This paper studies task adaptive pre-trained model selection, an underexplored problem of assessing pre-trained models for the target task and select best ones from the model zoo \emph{without fine-tuning}. A few pilot works addressed the problem in transferring supervised pre-trained models to classification tasks, but they cannot handle emerging unsupervised pre-trained models or regression tasks. In pursuit of a practical assessment method, we propose to estimate the maximum value of label evidence given features extracted by pre-trained models. Unlike the maximum likelihood, the maximum evidence is \emph{immune to over-fitting}, while its expensive computation can be dramatically reduced by our carefully designed algorithm. The Logarithm of Maximum Evidence (LogME) can be used to assess pre-trained models for transfer learning: a pre-trained model with a high LogME value is likely to have good transfer performance. LogME is \emph{fast, accurate, and general}, characterizing itself as the first practical method for assessing pre-trained models. Compared with brute-force fine-tuning, LogME brings at most $3000\times$ speedup in wall-clock time and requires only $1\%$ memory footprint. It outperforms prior methods by a large margin in their setting and is applicable to new settings. It is general enough for diverse pre-trained models (supervised pre-trained and unsupervised pre-trained), downstream tasks (classification and regression), and modalities (vision and language). Code is available at this repository: \href{https://github.com/thuml/LogME}{https://github.com/thuml/LogME}.
In model selection problems for machine learning, the desire for a well-performing model with meaningful structure is typically expressed through a regularized optimization problem. In many scenarios, however, the meaningful structure is specified in some discrete space, leading to difficult nonconvex optimization problems. In this paper, we connect the model selection problem with structure-promoting regularizers to submodular function minimization with continuous and discrete arguments. In particular, we leverage the theory of submodular functions to identify a class of these problems that can be solved exactly and efficiently with an agnostic combination of discrete and continuous optimization routines. We show how simple continuous or discrete constraints can also be handled for certain problem classes and extend these ideas to a robust optimization framework. We also show how some problems outside of this class can be embedded within the class, further extending the class of problems our framework can accommodate. Finally, we numerically validate our theoretical results with several proof-of-concept examples with synthetic and real-world data, comparing against state-of-the-art algorithms.
Statistical learning theory provides the foundation to applied machine learning, and its various successful applications in computer vision, natural language processing and other scientific domains. The theory, however, does not take into account the unique challenges of performing statistical learning in geospatial settings. For instance, it is well known that model errors cannot be assumed to be independent and identically distributed in geospatial (a.k.a. regionalized) variables due to spatial correlation; and trends caused by geophysical processes lead to covariate shifts between the domain where the model was trained and the domain where it will be applied, which in turn harm the use of classical learning methodologies that rely on random samples of the data. In this work, we introduce the geostatistical (transfer) learning problem, and illustrate the challenges of learning from geospatial data by assessing widely-used methods for estimating generalization error of learning models, under covariate shift and spatial correlation. Experiments with synthetic Gaussian process data as well as with real data from geophysical surveys in New Zealand indicate that none of the methods are adequate for model selection in a geospatial context. We provide general guidelines regarding the choice of these methods in practice while new methods are being actively researched.
Selecting causal inference models for estimating individualized treatment effects (ITE) from observational data presents a unique challenge since the counterfactual outcomes are never observed. The problem is challenged further in the unsupervised domain adaptation (UDA) setting where we only have access to labeled samples in the source domain, but desire selecting a model that achieves good performance on a target domain for which only unlabeled samples are available. Existing techniques for UDA model selection are designed for the predictive setting. These methods examine discriminative density ratios between the input covariates in the source and target domain and do not factor in the model's predictions in the target domain. Because of this, two models with identical performance on the source domain would receive the same risk score by existing methods, but in reality, have significantly different performance in the test domain. We leverage the invariance of causal structures across domains to propose a novel model selection metric specifically designed for ITE methods under the UDA setting. In particular, we propose selecting models whose predictions of interventions' effects satisfy known causal structures in the target domain. Experimentally, our method selects ITE models that are more robust to covariate shifts on several healthcare datasets, including estimating the effect of ventilation in COVID-19 patients from different geographic locations.
