We study the problem of $(\epsilon,\delta)$-differentially private learning of linear predictors with convex losses. We provide results for two subclasses of loss functions. The first case is when the loss is smooth and non-negative but not necessarily Lipschitz (such as the squared loss). For this case, we establish an upper bound on the excess population risk of $\tilde{O}\left(\frac{\Vert w^*\Vert}{\sqrt{n}} + \min\left\{\frac{\Vert w^* \Vert^2}{(n\epsilon)^{2/3}},\frac{\sqrt{d}\Vert w^*\Vert^2}{n\epsilon}\right\}\right)$, where $n$ is the number of samples, $d$ is the dimension of the problem, and $w^*$ is the minimizer of the population risk. Apart from the dependence on $\Vert w^\ast\Vert$, our bound is essentially tight in all parameters. In particular, we show a lower bound of $\tilde{\Omega}\left(\frac{1}{\sqrt{n}} + {\min\left\{\frac{\Vert w^*\Vert^{4/3}}{(n\epsilon)^{2/3}}, \frac{\sqrt{d}\Vert w^*\Vert}{n\epsilon}\right\}}\right)$. We also revisit the previously studied case of Lipschitz losses [SSTT20]. For this case, we close the gap in the existing work and show that the optimal rate is (up to log factors) $\Theta\left(\frac{\Vert w^*\Vert}{\sqrt{n}} + \min\left\{\frac{\Vert w^*\Vert}{\sqrt{n\epsilon}},\frac{\sqrt{\text{rank}}\Vert w^*\Vert}{n\epsilon}\right\}\right)$, where $\text{rank}$ is the rank of the design matrix. This improves over existing work in the high privacy regime. Finally, our algorithms involve a private model selection approach that we develop to enable attaining the stated rates without a-priori knowledge of $\Vert w^*\Vert$.
Identification of unknown physical processes and parameters of groundwater contaminant sources is a challenging task due to their ill-posed and non-unique nature. Numerous works have focused on determining nonlinear physical processes through model selection methods. However, identifying corresponding nonlinear systems for different physical phenomena using numerical methods can be computationally prohibitive. With the advent of machine learning (ML) algorithms, more efficient surrogate models based on neural networks (NNs) have been developed in various disciplines. In this work, a theory-guided U-net (TgU-net) framework is proposed for surrogate modeling of three-dimensional (3D) groundwater contaminant problems in order to efficiently elucidate their involved processes and unknown parameters. In TgU-net, the underlying governing equations are embedded into the loss function of U-net as soft constraints. For the considered groundwater contaminant problem, sorption is considered to be a potential process of an uncertain type, and three equilibrium sorption isotherm types (i.e., linear, Freundlich, and Langmuir) are considered. Different from traditional approaches in which one model corresponds to one equation, these three sorption types are modeled through only one TgU-net surrogate. The three mentioned sorption terms are integrated into one equation by assigning indicators. Accurate predictions illustrate the satisfactory generalizability and extrapolability of the constructed TgU-net. Furthermore, based on the constructed TgU-net surrogate, a data assimilation method is employed to identify the physical process and parameters simultaneously. This work shows the possibility of governing equation discovery of physical problems that contain multiple and even uncertain processes by using deep learning and data assimilation methods.
The current state-of-the-art for few-shot cross-lingual transfer learning first trains on abundant labeled data in the source language and then fine-tunes with a few examples on the target language, termed target-adapting. Though this has been demonstrated to work on a variety of tasks, in this paper we show some deficiencies of this approach and propose a one-step mixed training method that trains on both source and target data with \textit{stochastic gradient surgery}, a novel gradient-level optimization. Unlike the previous studies that focus on one language at a time when target-adapting, we use one model to handle all target languages simultaneously to avoid excessively language-specific models. Moreover, we discuss the unreality of utilizing large target development sets for model selection in previous literature. We further show that our method is both development-free for target languages, and is also able to escape from overfitting issues. We conduct a large-scale experiment on 4 diverse NLP tasks across up to 48 languages. Our proposed method achieves state-of-the-art performance on all tasks and outperforms target-adapting by a large margin, especially for languages that are linguistically distant from the source language, e.g., 7.36% F1 absolute gain on average for the NER task, up to 17.60% on Punjabi.
