I propose a novel approach for nonlinear Logistic regression using a two-layer neural network (NN) model structure with hierarchical priors on the network weights. I present a hybrid of expectation propagation called Variational Expectation Propagation approach (VEP) for approximate integration over the posterior distribution of the weights, the hierarchical scale parameters of the priors and zeta. Using a factorized posterior approximation I derive a computationally efficient algorithm, whose complexity scales similarly to an ensemble of independent sparse logistic models. The approach can be extended beyond standard activation functions and NN model structures to form flexible nonlinear binary predictors from multiple sparse linear models. I consider a hierarchical Bayesian model with logistic regression likelihood and a Gaussian prior distribution over the parameters called weights and hyperparameters. I work in the perspective of E step and M step for computing the approximating posterior and updating the parameters using the computed posterior respectively.

Time-series prediction has drawn considerable attention during the past decades fueled by the emerging advances of deep learning methods. However, most neural network based methods lack interpretability and fail in extracting the hidden mechanism of the targeted physical system. To overcome these shortcomings, an interpretable sparse system identification method without any prior knowledge is proposed in this study. This method adopts the Fourier transform to reduces the irrelevant items in the dictionary matrix, instead of indiscriminate usage of polynomial functions in most system identification methods. It shows an interpretable system representation and greatly reduces computing cost. With the adoption of $l_1$ norm in regularizing the parameter matrix, a sparse description of the system model can be achieved. Moreover, Three data sets including the water conservancy data, global temperature data and financial data are used to test the performance of the proposed method. Although no prior knowledge was known about the physical background, experimental results show that our method can achieve long-term prediction regardless of the noise and incompleteness in the original data more accurately than the widely-used baseline data-driven methods. This study may provide some insight into time-series prediction investigations, and suggests that an white-box system identification method may extract the easily overlooked yet inherent periodical features and may beat neural-network based black-box methods on long-term prediction tasks.

Language identification is an important first step in many IR and NLP applications. Most publicly available language identification datasets, however, are compiled under the assumption that the gold label of each instance is determined by where texts are retrieved from. Research has shown that this is a problematic assumption, particularly in the case of very similar languages (e.g., Croatian and Serbian) and national language varieties (e.g., Brazilian and European Portuguese), where texts may contain no distinctive marker of the particular language or variety. To overcome this important limitation, this paper presents DSL True Labels (DSL-TL), the first human-annotated multilingual dataset for language variety identification. DSL-TL contains a total of 12,900 instances in Portuguese, split between European Portuguese and Brazilian Portuguese; Spanish, split between Argentine Spanish and Castilian Spanish; and English, split between American English and British English. We trained multiple models to discriminate between these language varieties, and we present the results in detail. The data and models presented in this paper provide a reliable benchmark toward the development of robust and fairer language variety identification systems. We make DSL-TL freely available to the research community.

Within components (models, knowledge sources) of an ASR system the classical approach, deep learning has been introduced before coming to a decision. This is in line with Bayes' to acoustic and language modeling. In acoustic modeling, decision rule, which exactly requires a single global decision deep learning replaced Gaussian mixture distributions (hybrid integrating all available knowledge sources. HMM [3], [4]) or augmented the acoustic feature set c) Joint Training: In terms of model training, E2E suggests (nonlinear disciminant/tandem approach [5], [6]). In language estimating all parameters of all components of a model modeling, deep learning replaced count-based approaches [7], jointly using a single objective function that is consistent with [8], [9]. However, when introducing deep learning, the classical the task at hand, which in case of ASR means minimizing the ASR architecture was not yet touched. Classical stateof-the-art expected word error rate. ASR systems today are composed of many separate d) Training Data: Joint training of an integrated model components and knowledge sources, especially speech signal implies using a single kind of training data, which in case preprocessing, methods for robustness w.r.t.

