This paper presents a new supervised representation learning framework, namely structured probabilistic coding (SPC), to learn compact and informative representations from input related to the target task. SPC is an encoder-only probabilistic coding technology with a structured regularization from the target space. It can enhance the generalization ability of pre-trained language models for better language understanding. Specifically, our probabilistic coding simultaneously performs information encoding and task prediction in one module to more fully utilize the effective information from input data. It uses variational inference in the output space to reduce randomness and uncertainty. Besides, to better control the learning process of probabilistic representations, a structured regularization is proposed to promote uniformity across classes in the latent space. With the regularization term, SPC can preserve the Gaussian structure of the latent code and achieve better coverage of the hidden space with class uniformly. Experimental results on 12 natural language understanding tasks demonstrate that our SPC effectively improves the performance of pre-trained language models for classification and regression. Extensive experiments show that SPC can enhance the generalization capability, robustness to label noise, and clustering quality of output representations.

In modern recommendation systems, the standard pipeline involves training machine learning models on historical data to predict user behaviors and improve recommendations continuously. However, these data training loops can introduce interference in A/B tests, where data generated by control and treatment algorithms, potentially with different distributions, are combined. To address these challenges, we introduce a novel approach called weighted training. This approach entails training a model to predict the probability of each data point appearing in either the treatment or control data and subsequently applying weighted losses during model training. We demonstrate that this approach achieves the least variance among all estimators that do not cause shifts in the training distributions. Through simulation studies, we demonstrate the lower bias and variance of our approach compared to other methods.

We study the problem of agent selection in causal strategic learning under multiple decision makers and address two key challenges that come with it. Firstly, while much of prior work focuses on studying a fixed pool of agents that remains static regardless of their evaluations, we consider the impact of selection procedure by which agents are not only evaluated, but also selected. When each decision maker unilaterally selects agents by maximising their own utility, we show that the optimal selection rule is a trade-off between selecting the best agents and providing incentives to maximise the agents' improvement. Furthermore, this optimal selection rule relies on incorrect predictions of agents' outcomes. Hence, we study the conditions under which a decision maker's optimal selection rule will not lead to deterioration of agents' outcome nor cause unjust reduction in agents' selection chance. To that end, we provide an analytical form of the optimal selection rule and a mechanism to retrieve the causal parameters from observational data, under certain assumptions on agents' behaviour. Secondly, when there are multiple decision makers, the interference between selection rules introduces another source of biases in estimating the underlying causal parameters. To address this problem, we provide a cooperative protocol which all decision makers must collectively adopt to recover the true causal parameters. Lastly, we complement our theoretical results with simulation studies. Our results highlight not only the importance of causal modeling as a strategy to mitigate the effect of gaming, as suggested by previous work, but also the need of a benevolent regulator to enable it.

Fingerprinting arguments, first introduced by Bun, Ullman, and Vadhan (STOC 2014), are the most widely used method for establishing lower bounds on the sample complexity or error of approximately differentially private (DP) algorithms. Still, there are many problems in differential privacy for which we don't know suitable lower bounds, and even for problems that we do, the lower bounds are not smooth, and usually become vacuous when the error is larger than some threshold. In this work, we present a new framework and tools to generate smooth lower bounds on the sample complexity of differentially private algorithms satisfying very weak accuracy. We illustrate the applicability of our method by providing new lower bounds in various settings: 1. A tight lower bound for DP averaging in the low-accuracy regime, which in particular implies a lower bound for the private 1-cluster problem introduced by Nissim, Stemmer, and Vadhan (PODS 2016). 2. A lower bound on the additive error of DP algorithms for approximate k-means clustering, as a function of the multiplicative error, which is tight for a constant multiplication error. 3. A lower bound for estimating the top singular vector of a matrix under DP in low-accuracy regimes, which is a special case of DP subspace estimation studied by Singhal and Steinke (NeurIPS 2021). Our main technique is to apply a padding-and-permuting transformation to a fingerprinting code. However, rather than proving our results using a black-box access to an existing fingerprinting code (e.g., Tardos' code), we develop a new fingerprinting lemma that is stronger than those of Dwork et al. (FOCS 2015) and Bun et al. (SODA 2017), and prove our lower bounds directly from the lemma. Our lemma, in particular, gives a simpler fingerprinting code construction with optimal rate (up to polylogarithmic factors) that is of independent interest.

We introduce a novel semi-supervised learning approach, named Teacher-Student Bayesian Optimization (TSBO), integrating the teacher-student paradigm into BO to minimize expensive labeled data queries for the first time. TSBO incorporates a teacher model, an unlabeled data sampler, and a student model. The student is trained on unlabeled data locations generated by the sampler, with pseudo labels predicted by the teacher. The interplay between these three components implements a unique selective regularization to the teacher in the form of student feedback. This scheme enables the teacher to predict high-quality pseudo labels, enhancing the generalization of the Figure 1: Visualization of queried data (dots) and trends GP surrogate model in the search space. To fully (arrow sequences) on a high-dimensional molecule design exploit TSBO, we propose two optimized unlabeled task (Sterling & Irwin, 2015) to maximize the Penalized data samplers to construct effective student LogP score (Gómez-Bombarelli et al., 2018). Red and blue feedback that well aligns with the objective of colors represent TSBO and a baseline (with vanilla BO), respectively.