There is recent interest in using model hubs, a collection of pre-trained models, in computer vision tasks. To utilize the model hub, we first select a source model and then adapt the model for the target to compensate for differences. While there is yet limited research on model selection and adaption for computer vision tasks, this holds even more for the field of renewable power. At the same time, it is a crucial challenge to provide forecasts for the increasing demand for power forecasts based on weather features from a numerical weather prediction. We close these gaps by conducting the first thorough experiment for model selection and adaptation for transfer learning in renewable power forecast, adopting recent results from the field of computer vision on 667 wind and photovoltaic parks. To the best of our knowledge, this makes it the most extensive study for transfer learning in renewable power forecasts reducing the computational effort and improving the forecast error. Therefore, we adopt source models based on target data from different seasons and limit the amount of training data. As an extension of the current state of the art, we utilize a Bayesian linear regression for forecasting the response based on features extracted from a neural network. This approach outperforms the baseline with only seven days of training data. We further show how combining multiple models through ensembles can significantly improve the model selection and adaptation approach.
We present a series of new differentially private (DP) algorithms with dimension-independent margin guarantees. For the family of linear hypotheses, we give a pure DP learning algorithm that benefits from relative deviation margin guarantees, as well as an efficient DP learning algorithm with margin guarantees. We also present a new efficient DP learning algorithm with margin guarantees for kernel-based hypotheses with shift-invariant kernels, such as Gaussian kernels, and point out how our results can be extended to other kernels using oblivious sketching techniques. We further give a pure DP learning algorithm for a family of feed-forward neural networks for which we prove margin guarantees that are independent of the input dimension. Additionally, we describe a general label DP learning algorithm, which benefits from relative deviation margin bounds and is applicable to a broad family of hypothesis sets, including that of neural networks. Finally, we show how our DP learning algorithms can be augmented in a general way to include model selection, to select the best confidence margin parameter.
Deep neural networks trained by minimizing the average risk can achieve strong average performance. Still, their performance for a subgroup may degrade if the subgroup is underrepresented in the overall data population. Group distributionally robust optimization (Sagawa et al., 2020a), or group DRO in short, is a widely used baseline for learning models with strong worst-group performance. We note that this method requires group labels for every example at training time and can overfit to small groups, requiring strong regularization. Given a limited amount of group labels at training time, Just Train Twice (Liu et al., 2021), or JTT in short, is a two-stage method that infers a pseudo group label for every unlabeled example first, then applies group DRO based on the inferred group labels. The inference process is also sensitive to overfitting, sometimes involving additional hyperparameters. This paper designs a simple method based on the idea of classifier retraining on independent splits of the training data. We find that using a novel sample-splitting procedure achieves robust worst-group performance in the fine-tuning step. When evaluated on benchmark image and text classification tasks, our approach consistently performs favorably to group DRO, JTT, and other strong baselines when either group labels are available during training or are only given in validation sets. Importantly, our method only relies on a single hyperparameter, which adjusts the fraction of labels used for training feature extractors vs. training classification layers. We justify the rationale of our splitting scheme with a generalization-bound analysis of the worst-group loss.
The Bayesian information criterion (BIC), defined as the observed data log likelihood minus a penalty term based on the sample size $N$, is a popular model selection criterion for factor analysis with complete data. This definition has also been suggested for incomplete data. However, the penalty term based on the `complete' sample size $N$ is the same no matter whether in a complete or incomplete data case. For incomplete data, there are often only $N_i<N$ observations for variable $i$, which means that using the `complete' sample size $N$ implausibly ignores the amounts of missing information inherent in incomplete data. Given this observation, a novel criterion called hierarchical BIC (HBIC) for factor analysis with incomplete data is proposed. The novelty is that it only uses the actual amounts of observed information, namely $N_i$'s, in the penalty term. Theoretically, it is shown that HBIC is a large sample approximation of variational Bayesian (VB) lower bound, and BIC is a further approximation of HBIC, which means that HBIC shares the theoretical consistency of BIC. Experiments on synthetic and real data sets are conducted to access the finite sample performance of HBIC, BIC, and related criteria with various missing rates. The results show that HBIC and BIC perform similarly when the missing rate is small, but HBIC is more accurate when the missing rate is not small.
