Despite an extensive body of literature on deep learning optimization, our current understanding of what makes an optimization algorithm effective is fragmented. In particular, we do not understand well whether enhanced optimization translates to improved generalizability. Current research overlooks the inherent stochastic nature of stochastic gradient descent (SGD) and its variants, resulting in a lack of comprehensive benchmarking and insight into their statistical performance. This paper aims to address this gap by adopting a novel approach. Rather than solely evaluating the endpoint of individual optimization trajectories, we draw from an ensemble of trajectories to estimate the stationary distribution of stochastic optimizers. Our investigation encompasses a wide array of techniques, including SGD and its variants, flat-minima optimizers, and new algorithms we propose under the Basin Hopping framework. Through our evaluation, which encompasses synthetic functions with known minima and real-world problems in computer vision and natural language processing, we emphasize fair benchmarking under a statistical framework, comparing stationary distributions and establishing statistical significance. Our study uncovers several key findings regarding the relationship between training loss and hold-out accuracy, as well as the comparable performance of SGD, noise-enabled variants, and novel optimizers utilizing the BH framework. Notably, these algorithms demonstrate performance on par with flat-minima optimizers like SAM, albeit with half the gradient evaluations. We anticipate that our work will catalyze further exploration in deep learning optimization, encouraging a shift away from single-model approaches towards methodologies that acknowledge and leverage the stochastic nature of optimizers.

Language models (LMs) may appear insensitive to word order changes in natural language understanding (NLU) tasks. In this paper, we propose that linguistic redundancy can explain this phenomenon, whereby word order and other linguistic cues such as case markers provide overlapping and thus redundant information. Our hypothesis is that models exhibit insensitivity to word order when the order provides redundant information, and the degree of insensitivity varies across tasks. We quantify how informative word order is using mutual information (MI) between unscrambled and scrambled sentences. Our results show the effect that the less informative word order is, the more consistent the model's predictions are between unscrambled and scrambled sentences. We also find that the effect varies across tasks: for some tasks, like SST-2, LMs' prediction is almost always consistent with the original one even if the Pointwise-MI (PMI) changes, while for others, like RTE, the consistency is near random when the PMI gets lower, i.e., word order is really important.

Decision-makers are often experts of their domain and take actions based on their domain knowledge. Doctors, for instance, may prescribe treatments by predicting the likely outcome of each available treatment. Actions of an expert thus naturally encode part of their domain knowledge, and can help make inferences within the same domain: Knowing doctors try to prescribe the best treatment for their patients, we can tell treatments prescribed more frequently are likely to be more effective. Yet in machine learning, the fact that most decision-makers are experts is often overlooked, and "expertise" is seldom leveraged as an inductive bias. This is especially true for the literature on treatment effect estimation, where often the only assumption made about actions is that of overlap. In this paper, we argue that expertise - particularly the type of expertise the decision-makers of a domain are likely to have - can be informative in designing and selecting methods for treatment effect estimation. We formally define two types of expertise, predictive and prognostic, and demonstrate empirically that: (i) the prominent type of expertise in a domain significantly influences the performance of different methods in treatment effect estimation, and (ii) it is possible to predict the type of expertise present in a dataset, which can provide a quantitative basis for model selection.

Item Response Theory (IRT) models aim to assess latent abilities of $n$ examinees along with latent difficulty characteristics of $m$ test items from categorical data that indicates the quality of their corresponding answers. Classical psychometric assessments are based on a relatively small number of examinees and items, say a class of $200$ students solving an exam comprising $10$ problems. More recent global large scale assessments such as PISA, or internet studies, may lead to significantly increased numbers of participants. Additionally, in the context of Machine Learning where algorithms take the role of examinees and data analysis problems take the role of items, both $n$ and $m$ may become very large, challenging the efficiency and scalability of computations. To learn the latent variables in IRT models from large data, we leverage the similarity of these models to logistic regression, which can be approximated accurately using small weighted subsets called coresets. We develop coresets for their use in alternating IRT training algorithms, facilitating scalable learning from large data.

Real-world data is often incomplete and contains missing values. To train accurate models over real-world datasets, users need to spend a substantial amount of time and resources imputing and finding proper values for missing data items. In this paper, we demonstrate that it is possible to learn accurate models directly from data with missing values for certain training data and target models. We propose a unified approach for checking the necessity of data imputation to learn accurate models across various widely-used machine learning paradigms. We build efficient algorithms with theoretical guarantees to check this necessity and return accurate models in cases where imputation is unnecessary. Our extensive experiments indicate that our proposed algorithms significantly reduce the amount of time and effort needed for data imputation without imposing considerable computational overhead.