Unsupervised Domain Adaptation (UDA) is a key issue in visual recognition, as it allows to bridge different visual domains enabling robust performances in the real world. To date, all proposed approaches rely on human expertise to manually adapt a given UDA method (e.g. DANN) to a specific backbone architecture (e.g. ResNet). This dependency on handcrafted designs limits the applicability of a given approach in time, as old methods need to be constantly adapted to novel backbones. Existing Neural Architecture Search (NAS) approaches cannot be directly applied to mitigate this issue, as they rely on labels that are not available in the UDA setting. Furthermore, most NAS methods search for full architectures, which precludes the use of pre-trained models, essential in a vast range of UDA settings for reaching SOTA results. To the best of our knowledge, no prior work has addressed these aspects in the context of NAS for UDA. Here we tackle both aspects with an Adversarial Branch Architecture Search for UDA (ABAS): i. we address the lack of target labels by a novel data-driven ensemble approach for model selection; and ii. we search for an auxiliary adversarial branch, attached to a pre-trained backbone, which drives the domain alignment. We extensively validate ABAS to improve two modern UDA techniques, DANN and ALDA, on three standard visual recognition datasets (Office31, Office-Home and PACS). In all cases, ABAS robustly finds the adversarial branch architectures and parameters which yield best performances.
We study model selection in linear bandits, where the learner must adapt to the dimension (denoted by $d_\star$) of the smallest hypothesis class containing the true linear model while balancing exploration and exploitation. Previous papers provide various guarantees for this model selection problem, but have limitations; i.e., the analysis requires favorable conditions that allow for inexpensive statistical testing to locate the right hypothesis class or are based on the idea of "corralling" multiple base algorithms, which often performs relatively poorly in practice. These works also mainly focus on upper bounds. In this paper, we establish the first lower bound for the model selection problem. Our lower bound implies that, even with a fixed action set, adaptation to the unknown dimension $d_\star$ comes at a cost: There is no algorithm that can achieve the regret bound $\widetilde{O}(\sqrt{d_\star T})$ simultaneously for all values of $d_\star$. We propose Pareto optimal algorithms that match the lower bound. Empirical evaluations show that our algorithm enjoys superior performance compared to existing ones.
Knowledge base completion (KBC) methods aim at inferring missing facts from the information present in a knowledge base (KB) by estimating the likelihood of candidate facts. In the prevailing evaluation paradigm, models do not actually decide whether a new fact should be accepted or not but are solely judged on the position of true facts in a likelihood ranking with other candidates. We argue that consideration of binary predictions is essential to reflect the actual KBC quality, and propose a novel evaluation paradigm, designed to provide more transparent model selection criteria for a realistic scenario. We construct the data set FB14k-QAQ where instead of single facts, we use KB queries, i.e., facts where one entity is replaced with a variable, and construct corresponding sets of entities that are correct answers. We randomly remove some of these correct answers from the data set, simulating the realistic scenario of real-world entities missing from a KB. This way, we can explicitly measure a model's ability to handle queries that have more correct answers in the real world than in the KB, including the special case of queries without any valid answer. The latter especially contrasts the ranking setting. We evaluate a number of state-of-the-art KB embeddings models on our new benchmark. The differences in relative performance between ranking-based and classification-based evaluation that we observe in our experiments confirm our hypothesis that good performance on the ranking task does not necessarily translate to good performance on the actual completion task. Our results motivate future work on KB embedding models with better prediction separability and, as a first step in that direction, we propose a simple variant of TransE that encourages thresholding and achieves a significant improvement in classification F1 score relative to the original TransE.
