Transfer learning aims to improve the performance of a target model by leveraging data from related source populations, which is known to be especially helpful in cases with insufficient target data. In this paper, we study the problem of how to train a high-dimensional ridge regression model using limited target data and existing regression models trained in heterogeneous source populations. We consider a practical setting where only the parameter estimates of the fitted source models are accessible, instead of the individual-level source data. Under the setting with only one source model, we propose a novel flexible angle-based transfer learning (angleTL) method, which leverages the concordance between the source and the target model parameters. We show that angleTL unifies several benchmark methods by construction, including the target-only model trained using target data alone, the source model fitted on source data, and distance-based transfer learning method that incorporates the source parameter estimates and the target data under a distance-based similarity constraint. We also provide algorithms to effectively incorporate multiple source models accounting for the fact that some source models may be more helpful than others. Our high-dimensional asymptotic analysis provides interpretations and insights regarding when a source model can be helpful to the target model, and demonstrates the superiority of angleTL over other benchmark methods. We perform extensive simulation studies to validate our theoretical conclusions and show the feasibility of applying angleTL to transfer existing genetic risk prediction models across multiple biobanks.
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Recently, large-scale pre-trained Vision and Language (VL) models have set a new state-of-the-art (SOTA) in zero-shot visual classification enabling open-vocabulary recognition of potentially unlimited set of categories defined as simple language prompts. However, despite these great advances, the performance of these zeroshot classifiers still falls short of the results of dedicated (closed category set) classifiers trained with supervised fine tuning. In this paper we show, for the first time, how to reduce this gap without any labels and without any paired VL data, using an unlabeled image collection and a set of texts auto-generated using a Large Language Model (LLM) describing the categories of interest and effectively substituting labeled visual instances of those categories. Using our label-free approach, we are able to attain significant performance improvements over the zero-shot performance of the base VL model and other contemporary methods and baselines on a wide variety of datasets, demonstrating absolute improvement of up to 11.7% (3.8% on average) in the label-free setting. Moreover, despite our approach being label-free, we observe 1.3% average gains over leading few-shot prompting baselines that do use 5-shot supervision.
Model misspecification can create significant challenges for the implementation of probabilistic models, and this has led to development of a range of robust methods which directly account for this issue. However, whether these more involved methods are required will depend on whether the model is really misspecified, and there is a lack of generally applicable methods to answer this question. In this paper, we propose one such method. More precisely, we propose kernel-based hypothesis tests for the challenging composite testing problem, where we are interested in whether the data comes from any distribution in some parametric family. Our tests make use of minimum distance estimators based on the maximum mean discrepancy and the kernel Stein discrepancy. They are widely applicable, including whenever the density of the parametric model is known up to normalisation constant, or if the model takes the form of a simulator. As our main result, we show that we are able to estimate the parameter and conduct our test on the same data (without data splitting), while maintaining a correct test level. Our approach is illustrated on a range of problems, including testing for goodness-of-fit of an unnormalised non-parametric density model, and an intractable generative model of a biological cellular network.
This article describes an R package bqror that estimates Bayesian quantile regression for ordinal models introduced in Rahman (2016). The paper classifies ordinal models into two types and offers computationally efficient, yet simple, Markov chain Monte Carlo (MCMC) algorithms for estimating ordinal quantile regression. The generic ordinal model with 3 or more outcomes (labeled ORI model) is estimated by a combination of Gibbs sampling and Metropolis-Hastings algorithm. Whereas an ordinal model with exactly 3 outcomes (labeled ORII model) is estimated using Gibbs sampling only. In line with the Bayesian literature, we suggest using marginal likelihood for comparing alternative quantile regression models and explain how to compute the same. The models and their estimation procedures are illustrated via multiple simulation studies and implemented in two applications. The article also describes several other functions contained within the bqror package, which are necessary for estimation, inference, and assessing model fit.
The shocks which hit macroeconomic models such as Vector Autoregressions (VARs) have the potential to be non-Gaussian, exhibiting asymmetries and fat tails. This consideration motivates the VAR developed in this paper which uses a Dirichlet process mixture (DPM) to model the shocks. However, we do not follow the obvious strategy of simply modeling the VAR errors with a DPM since this would lead to computationally infeasible Bayesian inference in larger VARs and potentially a sensitivity to the way the variables are ordered in the VAR. Instead we develop a particular additive error structure inspired by Bayesian nonparametric treatments of random effects in panel data models. We show that this leads to a model which allows for computationally fast and order-invariant inference in large VARs with nonparametric shocks. Our empirical results with nonparametric VARs of various dimensions shows that nonparametric treatment of the VAR errors is particularly useful in periods such as the financial crisis and the pandemic.