Classification methods for binary (yes/no) tasks often produce a continuously valued score. Machine learning practitioners must perform model selection, calibration, discretization, performance assessment, tuning, and fairness assessment. Such tasks involve examining classifier results, typically using summary statistics and manual examination of details. In this paper, we provide an interactive visualization approach to support such continuously-valued classifier examination tasks. Our approach addresses the three phases of these tasks: calibration, operating point selection, and examination. We enhance standard views and introduce task-specific views so that they can be integrated into a multi-view coordination (MVC) system. We build on an existing comparison-based approach, extending it to continuous classifiers by treating the continuous values as trinary (positive, unsure, negative) even if the classifier will not ultimately use the 3-way classification. We provide use cases that demonstrate how our approach enables machine learning practitioners to accomplish key tasks.
Despite the remarkable performance that modern deep neural networks have achieved on independent and identically distributed (I.I.D.) data, they can crash under distribution shifts. Most current evaluation methods for domain generalization (DG) adopt the leave-one-out strategy as a compromise on the limited number of domains. We propose a large-scale benchmark with extensive labeled domains named NICO++ along with more rational evaluation methods for comprehensively evaluating DG algorithms. To evaluate DG datasets, we propose two metrics to quantify covariate shift and concept shift, respectively. Two novel generalization bounds from the perspective of data construction are proposed to prove that limited concept shift and significant covariate shift favor the evaluation capability for generalization. Through extensive experiments, NICO++ shows its superior evaluation capability compared with current DG datasets and its contribution in alleviating unfairness caused by the leak of oracle knowledge in model selection.
We consider the problem of estimating the interacting neighborhood of a Markov Random Field model with finite support and homogeneous pairwise interactions based on relative positions of a two-dimensional lattice. Using a Bayesian framework, we propose a Reversible Jump Monte Carlo Markov Chain algorithm that jumps across subsets of a maximal range neighborhood, allowing us to perform model selection based on a marginal pseudoposterior distribution of models. To show the strength of our proposed methodology we perform a simulation study and apply it to a real dataset from a discrete texture image analysis.
In addition to generating data and annotations, devising sensible data splitting strategies and evaluation metrics is essential for the creation of a benchmark dataset. This practice ensures consensus on the usage of the data, homogeneous assessment, and uniform comparison of research methods on the dataset. This study focuses on CholecT50, which is a 50 video surgical dataset that formalizes surgical activities as triplets of <instrument, verb, target>. In this paper, we introduce the standard splits for the CholecT50 and CholecT45 datasets and show how they compare with existing use of the dataset. CholecT45 is the first public release of 45 videos of CholecT50 dataset. We also develop a metrics library, ivtmetrics, for model evaluation on surgical triplets. Furthermore, we conduct a benchmark study by reproducing baseline methods in the most predominantly used deep learning frameworks (PyTorch and TensorFlow) to evaluate them using the proposed data splits and metrics and release them publicly to support future research. The proposed data splits and evaluation metrics will enable global tracking of research progress on the dataset and facilitate optimal model selection for further deployment.
Applying deep learning to science is a new trend in recent years which leads DL engineering to become an important problem. Although training data preparation, model architecture design, and model training are the normal processes to build DL models, all of them are complex and costly. Therefore, reusing the open-sourced pre-trained model is a practical way to bypass this hurdle for developers. Given a specific task, developers can collect massive pre-trained deep neural networks from public sources for re-using. However, testing the performance (e.g., accuracy and robustness) of multiple DNNs and recommending which model should be used is challenging regarding the scarcity of labeled data and the demand for domain expertise. In this paper, we propose a labeling-free (LaF) model selection approach to overcome the limitations of labeling efforts for automated model reusing. The main idea is to statistically learn a Bayesian model to infer the models' specialty only based on predicted labels. We evaluate LaF using 9 benchmark datasets including image, text, and source code, and 165 DNNs, considering both the accuracy and robustness of models. The experimental results demonstrate that LaF outperforms the baseline methods by up to 0.74 and 0.53 on Spearman's correlation and Kendall's $\tau$, respectively.