Reinforcement learning is about learning agent models that make the best sequential decisions in unknown environments. In an unknown environment, the agent needs to explore the environment while exploiting the collected information, which usually forms a sophisticated problem to solve. Derivative-free optimization, meanwhile, is capable of solving sophisticated problems. It commonly uses a sampling-and-updating framework to iteratively improve the solution, where exploration and exploitation are also needed to be well balanced. Therefore, derivative-free optimization deals with a similar core issue as reinforcement learning, and has been introduced in reinforcement learning approaches, under the names of learning classifier systems and neuroevolution/evolutionary reinforcement learning. Although such methods have been developed for decades, recently, derivative-free reinforcement learning exhibits attracting increasing attention. However, recent survey on this topic is still lacking. In this article, we summarize methods of derivative-free reinforcement learning to date, and organize the methods in aspects including parameter updating, model selection, exploration, and parallel/distributed methods. Moreover, we discuss some current limitations and possible future directions, hoping that this article could bring more attentions to this topic and serve as a catalyst for developing novel and efficient approaches.
We theoretically analyze the typical learning performance of $\ell_{1}$-regularized linear regression ($\ell_1$-LinR) for Ising model selection using the replica method from statistical mechanics. For typical random regular graphs in the paramagnetic phase, an accurate estimate of the typical sample complexity of $\ell_1$-LinR is obtained. Remarkably, despite the model misspecification, $\ell_1$-LinR is model selection consistent with the same order of sample complexity as $\ell_{1}$-regularized logistic regression ($\ell_1$-LogR), i.e., $M=\mathcal{O}\left(\log N\right)$, where $N$ is the number of variables of the Ising model. Moreover, we provide an efficient method to accurately predict the non-asymptotic behavior of $\ell_1$-LinR for moderate $M, N$, such as precision and recall. Simulations show a fairly good agreement between theoretical predictions and experimental results, even for graphs with many loops, which supports our findings. Although this paper mainly focuses on $\ell_1$-LinR, our method is readily applicable for precisely characterizing the typical learning performances of a wide class of $\ell_{1}$-regularized $M$-estimators including $\ell_1$-LogR and interaction screening.
There has been an increasing interest in harnessing deep learning to tackle combinatorial optimization (CO) problems in recent years. Typical CO deep learning approaches leverage the problem structure in the model architecture. Nevertheless, the model selection is still mainly based on the conventional machine learning setting. Due to the discrete nature of CO problems, a single model is unlikely to learn the problem entirely. We introduce ZTop, which stands for Zero Training Overhead Portfolio, a simple yet effective model selection and ensemble mechanism for learning to solve combinatorial problems. ZTop is inspired by algorithm portfolios, a popular CO ensembling strategy, particularly restart portfolios, which periodically restart a randomized CO algorithm, de facto exploring the search space with different heuristics. We have observed that well-trained models acquired in the same training trajectory, with similar top validation performance, perform well on very different validation instances. Following this observation, ZTop ensembles a set of well-trained models, each providing a unique heuristic with zero training overhead, and applies them, sequentially or in parallel, to solve the test instances. We show how ZTopping, i.e., using a ZTop ensemble strategy with a given deep learning approach, can significantly improve the performance of the current state-of-the-art deep learning approaches on three prototypical CO domains, the hardest unique-solution Sudoku instances, challenging routing problems, and the graph maximum cut problem, as well as on multi-label classification, a machine learning task with a large combinatorial label space.
The majority of finite mixture models suffer from not allowing asymmetric tail dependencies within components and not capturing non-elliptical clusters in clustering applications. Since vine copulas are very flexible in capturing these types of dependencies, we propose a novel vine copula mixture model for continuous data. We discuss the model selection and parameter estimation problems and further formulate a new model-based clustering algorithm. The use of vine copulas in clustering allows for a range of shapes and dependency structures for the clusters. Our simulation experiments illustrate a significant gain in clustering accuracy when notably asymmetric tail dependencies or/and non-Gaussian margins within the components exist. The analysis of real data sets accompanies the proposed method. We show that the model-based clustering algorithm with vine copula mixture models outperforms the other model-based clustering techniques, especially for the non-Gaussian multivariate data.