In recent years, Bayesian inference in large-scale inverse problems found in science, engineering and machine learning has gained significant attention. This paper examines the robustness of the Bayesian approach by analyzing the stability of posterior measures in relation to perturbations in the likelihood potential and the prior measure. We present new stability results using a family of integral probability metrics (divergences) akin to dual problems that arise in optimal transport. Our results stand out from previous works in three directions: (1) We construct new families of integral probability metrics that are adapted to the problem at hand; (2) These new metrics allow us to study both likelihood and prior perturbations in a convenient way; and (3) our analysis accommodates likelihood potentials that are only locally Lipschitz, making them applicable to a wide range of nonlinear inverse problems. Our theoretical findings are further reinforced through specific and novel examples where the approximation rates of posterior measures are obtained for different types of perturbations and provide a path towards the convergence analysis of recently adapted machine learning techniques for Bayesian inverse problems such as data-driven priors and neural network surrogates.

We introduce two new classes of exact Markov chain Monte Carlo (MCMC) samplers for inference in latent dynamical models. The first one, which we coin auxiliary Kalman samplers, relies on finding a linear Gaussian state-space model approximation around the running trajectory corresponding to the state of the Markov chain. The second, that we name auxiliary particle Gibbs samplers corresponds to deriving good local proposals in an auxiliary Feynman--Kac model for use in particle Gibbs. Both samplers are controlled by augmenting the target distribution with auxiliary observations, resulting in an efficient Gibbs sampling routine. We discuss the relative statistical and computational performance of the samplers introduced, and show how to parallelise the auxiliary samplers along the time dimension. We illustrate the respective benefits and drawbacks of the resulting algorithms on classical examples from the particle filtering literature.

Sampling from a target measure whose density is only known up to a normalization constant is a fundamental problem in computational statistics and machine learning. In this paper, we present a new optimization-based method for sampling called mollified interaction energy descent (MIED). MIED minimizes a new class of energies on probability measures called mollified interaction energies (MIEs). These energies rely on mollifier functions--smooth approximations of the Dirac delta originated from PDE theory. We show that as the mollifier approaches the Dirac delta, the MIE converges to the chi-square divergence with respect to the target measure and the minimizers of MIE converge to the target measure. Optimizing this energy with proper discretization yields a practical firstorder particle-based algorithm for sampling in both unconstrained and constrained domains. We show experimentally that for unconstrained sampling problems, our algorithm performs on par with existing particle-based algorithms like SVGD, while for constrained sampling problems our method readily incorporates constrained optimization techniques to handle more flexible constraints with strong performance compared to alternatives. Sampling from an unnormalized probability density is a ubiquitous task in statistics, mathematical physics, and machine learning. While Markov chain Monte Carlo (MCMC) methods (Brooks et al., 2011) provide a way to obtain unbiased samples at the price of potentially long mixing times, variational inference (VI) methods (Blei et al., 2017) approximate the target measure with simpler (e.g., parametric) distributions at a lower computational cost. In this work, we focus on a particular class of VI methods that approximate the target measure using a collection of interacting particles.

Climate change has increased the severity and frequency of weather disasters all around the world. Flood inundation mapping based on earth observation data can help in this context, by providing cheap and accurate maps depicting the area affected by a flood event to emergency-relief units in near-real-time. Building upon the recent development of the Sen1Floods11 dataset, which provides a limited amount of hand-labeled high-quality training data, this paper evaluates the potential of five traditional machine learning approaches such as gradient boosted decision trees, support vector machines or quadratic discriminant analysis. By performing a grid-search-based hyperparameter optimization on 23 feature spaces we can show that all considered classifiers are capable of outperforming the current state-of-the-art neural network-based approaches in terms of total IoU on their best-performing feature spaces. With total and mean IoU values of 0.8751 and 0.7031 compared to 0.70 and 0.5873 as the previous best-reported results, we show that a simple gradient boosting classifier can significantly improve over deep neural network based approaches, despite using less training data. Furthermore, an analysis of the regional distribution of the Sen1Floods11 dataset reveals a problem of spatial imbalance. We show that traditional machine learning models can learn this bias and argue that modified metric evaluations are required to counter artifacts due to spatial imbalance. Lastly, a qualitative analysis shows that this pixel-wise classifier provides highly-precise surface water classifications indicating that a good choice of a feature space and pixel-wise classification can generate high-quality flood maps using optical and SAR data. We make our code publicly available at: https://github.com/DFKI-Earth-And-Space-Applications/Flood_Mapping_Feature_Space_Importance