Dialogue State Tracking (DST) is primarily evaluated using Joint Goal Accuracy (JGA) defined as the fraction of turns where the ground-truth dialogue state exactly matches the prediction. Generally in DST, the dialogue state or belief state for a given turn contains all the intents shown by the user till that turn. Due to this cumulative nature of the belief state, it is difficult to get a correct prediction once a misprediction has occurred. Thus, although being a useful metric, it can be harsh at times and underestimate the true potential of a DST model. Moreover, an improvement in JGA can sometimes decrease the performance of turn-level or non-cumulative belief state prediction due to inconsistency in annotations. So, using JGA as the only metric for model selection may not be ideal for all scenarios. In this work, we discuss various evaluation metrics used for DST along with their shortcomings. To address the existing issues, we propose a new evaluation metric named Flexible Goal Accuracy (FGA). FGA is a generalized version of JGA. But unlike JGA, it tries to give penalized rewards to mispredictions that are locally correct i.e. the root cause of the error is an earlier turn. By doing so, FGA considers the performance of both cumulative and turn-level prediction flexibly and provides a better insight than the existing metrics. We also show that FGA is a better discriminator of DST model performance.
We propose a framework for the statistical evaluation of variational auto-encoders (VAEs) and test two instances of this framework in the context of modelling images of handwritten digits and a corpus of English text. Our take on evaluation is based on the idea of statistical model criticism, popular in Bayesian data analysis, whereby a statistical model is evaluated in terms of its ability to reproduce statistics of an unknown data generating process from which we can obtain samples. A VAE learns not one, but two joint distributions over a shared sample space, each exploiting a choice of factorisation that makes sampling tractable in one of two directions (latent-to-data, data-to-latent). We evaluate samples from these distributions, assessing their (marginal) fit to the observed data and our choice of prior, and we also evaluate samples through a pipeline that connects the two distributions starting from a data sample, assessing whether together they exploit and reveal latent factors of variation that are useful to a practitioner. We show that this methodology offers possibilities for model selection qualitatively beyond intrinsic evaluation metrics and at a finer granularity than commonly used statistics can offer.
Given a finite and noisy dataset generated with a closed-form mathematical model, when is it possible to learn the true generating model from the data alone? This is the question we investigate here. We show that this model-learning problem displays a transition from a low-noise phase in which the true model can be learned, to a phase in which the observation noise is too high for the true model to be learned by any method. Both in the low-noise phase and in the high-noise phase, probabilistic model selection leads to optimal generalization to unseen data. This is in contrast to standard machine learning approaches, including artificial neural networks, which in this particular problem are limited, in the low-noise phase, by their ability to interpolate. In the transition region between the learnable and unlearnable phases, generalization is hard for all approaches including probabilistic model selection.
In this paper, we present a study of a kernel-based consensual aggregation on randomly projected high-dimensional features of predictions for regression. The aggregation scheme is composed of two steps: the high-dimensional features of predictions, given by a large number of regression estimators, are randomly projected into a smaller subspace using Johnson-Lindenstrauss Lemma in the first step, and a kernel-based consensual aggregation is implemented on the projected features in the second step. We theoretically show that the performance of the aggregation scheme is close to the performance of the aggregation implemented on the original high-dimensional features, with high probability. Moreover, we numerically illustrate that the aggregation scheme upholds its performance on very large and highly correlated features of predictions given by different types of machines. The aggregation scheme allows us to flexibly merge a large number of redundant machines, plainly constructed without model selection or cross-validation. The efficiency of the proposed method is illustrated through several experiments evaluated on different types of synthetic and real datasets.