A classic application of description length is for model selection with the minimum description length (MDL) principle. The focus of this paper is to extend description length for data analysis beyond simple model selection and sequences of scalars. More specifically, we extend the description length for data analysis in Gaussian graphical models. These are powerful tools to model interactions among variables in a sequence of i.i.d Gaussian data in the form of a graph. Our method uses universal graph coding methods to accurately account for model complexity, and therefore provide a more rigorous approach for graph model selection. The developed method is tested with synthetic and electrocardiogram (ECG) data to find the graph model and anomaly in Gaussian graphical models. The experiments show that our method gives better performance compared to commonly used methods.
The discovery of Partial Differential Equations (PDEs) is an essential task for applied science and engineering. However, data-driven discovery of PDEs is generally challenging, primarily stemming from the sensitivity of the discovered equation to noise and the complexities of model selection. In this work, we propose an advanced Bayesian sparse learning algorithm for PDE discovery with variable coefficients, predominantly when the coefficients are spatially or temporally dependent. Specifically, we apply threshold Bayesian group Lasso regression with a spike-and-slab prior (tBGL-SS) and leverage a Gibbs sampler for Bayesian posterior estimation of PDE coefficients. This approach not only enhances the robustness of point estimation with valid uncertainty quantification but also relaxes the computational burden from Bayesian inference through the integration of coefficient thresholds as an approximate MCMC method. Moreover, from the quantified uncertainties, we propose a Bayesian total error bar criteria for model selection, which outperforms classic metrics including the root mean square and the Akaike information criterion. The capability of this method is illustrated by the discovery of several classical benchmark PDEs with spatially or temporally varying coefficients from solution data obtained from the reference simulations. In the experiments, we show that the tBGL-SS method is more robust than the baseline methods under noisy environments and provides better model selection criteria along the regularization path.
Fine-tuning from a collection of models pre-trained on different domains (a "model zoo") is emerging as a technique to improve test accuracy in the low-data regime. However, model selection, i.e. how to pre-select the right model to fine-tune from a model zoo without performing any training, remains an open topic. We use a linearized framework to approximate fine-tuning, and introduce two new baselines for model selection -- Label-Gradient and Label-Feature Correlation. Since all model selection algorithms in the literature have been tested on different use-cases and never compared directly, we introduce a new comprehensive benchmark for model selection comprising of: i) A model zoo of single and multi-domain models, and ii) Many target tasks. Our benchmark highlights accuracy gain with model zoo compared to fine-tuning Imagenet models. We show our model selection baseline can select optimal models to fine-tune in few selections and has the highest ranking correlation to fine-tuning accuracy compared to existing algorithms.
We consider the question of sequential prediction under the log-loss in terms of cumulative regret. Namely, given a hypothesis class of distributions, learner sequentially predicts the (distribution of the) next letter in sequence and its performance is compared to the baseline of the best constant predictor from the hypothesis class. The well-specified case corresponds to an additional assumption that the data-generating distribution belongs to the hypothesis class as well. Here we present results in the more general misspecified case. Due to special properties of the log-loss, the same problem arises in the context of competitive-optimality in density estimation, and model selection. For the $d$-dimensional Gaussian location hypothesis class, we show that cumulative regrets in the well-specified and misspecified cases asymptotically coincide. In other words, we provide an $o(1)$ characterization of the distribution-free (or PAC) regret in this case -- the first such result as far as we know. We recall that the worst-case (or individual-sequence) regret in this case is larger by an additive constant ${d\over 2} + o(1)$. Surprisingly, neither the traditional Bayesian estimators, nor the Shtarkov's normalized maximum likelihood achieve the PAC regret and our estimator requires special "robustification" against heavy-tailed data. In addition, we show two general results for misspecified regret: the existence and uniqueness of the optimal estimator, and the bound sandwiching the misspecified regret between well-specified regrets with (asymptotically) close hypotheses classes.
