplicative factor of the entropy of $Y$, in terms of the average number of tests needed to make accurate predictions.

Diffusion models are a remarkably effective way of learning and sampling from a distribution $p(x)$. In posterior sampling, one is also given a measurement model $p(y \mid x)$ and a measurement $y$, and would like to sample from $p(x \mid y)$. Posterior sampling is useful for tasks such as inpainting, super-resolution, and MRI reconstruction, so a number of recent works have given algorithms to heuristically approximate it; but none are known to converge to the correct distribution in polynomial time. In this paper we show that posterior sampling is *computationally intractable*: under the most basic assumption in cryptography---that one-way functions exist---there are instances for which *every* algorithm takes superpolynomial time, even though *unconditional* sampling is provably fast. We also show that the exponential-time rejection sampling algorithm is essentially optimal under the stronger plausible assumption that there are one-way functions that take exponential time to invert.

Neural Network-based active learning (NAL) is a cost-effective data selection technique that utilizes neural networks to select and train on a small subset of samples. While existing work successfully develops various effective or theory-justified NAL algorithms, the understanding of the two commonly used query criteria of NAL: uncertainty-based and diversity-based, remains in its infancy. In this work, we try to move one step forward by offering a unified explanation for the success of both query criteria-based NAL from a feature learning view. Specifically, we consider a feature-noise data model comprising easy-to-learn or hard-to-learn features disrupted by noise, and conduct analysis over 2-layer NN-based NALs in the pool-based scenario. We provably show that both uncertainty-based and diversity-based NAL are inherently amenable to one and the same principle, i.e., striving to prioritize samples that contain yet-to-be-learned features. We further prove that this shared principle is the key to their success-achieve small test error within a small labeled set. Contrastingly, the strategy-free passive learning exhibits a large test error due to the inadequate learning of yet-to-be-learned features, necessitating resort to a significantly larger label complexity for a sufficient test error reduction. Experimental results validate our findings.

We develop novel methodology for active feature acquisition (AFA), the study of sequentially acquiring a dynamic subset of features that minimizes acquisition costs whilst still yielding accurate inference. The AFA framework can be useful in a myriad of domains, including health care applications where the cost of acquiring additional features for a patient (in terms of time, money, risk, etc.) can be weighed against the expected improvement to diagnostic performance. Previous approaches for AFA have employed either: deep learning RL techniques, which have difficulty training policies due to a complicated state and action space; deep learning surrogate generative models, which require modeling complicated multidimensional conditional distributions; or greedy policies, which cannot account for jointly informative feature acquisitions. We show that we can bypass many of these challenges with a novel, nonparametric oracle based approach, which we coin the acquisition conditioned oracle (ACO). Extensive experiments show the superiority of the ACO to state-of-the-art AFA methods when acquiring features for both predictions and general decision-making.

Efficient sampling of the Boltzmann distribution of molecular systems is a long-standing challenge. Recently, instead of generating long molecular dynamics simulations, generative machine learning methods such as normalizing flows have been used to learn the Boltzmann distribution directly, without samples. However, this approach is susceptible to mode collapse and thus often does not explore the full configurational space. In this work, we address this challenge by separating the problem into two levels, the fine-grained and coarse-grained degrees of freedom. A normalizing flow conditioned on the coarse-grained space yields a probabilistic connection between the two levels. To explore the configurational space, we employ coarse-grained simulations with active learning which allows us to update the flow and make all-atom potential energy evaluations only when necessary. Using alanine dipeptide as an example, we show that our methods obtain a speedup to molecular dynamics simulations of approximately $15.9$ to $216.2$ compared to the speedup of $4.5$ of the current state-of-the-art machine learning approach.

Particle-based Bayesian inference methods by sampling from a partition-free target (posterior) distribution, e.g., Stein variational gradient descent (SVGD), have attracted significant attention. We propose a path-guided particle-based sampling (PGPS) method based on a novel Log-weighted Shrinkage (LwS) density path linking an initial distribution to the target distribution. We propose to utilize a Neural network to learn a vector field motivated by the Fokker-Planck equation of the designed density path. Particles, initiated from the initial distribution, evolve according to the ordinary differential equation defined by the vector field. The distribution of these particles is guided along a density path from the initial distribution to the target distribution. The proposed LwS density path allows for an efficient search of modes of the target distribution while canonical methods fail. We theoretically analyze the Wasserstein distance of the distribution of the PGPS-generated samples and the target distribution due to approximation and discretization errors. Practically, the proposed PGPS-LwS method demonstrates higher Bayesian inference accuracy and better calibration ability in experiments conducted on both synthetic and real-world Bayesian learning tasks, compared to baselines, such as SVGD and Langevin dynamics, etc.