Influenza viruses mutate rapidly and can pose a threat to public health, especially to those in vulnerable groups. Throughout history, influenza A viruses have caused pandemics between different species. It is important to identify the origin of a virus in order to prevent the spread of an outbreak. Recently, there has been increasing interest in using machine learning algorithms to provide fast and accurate predictions for viral sequences. In this study, real testing data sets and a variety of evaluation metrics were used to evaluate machine learning algorithms at different taxonomic levels. As hemagglutinin is the major protein in the immune response, only hemagglutinin sequences were used and represented by position-specific scoring matrix and word embedding. The results suggest that the 5-grams-transformer neural network is the most effective algorithm for predicting viral sequence origins, with approximately 99.54% AUCPR, 98.01% F1 score and 96.60% MCC at a higher classification level, and approximately 94.74% AUCPR, 87.41% F1 score and 80.79% MCC at a lower classification level.

The Sliced-Wasserstein (SW) distance between probability measures is defined as the average of the Wasserstein distances resulting for the associated one-dimensional projections. As a consequence, the SW distance can be written as an integral with respect to the uniform measure on the sphere and the Monte Carlo framework can be employed for calculating the SW distance. Spherical harmonics are polynomials on the sphere that form an orthonormal basis of the set of square-integrable functions on the sphere. Putting these two facts together, a new Monte Carlo method, hereby referred to as Spherical Harmonics Control Variates (SHCV), is proposed for approximating the SW distance using spherical harmonics as control variates. The resulting approach is shown to have good theoretical properties, e.g., a no-error property for Gaussian measures under a certain form of linear dependency between the variables. Moreover, an improved rate of convergence, compared to Monte Carlo, is established for general measures. The convergence analysis relies on the Lipschitz property associated to the SW integrand. Several numerical experiments demonstrate the superior performance of SHCV against state-of-the-art methods for SW distance computation.

Honeybees are vital for pollination and food production. Among many factors, extreme temperature (e.g., due to climate change) is particularly dangerous for bee health. Anticipating such extremities would allow beekeepers to take early preventive action. Thus, given sensor (temperature) time series data from beehives, how can we find patterns and do forecasting? Forecasting is crucial as it helps spot unexpected behavior and thus issue warnings to the beekeepers. In that case, what are the right models for forecasting? ARIMA, RNNs, or something else? We propose the EBV (Electronic Bee-Veterinarian) method, which has the following desirable properties: (i) principled: it is based on a) diffusion equations from physics and b) control theory for feedback-loop controllers; (ii) effective: it works well on multiple, real-world time sequences, (iii) explainable: it needs only a handful of parameters (e.g., bee strength) that beekeepers can easily understand and trust, and (iv) scalable: it performs linearly in time. We applied our method to multiple real-world time sequences, and found that it yields accurate forecasting (up to 49% improvement in RMSE compared to baselines), and segmentation. Specifically, discontinuities detected by EBV mostly coincide with domain expert's opinions, showcasing our approach's potential and practical feasibility. Moreover, EBV is scalable and fast, taking about 20 minutes on a stock laptop for reconstructing two months of sensor data.

Kernel methods are widely used in machine learning, especially for classification problems. However, the theoretical analysis of kernel classification is still limited. This paper investigates the statistical performances of kernel classifiers. With some mild assumptions on the conditional probability $\eta(x)=\mathbb{P}(Y=1\mid X=x)$, we derive an upper bound on the classification excess risk of a kernel classifier using recent advances in the theory of kernel regression. We also obtain a minimax lower bound for Sobolev spaces, which shows the optimality of the proposed classifier. Our theoretical results can be extended to the generalization error of overparameterized neural network classifiers. To make our theoretical results more applicable in realistic settings, we also propose a simple method to estimate the interpolation smoothness of $2\eta(x)-1$ and apply the method to real datasets.

Generative diffusion models and many stochastic models in science and engineering naturally live in infinite dimensions before discretisation. To incorporate observed data for statistical and learning tasks, one needs to condition on observations. While recent work has treated conditioning linear processes in infinite dimensions, conditioning non-linear processes in infinite dimensions has not been explored. This paper conditions function valued stochastic processes without prior discretisation. To do so, we use an infinite-dimensional version of Girsanov's theorem to condition a function-valued stochastic process, leading to a stochastic differential equation (SDE) for the conditioned process involving the score. We apply this technique to do time series analysis for shapes of organisms in evolutionary biology, where we discretise via the Fourier basis and then learn the coefficients of the score function with score matching methods.