Learning with few labeled tabular samples is often an essential requirement for industrial machine learning applications as varieties of tabular data suffer from high annotation costs or have difficulties in collecting new samples for novel tasks. Despite the utter importance, such a problem is quite under-explored in the field of tabular learning, and existing few-shot learning schemes from other domains are not straightforward to apply, mainly due to the heterogeneous characteristics of tabular data. In this paper, we propose a simple yet effective framework for few-shot semi-supervised tabular learning, coined Self-generated Tasks from UNlabeled Tables (STUNT). Our key idea is to self-generate diverse few-shot tasks by treating randomly chosen columns as a target label. We then employ a meta-learning scheme to learn generalizable knowledge with the constructed tasks. Moreover, we introduce an unsupervised validation scheme for hyperparameter search (and early stopping) by generating a pseudo-validation set using STUNT from unlabeled data. Our experimental results demonstrate that our simple framework brings significant performance gain under various tabular few-shot learning benchmarks, compared to prior semi-and self-supervised baselines. Learning with few labeled samples is often an essential ingredient of machine learning applications for practical deployment. However, while various few-shot learning schemes have been actively developed over several domains, including images (Chen et al., 2019) and languages (Min et al., 2022), such research has been under-explored in the tabular domain despite its practical importance in industries (Guo et al., 2017; Zhang et al., 2020; Ulmer et al., 2020). In particular, few-shot tabular learning is a crucial application as varieties of tabular datasets (i) suffer from high labeling costs, e.g., the credit risk in financial datasets (Clements et al., 2020), and (ii) even show difficulties in collecting new samples for novel tasks, e.g., a patient with a rare or new disease (Peplow, 2016) such as an early infected patient of COVID-19 (Zhou et al., 2020). To tackle such limited label issues, a common consensus across various domains is to utilize unlabeled datasets for learning a generalizable and transferable representation, e.g., images (Chen et al., 2020a) and languages (Radford et al., 2019). Especially, prior works have shown that representations learned with self-supervised learning are notably effective when fine-tuned or jointly learned with few labeled samples (Tian et al., 2020; Perez et al., 2021; Lee et al., 2021b; Lee & Shin, 2022).

Semi-supervised learning aims to train a model using limited labels. State-of-theart semi-supervised methods for image classification such as PAWS rely on selfsupervised representations learned with large-scale unlabeled but curated data. However, PAWS is often less effective when using real-world unlabeled data that is uncurated, e.g., contains out-of-class data. We propose RoPAWS, a robust extension of PAWS that can work with real-world unlabeled data. From this probabilistic perspective, we calibrate its prediction based on the densities of labeled and unlabeled data, which leads to a simple closed-form solution from the Bayes' rule. Semi-supervised learning aims to address the fundamental challenge of training models with limited labeled data by leveraging large-scale unlabeled data. Recent works exploit the success of selfsupervised learning (He et al., 2020; Chen et al., 2020a) in learning representations from unlabeled data for training large-scale semi-supervised models (Chen et al., 2020b; Cai et al., 2022). Instead of self-supervised pre-training followed by semi-supervised fine-tuning, PAWS (Assran et al., 2021) proposed a single-stage approach that combines supervised and self-supervised learning and achieves state-of-the-art accuracy and convergence speed. While PAWS can leverage curated unlabeled data, we empirically show that it is not robust to realworld uncurated data, which often contains out-of-class data. A common approach to tackle uncurated data in semi-supervised learning is to filter unlabeled data using out-of-distribution (OOD) classification (Chen et al., 2020d; Saito et al., 2021; Liu et al., 2022). However, OOD filtering methods did not fully utilize OOD data, which could be beneficial to learn the representations especially on large-scale realistic datasets. Furthermore, filtering OOD data could be ineffective since in-class and out-of-class data are often hard to discriminate in practical scenarios. To this end, we propose RoPAWS, a robust semi-supervised learning method that can leverage uncurated unlabeled data. PAWS predicts out-of-class data overconfidently in the known classes since it assigns the pseudo-label to nearby labeled data. To handle this, RoPAWS regularizes the pseudolabels by measuring the similarities between labeled and unlabeled data. These pseudo-labels are further calibrated by label propagation between unlabeled data. Figure 1 shows the conceptual illustration of RoPAWS and Figure 4 visualizes the learned representations. We first introduce a new interpretation of PAWS as a generative classifier, modeling densities over representation by kernel density estimation (KDE) (Rosenblatt, 1956).