Gibbs samplers [12] are a family of Markov Chain Monte Carlo (MCMC) algorithms [10] commonly used in various scientific fields. In the context of Bayesian Statistics, they are routinely employed to draw samples from posterior distributions of unknown parameters conditional to the observed data [28, 37]. Like most MCMC methods, they are guaranteed to converge to the correct posterior distribution as the number of iterations tends to infinity under mild assumptions [54]. However, understanding how quickly this convergence occurs, for example by quantifying the so-called mixing time of the Markov chain generated by the algorithm, is in general a hard task. In this paper we address this question for Gibbs samplers targeting certain classes of high-dimensional Bayesian hierarchical models. Analysing convergence properties, such as mixing times, is the key technical step needed to rigorously quantify the computational cost of MCMC algorithms.

This article describes an efficient method to learn distributed representations, also known as embeddings. This is accomplished minimizing an objective function similar to the one introduced in the Word2Vec algorithm and later adopted in several works. The optimization computational bottleneck is the calculation of the softmax normalization constants for which a number of operations scaling quadratically with the sample size is required. This complexity is unsuited for large datasets and negative sampling is a popular workaround, allowing one to obtain distributed representations in linear time with respect to the sample size. Negative sampling consists, however, in a change of the loss function and hence solves a different optimization problem from the one originally proposed. Our contribution is to show that the sotfmax normalization constants can be estimated in linear time, allowing us to design an efficient optimization strategy to learn distributed representations. We test our approximation on two popular applications related to word and node embeddings. The results evidence competing performance in terms of accuracy with respect to negative sampling with a remarkably lower computational time.

We introduce Three Towers (3T), a flexible method to improve the contrastive learning of vision-language models by incorporating pretrained image classifiers. While contrastive models are usually trained from scratch, LiT (Zhai et al., 2022) has recently shown performance gains from using pretrained classifier embeddings. However, LiT directly replaces the image tower with the frozen embeddings, excluding any potential benefits from training the image tower contrastively. With 3T, we propose a more flexible strategy that allows the image tower to benefit from both pretrained embeddings and contrastive training. To achieve this, we introduce a third tower that contains the frozen pretrained embeddings, and we encourage alignment between this third tower and the main image-text towers. Empirically, 3T consistently improves over LiT and the CLIP-style from-scratch baseline for retrieval tasks. For classification, 3T reliably improves over the from-scratch baseline, and while it underperforms relative to LiT for JFT-pretrained models, it outperforms LiT for ImageNet-21k and Places365 pretraining.

It has become increasingly common nowadays to collect observations of feature and response pairs from different environments. As a consequence, one has to apply learned predictors to data with a different distribution due to distribution shifts. One principled approach is to adopt the structural causal models to describe training and test models, following the invariance principle which says that the conditional distribution of the response given its predictors remains the same across environments. However, this principle might be violated in practical settings when the response is intervened. A natural question is whether it is still possible to identify other forms of invariance to facilitate prediction in unseen environments. To shed light on this challenging scenario, we focus on linear structural causal models (SCMs) and introduce invariant matching property (IMP), an explicit relation to capture interventions through an additional feature, leading to an alternative form of invariance that enables a unified treatment of general interventions on the response as well as the predictors. We analyze the asymptotic generalization errors of our method under both the discrete and continuous environment settings, where the continuous case is handled by relating it to the semiparametric varying coefficient models. We present algorithms that show competitive performance compared to existing methods over various experimental settings including a COVID dataset.

To the best of our knowledge, there are no methods today for training differentially private regression models on sparse input data. To remedy this, we adapt the Frank-Wolfe algorithm for $L_1$ penalized linear regression to be aware of sparse inputs and to use them effectively. In doing so, we reduce the training time of the algorithm from $\mathcal{O}( T D S + T N S)$ to $\mathcal{O}(N S + T \sqrt{D} \log{D} + T S^2)$, where $T$ is the number of iterations and a sparsity rate $S$ of a dataset with $N$ rows and $D$ features. Our results demonstrate that this procedure can reduce runtime by a factor of up to $2,200\times$, depending on the value of the privacy parameter $\epsilon$ and the sparsity of the dataset.

