Learning DNF Expressions from Fourier Spectrum

Since its introduction by Valiant in 1984, PAC learning of DNF expressions remains one of the central problems in learning theory. We consider this problem in the setting where the underlying distribution is uniform, or more generally, a product distribution. Kalai, Samorodnitsky and Teng (2009) showed that in this setting a DNF expression can be efficiently approximated from its "heavy" low-degree Fourier coefficients alone. This is in contrast to previous approaches where boosting was used and thus Fourier coefficients of the target function modified by various distributions were needed. This property is crucial for learning of DNF expressions over smoothed product distributions, a learning model introduced by Kalai et al. (2009) and inspired by the seminal smoothed analysis model of Spielman and Teng (2001). We introduce a new approach to learning (or approximating) a polynomial threshold functions which is based on creating a function with range [-1,1] that approximately agrees with the unknown function on low-degree Fourier coefficients. We then describe conditions under which this is sufficient for learning polynomial threshold functions. Our approach yields a new, simple algorithm for approximating any polynomial-size DNF expression from its "heavy" low-degree Fourier coefficients alone. Our algorithm greatly simplifies the proof of learnability of DNF expressions over smoothed product distributions. We also describe an application of our algorithm to learning monotone DNF expressions over product distributions. Building on the work of Servedio (2001), we give an algorithm that runs in time \poly((s \cdot \log{(s/\eps)})^{\log{(s/\eps)}}, n), where $s$ is the size of the target DNF expression and \eps is the accuracy. This improves on \poly((s \cdot \log{(ns/\eps)})^{\log{(s/\eps)} \cdot \log{(1/\eps)}}, n) bound of Servedio (2001).Comment: Appears in Conference on Learning Theory (COLT) 201

Subsampled Power Iteration: a Unified Algorithm for Block Models and Planted CSP's

We present an algorithm for recovering planted solutions in two well-known models, the stochastic block model and planted constraint satisfaction problems, via a common generalization in terms of random bipartite graphs. Our algorithm matches up to a constant factor the best-known bounds for the number of edges (or constraints) needed for perfect recovery and its running time is linear in the number of edges used. The time complexity is significantly better than both spectral and SDP-based approaches. The main contribution of the algorithm is in the case of unequal sizes in the bipartition (corresponding to odd uniformity in the CSP). Here our algorithm succeeds at a significantly lower density than the spectral approaches, surpassing a barrier based on the spectral norm of a random matrix. Other significant features of the algorithm and analysis include (i) the critical use of power iteration with subsampling, which might be of independent interest; its analysis requires keeping track of multiple norms of an evolving solution (ii) it can be implemented statistically, i.e., with very limited access to the input distribution (iii) the algorithm is extremely simple to implement and runs in linear time, and thus is practical even for very large instances

A Survey on Deep Multi-modal Learning for Body Language Recognition and Generation

Body language (BL) refers to the non-verbal communication expressed through physical movements, gestures, facial expressions, and postures. It is a form of communication that conveys information, emotions, attitudes, and intentions without the use of spoken or written words. It plays a crucial role in interpersonal interactions and can complement or even override verbal communication. Deep multi-modal learning techniques have shown promise in understanding and analyzing these diverse aspects of BL. The survey emphasizes their applications to BL generation and recognition. Several common BLs are considered i.e., Sign Language (SL), Cued Speech (CS), Co-speech (CoS), and Talking Head (TH), and we have conducted an analysis and established the connections among these four BL for the first time. Their generation and recognition often involve multi-modal approaches. Benchmark datasets for BL research are well collected and organized, along with the evaluation of SOTA methods on these datasets. The survey highlights challenges such as limited labeled data, multi-modal learning, and the need for domain adaptation to generalize models to unseen speakers or languages. Future research directions are presented, including exploring self-supervised learning techniques, integrating contextual information from other modalities, and exploiting large-scale pre-trained multi-modal models. In summary, this survey paper provides a comprehensive understanding of deep multi-modal learning for various BL generations and recognitions for the first time. By analyzing advancements, challenges, and future directions, it serves as a valuable resource for researchers and practitioners in advancing this field. n addition, we maintain a continuously updated paper list for deep multi-modal learning for BL recognition and generation: https://github.com/wentaoL86/awesome-body-language

LIPIcs, Volume 251, ITCS 2023, Complete Volume

LIPIcs, Volume 251, ITCS 2023, Complete Volum