At the heart of both lossy compression and clustering is a trade-off between the fidelity and size of the learned representation. Our goal is to map out and study the Pareto frontier that quantifies this trade-off. We focus on the optimization of the Deterministic Information Bottleneck (DIB) objective over the space of hard clusterings. To this end, we introduce the primal DIB problem, which we show results in a much richer frontier than its previously studied Lagrangian relaxation when optimized over discrete search spaces. We present an algorithm for mapping out the Pareto frontier of the primal DIB trade-off that is also applicable to other two-objective clustering problems. We study general properties of the Pareto frontier, and we give both analytic and numerical evidence for logarithmic sparsity of the frontier in general. We provide evidence that our algorithm has polynomial scaling despite the super-exponential search space, and additionally, we propose a modification to the algorithm that can be used where sampling noise is expected to be significant. Finally, we use our algorithm to map the DIB frontier of three different tasks: compressing the English alphabet, extracting informative color classes from natural images, and compressing a group theory-inspired dataset, revealing interesting features of frontier, and demonstrating how the structure of the frontier can be used for model selection with a focus on points previously hidden by the cloak of the convex hull.
This paper studies the problem of identifying low-order linear systems via Hankel nuclear norm regularization. Hankel regularization encourages the low-rankness of the Hankel matrix, which maps to the low-orderness of the system. We provide novel statistical analysis for this regularization and carefully contrast it with the unregularized ordinary least-squares (OLS) estimator. Our analysis leads to new bounds on estimating the impulse response and the Hankel matrix associated with the linear system. We first design an input excitation and show that Hankel regularization enables one to recover the system using optimal number of observations in the true system order and achieve strong statistical estimation rates. Surprisingly, we demonstrate that the input design indeed matters, by showing that intuitive choices such as i.i.d. Gaussian input leads to provably sub-optimal sample complexity. To better understand the benefits of regularization, we also revisit the OLS estimator. Besides refining existing bounds, we experimentally identify when regularized approach improves over OLS: (1) For low-order systems with slow impulse-response decay, OLS method performs poorly in terms of sample complexity, (2) Hankel matrix returned by regularization has a more clear singular value gap that ease identification of the system order, (3) Hankel regularization is less sensitive to hyperparameter choice. Finally, we establish model selection guarantees through a joint train-validation procedure where we tune the regularization parameter for near-optimal estimation.
We propose a method to infer a dense depth map from a single image, its calibration, and the associated sparse point cloud. In order to leverage existing models (teachers) that produce putative depth maps, we propose an adaptive knowledge distillation approach that yields a positive congruent training process, wherein a student model avoids learning the error modes of the teachers. In the absence of ground truth for model selection and training, our method, termed Monitored Distillation, allows a student to exploit a blind ensemble of teachers by selectively learning from predictions that best minimize the reconstruction error for a given image. Monitored Distillation yields a distilled depth map and a confidence map, or ``monitor'', for how well a prediction from a particular teacher fits the observed image. The monitor adaptively weights the distilled depth where if all of the teachers exhibit high residuals, the standard unsupervised image reconstruction loss takes over as the supervisory signal. On indoor scenes (VOID), we outperform blind ensembling baselines by 17.53% and unsupervised methods by 24.25%; we boast a 79% model size reduction while maintaining comparable performance to the best supervised method. For outdoors (KITTI), we tie for 5th overall on the benchmark despite not using ground truth. Code available at: https://github.com/alexklwong/mondi-python.
There often is a dilemma between ease of optimization and robust out-of-distribution (OoD) generalization. For instance, many OoD methods rely on penalty terms whose optimization is challenging. They are either too strong to optimize reliably or too weak to achieve their goals. We propose to initialize the networks with a rich representation containing a palette of potentially useful features, ready to be used by even simple models. On the one hand, a rich representation provides a good initialization for the optimizer. On the other hand, it also provides an inductive bias that helps OoD generalization. Such a representation is constructed with the Rich Feature Construction (RFC) algorithm, also called the Bonsai algorithm, which consists of a succession of training episodes. During discovery episodes, we craft a multi-objective optimization criterion and its associated datasets in a manner that prevents the network from using the features constructed in the previous iterations. During synthesis episodes, we use knowledge distillation to force the network to simultaneously represent all the previously discovered features. Initializing the networks with Bonsai representations consistently helps six OoD methods achieve top performance on ColoredMNIST benchmark. The same technique substantially outperforms comparable results on the Wilds Camelyon17 task, eliminates the high result variance that plagues other methods, and makes hyperparameter tuning and model selection more reliable.