In this paper, we consider the problem of learning a linear regression model on a data domain of interest (target) given few samples. To aid learning, we are provided with a set of pre-trained regression models that are trained on potentially different data domains (sources). Assuming a representation structure for the data generating linear models at the sources and the target domains, we propose a representation transfer based learning method for constructing the target model. The proposed scheme is comprised of two phases: (i) utilizing the different source representations to construct a representation that is adapted to the target data, and (ii) using the obtained model as an initialization to a fine-tuning procedure that re-trains the entire (over-parameterized) regression model on the target data. For each phase of the training method, we provide excess risk bounds for the learned model compared to the true data generating target model. The derived bounds show a gain in sample complexity for our proposed method compared to the baseline method of not leveraging source representations when achieving the same excess risk, therefore, theoretically demonstrating the effectiveness of transfer learning for linear regression.
Most modern imaging systems incorporate a computational pipeline to infer the image of interest from acquired measurements. The Bayesian approach to solve such ill-posed inverse problems involves the characterization of the posterior distribution of the image. It depends on the model of the imaging system and on prior knowledge on the image of interest. In this work, we present a Bayesian reconstruction framework for nonlinear imaging models where we specify the prior knowledge on the image through a deep generative model. We develop a tractable posterior-sampling scheme based on the Metropolis-adjusted Langevin algorithm for the class of nonlinear inverse problems where the forward model has a neural-network-like structure. This class includes most practical imaging modalities. We introduce the notion of augmented deep generative priors in order to suitably handle the recovery of quantitative images.We illustrate the advantages of our framework by applying it to two nonlinear imaging modalities-phase retrieval and optical diffraction tomography.
In practical compressed sensing (CS), the obtained measurements typically necessitate quantization to a limited number of bits prior to transmission or storage. This nonlinear quantization process poses significant recovery challenges, particularly with extreme coarse quantization such as 1-bit. Recently, an efficient algorithm called QCS-SGM was proposed for quantized CS (QCS) which utilizes score-based generative models (SGM) as an implicit prior. Due to the adeptness of SGM in capturing the intricate structures of natural signals, QCS-SGM substantially outperforms previous QCS methods. However, QCS-SGM is constrained to (approximately) row-orthogonal sensing matrices as the computation of the likelihood score becomes intractable otherwise. To address this limitation, we introduce an advanced variant of QCS-SGM, termed QCS-SGM+, capable of handling general matrices effectively. The key idea is a Bayesian inference perspective on the likelihood score computation, wherein an expectation propagation algorithm is employed for its approximate computation. We conduct extensive experiments on various settings, demonstrating the substantial superiority of QCS-SGM+ over QCS-SGM for general sensing matrices beyond mere row-orthogonality.
Multi-Task Learning (MTL) is a learning paradigm in machine learning and its aim is to leverage useful information contained in multiple related tasks to help improve the generalization performance of all the tasks. In this paper, we give a survey for MTL from the perspective of algorithmic modeling, applications and theoretical analyses. For algorithmic modeling, we give a definition of MTL and then classify different MTL algorithms into five categories, including feature learning approach, low-rank approach, task clustering approach, task relation learning approach and decomposition approach as well as discussing the characteristics of each approach. In order to improve the performance of learning tasks further, MTL can be combined with other learning paradigms including semi-supervised learning, active learning, unsupervised learning, reinforcement learning, multi-view learning and graphical models. When the number of tasks is large or the data dimensionality is high, we review online, parallel and distributed MTL models as well as dimensionality reduction and feature hashing to reveal their computational and storage advantages. Many real-world applications use MTL to boost their performance and we review representative works in this paper. Finally, we present theoretical analyses and discuss several future directions for MTL.
This paper addresses the difficulty of forecasting multiple financial time series (TS) conjointly using deep neural networks (DNN). We investigate whether DNN-based models could forecast these TS more efficiently by learning their representation directly. To this end, we make use of the dynamic factor graph (DFG) from that we enhance by proposing a novel variable-length attention-based mechanism to render it memory-augmented. Using this mechanism, we propose an unsupervised DNN architecture for multivariate TS forecasting that allows to learn and take advantage of the relationships between these TS. We test our model on two datasets covering 19 years of investment funds activities. Our experimental results show that our proposed approach outperforms significantly typical DNN-based and statistical models at forecasting their 21-day price trajectory.
The world we see is ever-changing and it always changes with people, things, and the environment. Domain is referred to as the state of the world at a certain moment. A research problem is characterized as domain transfer adaptation when it needs knowledge correspondence between different moments. Conventional machine learning aims to find a model with the minimum expected risk on test data by minimizing the regularized empirical risk on the training data, which, however, supposes that the training and test data share similar joint probability distribution. Transfer adaptation learning aims to build models that can perform tasks of target domain by learning knowledge from a semantic related but distribution different source domain. It is an energetic research filed of increasing influence and importance. This paper surveys the recent advances in transfer adaptation learning methodology and potential benchmarks. Broader challenges being faced by transfer adaptation learning researchers are identified, i.e., instance re-weighting adaptation, feature adaptation, classifier adaptation, deep network adaptation, and adversarial adaptation, which are beyond the early semi-supervised and unsupervised split. The survey provides researchers a framework for better understanding and identifying the research status, challenges and future directions of the field.
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