Decision support systems have become increasingly popular in the domain of agriculture. With the development of automated machine learning, agricultural experts are now able to train, evaluate and make predictions using cutting edge machine learning (ML) models without the need for much ML knowledge. Although this automated approach has led to successful results in many scenarios, in certain cases (e.g., when few labeled datasets are available) choosing among different models with similar performance metrics is a difficult task. Furthermore, these systems do not commonly allow users to incorporate their domain knowledge that could facilitate the task of model selection, and to gain insight into the prediction system for eventual decision making. To address these issues, in this paper we present AHMoSe, a visual support system that allows domain experts to better understand, diagnose and compare different regression models, primarily by enriching model-agnostic explanations with domain knowledge. To validate AHMoSe, we describe a use case scenario in the viticulture domain, grape quality prediction, where the system enables users to diagnose and select prediction models that perform better. We also discuss feedback concerning the design of the tool from both ML and viticulture experts.
Since its inception, the choice modelling field has been dominated by theory-driven modelling approaches. Machine learning offers an alternative data-driven approach for modelling choice behaviour and is increasingly drawing interest in our field. Cross-pollination of machine learning models, techniques and practices could help overcome problems and limitations encountered in the current theory-driven modelling paradigm, such as subjective labour-intensive search processes for model selection, and the inability to work with text and image data. However, despite the potential benefits of using the advances of machine learning to improve choice modelling practices, the choice modelling field has been hesitant to embrace machine learning. This discussion paper aims to consolidate knowledge on the use of machine learning models, techniques and practices for choice modelling, and discuss their potential. Thereby, we hope not only to make the case that further integration of machine learning in choice modelling is beneficial, but also to further facilitate it. To this end, we clarify the similarities and differences between the two modelling paradigms; we review the use of machine learning for choice modelling; and we explore areas of opportunities for embracing machine learning models and techniques to improve our practices. To conclude this discussion paper, we put forward a set of research questions which must be addressed to better understand if and how machine learning can benefit choice modelling.
In this paper we propose the adaptive lasso for predictive quantile regression (ALQR). Reflecting empirical findings, we allow predictors to have various degrees of persistence and exhibit different signal strengths. The number of predictors is allowed to grow with the sample size. We study regularity conditions under which stationary, local unit root, and cointegrated predictors are present simultaneously. We next show the convergence rates, model selection consistency, and asymptotic distributions of ALQR. We apply the proposed method to the out-of-sample quantile prediction problem of stock returns and find that it outperforms the existing alternatives. We also provide numerical evidence from additional Monte Carlo experiments, supporting the theoretical results.
This paper studies optimal bundling of products with non-additive values. Under monotonic preferences and single-peaked profits, I show a monopolist finds pure bundling optimal if and only if the optimal sales volume for the grand bundle is larger than the optimal sales volume for any smaller bundle. I then (i) detail how my analysis relates to "ratio monotonicity" results on bundling; and (ii) describe the implications for non-linear pricing.
Few-shot learning aims to transfer information from one task to enable generalization on novel tasks given a few examples. This information is present both in the domain and the class labels. In this work we investigate the complementary roles of these two sources of information by combining instance-discriminative contrastive learning and supervised learning in a single framework called Supervised Momentum Contrastive learning (SUPMOCO). Our approach avoids a problem observed in supervised learning where information in images not relevant to the task is discarded, which hampers their generalization to novel tasks. We show that (self-supervised) contrastive learning and supervised learning are mutually beneficial, leading to a new state-of-the-art on the META-DATASET - a recently introduced benchmark for few-shot learning. Our method is based on a simple modification of MOCO and scales better than prior work on combining supervised and self-supervised learning. This allows us to easily combine data from multiple domains leading to further improvements.