We study the fundamental problem of sequential probability assignment, also known as online learning with logarithmic loss, with respect to an arbitrary, possibly nonparametric hypothesis class. Our goal is to obtain a complexity measure for the hypothesis class that characterizes the minimax regret and to determine a general, minimax optimal algorithm.

Our approach establishes a general-purpose reduction from minimax rates for sequential probability assignment for smoothed adversaries to minimax rates for transductive learning. This leads to optimal (logarithmic) fast rates for parametric classes and classes with finite VC dimension.

Detecting out-of-distribution (OOD) samples is vital for developing machine learning based models for critical safety systems.

We study the problem of sequential probability assignment under logarithmic loss, both with and without side information. Our objective is to analyze the minimax regret -- a notion extensively studied in the literature -- in terms of geometric quantities, such as covering numbers and scale-sensitive dimensions. We show that the minimax regret for the case of no side information (equivalently, the Shtarkov sum) can be upper bounded in terms of sequential square-root entropy, a notion closely related to Hellinger distance. For the problem of sequential probability assignment with side information, we develop both upper and lower bounds based on the aforementioned entropy. The lower bound matches the upper bound, up to log factors, for classes in the Donsker regime (according to our definition of entropy).

Contrastive learning has gained significant attention in short text clustering, yet it has an inherent drawback of mistakenly identifying samples from the same category as negatives and then separating them in the feature space (false negative separation), which hinders the generation of superior representations. To generate more discriminative representations for efficient clustering, we propose a novel short text clustering method, called Discriminative Representation learning via \textbf{A}ttention-\textbf{E}nhanced \textbf{C}ontrastive \textbf{L}earning for Short Text Clustering (\textbf{AECL}). The \textbf{AECL} consists of two modules which are the pseudo-label generation module and the contrastive learning module. Both modules build a sample-level attention mechanism to capture similarity relationships between samples and aggregate cross-sample features to generate consistent representations. Then, the former module uses the more discriminative consistent representation to produce reliable supervision information for assist clustering, while the latter module explores similarity relationships and consistent representations optimize the construction of positive samples to perform similarity-guided contrastive learning, effectively addressing the false negative separation issue. Experimental results demonstrate that the proposed \textbf{AECL} outperforms state-of-the-art methods. If the paper is accepted, we will open-source the code.