Co-training is a classical semi-supervised learning method which only requires a small number of labeled examples for learning, under reasonable assumptions. Despite extensive literature on the topic, very few hypothesis classes are known to be provably efficiently learnable via co-training, even under very strong distributional assumptions. In this work, we study the co-training problem in the stream-based active learning model. We show that a range of natural concept classes are efficiently learnable via co-training, in terms of both label efficiency and computational efficiency. We provide an efficient reduction of co-training under the standard assumption of weak dependence, in the stream-based active model, to online classification. As a corollary, we obtain efficient co-training algorithms with error independent label complexity for every concept class class efficiently learnable in the mistake bound online model. Our framework also gives co-training algorithms with label complexity $\tilde{O}(d\log (1/\epsilon))$ for any concept class with VC dimension $d$, though in general this reduction is not computationally efficient. Finally, using additional ideas from online learning, we design the first efficient co-training algorithms with label complexity $\tilde{O}(d^2\log (1/\epsilon))$ for several concept classes, including unions of intervals and homogeneous halfspaces.

Inspired by the concept of active learning, we propose active inference---a methodology for statistical inference with machine-learning-assisted data collection. Assuming a budget on the number of labels that can be collected, the methodology uses a machine learning model to identify which data points would be most beneficial to label, thus effectively utilizing the budget. It operates on a simple yet powerful intuition: prioritize the collection of labels for data points where the model exhibits uncertainty, and rely on the model's predictions where it is confident. Active inference constructs valid confidence intervals and hypothesis tests while leveraging any black-box machine learning model and handling any data distribution. The key point is that it achieves the same level of accuracy with far fewer samples than existing baselines relying on non-adaptively-collected data. This means that for the same number of collected samples, active inference enables smaller confidence intervals and more powerful tests. We evaluate active inference on datasets from public opinion research, census analysis, and proteomics.

Model extraction is to obtain a cloned model that replicates the functionality of a black-box victim model solely through query-based access. Present defense strategies exhibit shortcomings, manifesting as: (1) computational or memory inefficiencies during deployment; or (2) dependence on expensive defensive training methods that mandate the re-training of the victim model; or (3) watermarking-based methods only *passively* detect model theft without actively preventing model extraction. To address these limitations, we introduce an innovative Bayesian *active* watermarking technique to fine-tune the victim model and learn the watermark posterior distribution conditioned on input data. The fine-tuning process aims to maximize the log-likelihood on watermarked in-distribution training data for preserving model utility while simultaneously maximizing the change of model's outputs on watermarked out-of-distribution data, thereby achieving effective defense. During deployment, a watermark is randomly sampled from the estimated watermark posterior. This watermark is then added to the input query, and the victim model returns the prediction based on the watermarked input query to users. This proactive defense approach requires only slight fine-tuning of the victim model without the need of full re-training and demonstrates high efficiency in terms of memory and computation during deployment. Rigorous theoretical analysis and comprehensive experimental results demonstrate the efficacy of our proposed method.

Uncertainty Sampling is an Active Learning strategy that aims to improve the data efficiency of machine learning models by iteratively acquiring labels of data points with the highest uncertainty. While it has proven effective for independent data its applicability to graphs remains under-explored. We propose the first extensive study of Uncertainty Sampling for node classification: **(1)** We benchmark Uncertainty Sampling beyond predictive uncertainty and highlight a significant performance gap to other Active Learning strategies. **(2)** We develop ground-truth Bayesian uncertainty estimates in terms of the data generating process and prove their effectiveness in guiding Uncertainty Sampling toward optimal queries. We confirm our results on synthetic data and design an approximate approach that consistently outperforms other uncertainty estimators on real datasets. **(3)** Based on this analysis, we relate pitfalls in modeling uncertainty to existing methods. Our analysis enables and informs the development of principled uncertainty estimation on graphs.

Stochastic gradients have been widely integrated into Langevin-based methods to improve their scalability and efficiency in solving large-scale sampling problems. However, the proximal sampler, which exhibits much faster convergence than Langevin-based algorithms in the deterministic setting (Lee et al., 2021), has yet to be explored in its stochastic variants. In this paper, we study the Stochastic Proximal Samplers (SPS) for sampling from non-log-concave distributions. We first establish a general framework for implementing stochastic proximal samplers and establish the convergence theory accordingly. We show that the convergence to the target distribution can be guaranteed as long as the second moment of the algorithm trajectory is bounded and restricted Gaussian oracles can be well approximated. We then provide two implementable variants based on Stochastic gradient Langevin dynamics (SGLD) and Metropolis-adjusted Langevin algorithm (MALA), giving rise to SPS-SGLD and SPS-MALA. We further show that SPS-SGLD and SPS-MALA can achieve $\epsilon$-sampling error in total variation (TV) distance within $\tilde{\mathcal{O}}(d\epsilon^{-2})$ and $\tilde{\mathcal{O}}(d^{1/2}\epsilon^{-2})$ gradient complexities, which outperform the best-known result by at least an $\tilde{\mathcal{O}}(d^{1/3})$ factor. This enhancement in performance is corroborated by our empirical studies on synthetic data with various dimensions, demonstrating the efficiency of our proposed algorithm.