Related papers: Transductive Learning with Multi-class Volume Appr…

We present a transductive learning algorithm that takes as input training examples from a distribution $P$ and arbitrary (unlabeled) test examples, possibly chosen by an adversary. This is unlike prior work that assumes that test examples…

We present the viewpoint that optimization problems encountered in machine learning can often be interpreted as minimizing a convex functional over a function space, but with a non-convex constraint set introduced by model parameterization.…

Large language models are capable of in-context learning, the ability to perform new tasks at test time using a handful of input-output examples, without parameter updates. We develop a universal approximation theory to elucidate how…

Self-learning is a classical approach for learning with both labeled and unlabeled observations which consists in giving pseudo-labels to unlabeled training instances with a confidence score over a predetermined threshold. At the same time,…

Most machine learning theory and practice is concerned with learning a single task. In this thesis it is argued that in general there is insufficient information in a single task for a learner to generalise well and that what is required…

Recognition of speech, and in particular the ability to generalize and learn from small sets of labelled examples like humans do, depends on an appropriate representation of the acoustic input. We formulate the problem of finding robust…

We study the problem of finding the Lowner-John ellipsoid, i.e., an ellipsoid with minimum volume that contains a given convex set. We reformulate the problem as a generalized copositive program, and use that reformulation to derive…

It is a well known fact that in $\mathbb{R}^n$ a subset of minimal perimeter $L$ among all sets of a given volume is also a set of maximal volume among all sets of the same perimeter $L$. This is called the reciprocity principle for…

Large language models (LLMs) perform in-context learning (ICL) with minimal supervised examples, which benefits various natural language processing (NLP) tasks. One of the critical research focus is the selection of prompt demonstrations.…

Hyperbolic spaces have increasingly been recognized for their outstanding performance in handling data with inherent hierarchical structures compared to their Euclidean counterparts. However, learning in hyperbolic spaces poses significant…

We consider the fundamental question of learnability of a hypotheses class in the supervised learning setting and in the general learning setting introduced by Vladimir Vapnik. We survey classic results characterizing learnability in term…

A common strategy in modern learning systems is to learn a representation that is useful for many tasks, a.k.a. representation learning. We study this strategy in the imitation learning setting for Markov decision processes (MDPs) where…

Transductive inference is an effective means of tackling the data deficiency problem in few-shot learning settings. A popular transductive inference technique for few-shot metric-based approaches, is to update the prototype of each class…

Let ${\bf K} = (K_1, ..., K_n)$ be an $n$-tuple of convex compact subsets in the Euclidean space $\R^n$, and let $V(\cdot)$ be the Euclidean volume in $\R^n$. The Minkowski polynomial $V_{{\bf K}}$ is defined as $V_{{\bf K}}(\lambda_1, ...…

Metric learning seeks perceptual embeddings where visually similar instances are close and dissimilar instances are apart, but learned representations can be sub-optimal when the distribution of intra-class samples is diverse and distinct…

We study a generalization of classical active learning to real-world settings with concrete prediction targets where sampling is restricted to an accessible region of the domain, while prediction targets may lie outside this region. We…

While existing end-to-end beamformers achieve impressive performance in various front-end speech processing tasks, they usually encapsulate the whole process into a black box and thus lack adequate interpretability. As an attempt to fill…

Recently, there has been a surge of interest in representation learning in hyperbolic spaces, driven by their ability to represent hierarchical data with significantly fewer dimensions than standard Euclidean spaces. However, the viability…

We propose a scalable method for semi-supervised (transductive) learning from massive network-structured datasets. Our approach to semi-supervised learning is based on representing the underlying hypothesis as a graph signal with small…

Contrastive learning produces coherent semantic feature embeddings by encouraging positive samples to cluster closely while separating negative samples. However, existing contrastive learning methods lack principled guarantees on coverage…