Average treatment effect estimation is the most central problem in causal inference with application to numerous disciplines. While many estimation strategies have been proposed in the literature, the statistical optimality of these methods has still remained an open area of investigation, especially in regimes where these methods do not achieve parametric rates. In this paper, we adopt the recently introduced structure-agnostic framework of statistical lower bounds, which poses no structural properties on the nuisance functions other than access to black-box estimators that achieve some statistical estimation rate. This framework is particularly appealing when one is only willing to consider estimation strategies that use non-parametric regression and classification oracles as black-box sub-processes. Within this framework, we prove the statistical optimality of the celebrated and widely used doubly robust estimators for both the Average Treatment Effect (ATE) and the Average Treatment Effect on the Treated (ATT), as well as weighted variants of the former, which arise in policy evaluation.

Optimization metrics are crucial for building recommendation systems at scale. However, an effective and efficient metric for practical use remains elusive. While Top-K ranking metrics are the gold standard for optimization, they suffer from significant computational overhead. Alternatively, the more efficient accuracy and AUC metrics often fall short of capturing the true targets of recommendation tasks, leading to suboptimal performance. To overcome this dilemma, we propose a new optimization metric, Lower-Left Partial AUC (LLPAUC), which is computationally efficient like AUC but strongly correlates with Top-K ranking metrics. Compared to AUC, LLPAUC considers only the partial area under the ROC curve in the Lower-Left corner to push the optimization focus on Top-K. We provide theoretical validation of the correlation between LLPAUC and Top-K ranking metrics and demonstrate its robustness to noisy user feedback. We further design an efficient point-wise recommendation loss to maximize LLPAUC and evaluate it on three datasets, validating its effectiveness and robustness.

Distributed optimization and learning has recently garnered great attention due to its wide applications in sensor networks, smart grids, machine learning, and so forth. Despite rapid development, existing distributed optimization and learning algorithms require each agent to exchange messages with its neighbors, which may expose sensitive information and raise significant privacy concerns. In this survey paper, we overview privacy-preserving distributed optimization and learning methods. We first discuss cryptography, differential privacy, and other techniques that can be used for privacy preservation and indicate their pros and cons for privacy protection in distributed optimization and learning. We believe that among these approaches, differential privacy is most promising due to its low computational and communication complexities, which are extremely appealing for modern learning based applications with high dimensions of optimization variables. We then introduce several differential-privacy algorithms that can simultaneously ensure privacy and optimization accuracy. Moreover, we provide example applications in several machine learning problems to confirm the real-world effectiveness of these algorithms. Finally, we highlight some challenges in this research domain and discuss future directions.

Multi-domain generalization (mDG) is universally aimed to minimize the discrepancy between training and testing distributions to enhance marginal-to-label distribution mapping. However, existing mDG literature lacks a general learning objective paradigm and often imposes constraints on static target marginal distributions. In this paper, we propose to leverage a $Y$-mapping to relax the constraint. We rethink the learning objective for mDG and design a new \textbf{general learning objective} to interpret and analyze most existing mDG wisdom. This general objective is bifurcated into two synergistic amis: learning domain-independent conditional features and maximizing a posterior. Explorations also extend to two effective regularization terms that incorporate prior information and suppress invalid causality, alleviating the issues that come with relaxed constraints. We theoretically contribute an upper bound for the domain alignment of domain-independent conditional features, disclosing that many previous mDG endeavors actually \textbf{optimize partially the objective} and thus lead to limited performance. As such, our study distills a general learning objective into four practical components, providing a general, robust, and flexible mechanism to handle complex domain shifts. Extensive empirical results indicate that the proposed objective with $Y$-mapping leads to substantially better mDG performance in various downstream tasks, including regression, segmentation, and classification.

Pixel-aligned implicit models, such as PIFu, PIFuHD, and ICON, are used for single-view clothed human reconstruction. These models need to be trained using a sampling training scheme. Existing sampling training schemes either fail to capture thin surfaces (e.g. ears, fingers) or cause noisy artefacts in reconstructed meshes. To address these problems, we introduce Fine Structured-Aware Sampling (FSS), a new sampling training scheme to train pixel-aligned implicit models for single-view human reconstruction. FSS resolves the aforementioned problems by proactively adapting to the thickness and complexity of surfaces. In addition, unlike existing sampling training schemes, FSS shows how normals of sample points can be capitalized in the training process to improve results. Lastly, to further improve the training process, FSS proposes a mesh thickness loss signal for pixel-aligned implicit models. It becomes computationally feasible to introduce this loss once a slight reworking of the pixel-aligned implicit function framework is carried out. Our results show that our methods significantly outperform SOTA methods qualitatively and quantitatively. Our code is publicly available at https://github.com/kcyt/FSS.