Recently, spam on online social networks has attracted attention in the research and business world. Twitter has become the preferred medium to spread spam content. Many research efforts attempted to encounter social networks spam. Twitter brought extra challenges represented by the feature space size, and imbalanced data distributions. Usually, the related research works focus on part of these main challenges or produce black-box models. In this paper, we propose a modified genetic algorithm for simultaneous dimensionality reduction and hyper parameter optimization over imbalanced datasets. The algorithm initialized an eXtreme Gradient Boosting classifier and reduced the features space of tweets dataset; to generate a spam prediction model. The model is validated using a 50 times repeated 10-fold stratified cross-validation, and analyzed using nonparametric statistical tests. The resulted prediction model attains on average 82.32\% and 92.67\% in terms of geometric mean and accuracy respectively, utilizing less than 10\% of the total feature space. The empirical results show that the modified genetic algorithm outperforms $Chi^2$ and $PCA$ feature selection methods. In addition, eXtreme Gradient Boosting outperforms many machine learning algorithms, including BERT-based deep learning model, in spam prediction. Furthermore, the proposed approach is applied to SMS spam modeling and compared to related works.

We employ a characterization of linguistic complexity from psycholinguistic and language acquisition research to develop data-driven curricula to understand the underlying linguistic knowledge that models learn to address NLP tasks. The novelty of our approach is in the development of linguistic curricula derived from data, existing knowledge about linguistic complexity, and model behavior during training. By analyzing several benchmark NLP datasets, our curriculum learning approaches identify sets of linguistic metrics (indices) that inform the challenges and reasoning required to address each task. Our work will inform future research in all NLP areas, allowing linguistic complexity to be considered early in the research and development process. In addition, our work prompts an examination of gold standards and fair evaluation in NLP.

This paper proposes a novel contrastive learning framework, called FOCAL, for extracting comprehensive features from multimodal time-series sensing signals through self-supervised training. Existing multimodal contrastive frameworks mostly rely on the shared information between sensory modalities, but do not explicitly consider the exclusive modality information that could be critical to understanding the underlying sensing physics. Besides, contrastive frameworks for time series have not handled the temporal information locality appropriately. FOCAL solves these challenges by making the following contributions: First, given multimodal time series, it encodes each modality into a factorized latent space consisting of shared features and private features that are orthogonal to each other. The shared space emphasizes feature patterns consistent across sensory modalities through a modal-matching objective. In contrast, the private space extracts modality-exclusive information through a transformation-invariant objective. Second, we propose a temporal structural constraint for modality features, such that the average distance between temporally neighboring samples is no larger than that of temporally distant samples. Extensive evaluations are performed on four multimodal sensing datasets with two backbone encoders and two classifiers to demonstrate the superiority of FOCAL. It consistently outperforms the state-of-the-art baselines in downstream tasks with a clear margin, under different ratios of available labels. The code and self-collected dataset are available at https://github.com/tomoyoshki/focal.

Large language models (LLMs) have significantly improved various aspects of our daily lives. These models have impacted numerous domains, from healthcare to education, enhancing productivity, decision-making processes, and accessibility. As a result, they have influenced and, to some extent, reshaped people's lifestyles. However, the quadratic complexity of attention in transformer architectures poses a challenge when scaling up these models for processing long textual contexts. This issue makes it impractical to train very large models on lengthy texts or use them efficiently during inference. While a recent study by [KMZ23] introduced a technique that replaces the softmax with a polynomial function and polynomial sketching to speed up attention mechanisms, the theoretical understandings of this new approach are not yet well understood. In this paper, we offer a theoretical analysis of the expressive capabilities of polynomial attention. Our study reveals a disparity in the ability of high-degree and low-degree polynomial attention. Specifically, we construct two carefully designed datasets, namely $\mathcal{D}_0$ and $\mathcal{D}_1$, where $\mathcal{D}_1$ includes a feature with a significantly larger value compared to $\mathcal{D}_0$. We demonstrate that with a sufficiently high degree $\beta$, a single-layer polynomial attention network can distinguish between $\mathcal{D}_0$ and $\mathcal{D}_1$. However, with a low degree $\beta$, the network cannot effectively separate the two datasets. This analysis underscores the greater effectiveness of high-degree polynomials in amplifying large values and distinguishing between datasets. Our analysis offers insight into the representational capacity of polynomial attention and provides a rationale for incorporating higher-degree polynomials in attention mechanisms to capture intricate linguistic correlations.

Optimal topology synthesis is generally resource-intensive and time-consuming to be done in real time for large ad-hoc robot networks. One should only perform topology re-computations if the probability of topology recoverability after the occurrence of any fault surpasses that of its irrecoverability. We formulate this problem as a binary classification problem. Then, we develop a two-pathway data-driven model based on Bayesian Gaussian mixture models that predicts the solution to a typical problem by two different pre-fault and post-fault prediction pathways. The results, obtained by the integration of the predictions of those pathways, clearly indicate the success of our model in solving the topology (ir)recoverability prediction problem compared to the best of current strategies found in the literature.