Recently, encoder-only pre-trained models such as BERT have been successfully applied in automated essay scoring (AES) to predict a single overall score. However, studies have yet to explore these models in multi-trait AES, possibly due to the inefficiency of replicating BERT-based models for each trait. Breaking away from the existing sole use of encoder, we propose an autoregressive prediction of multi-trait scores (ArTS), incorporating a decoding process by leveraging the pre-trained T5. Unlike prior regression or classification methods, we redefine AES as a score-generation task, allowing a single model to predict multiple scores. During decoding, the subsequent trait prediction can benefit by conditioning on the preceding trait scores. Experimental results proved the efficacy of ArTS, showing over 5% average improvements in both prompts and traits.

We consider an adversarial formulation of the problem of predicting a time series with square loss. The aim is to predict an arbitrary sequence of vectors almost as well as the best smooth comparator sequence in retrospect. Our approach allows natural measures of smoothness such as the squared norm of increments. More generally, we consider a linear time series model and penalize the comparator sequence through the energy of the implied driving noise terms. We derive the minimax strategy for all problems of this type and show that it can be implemented efficiently. The optimal predictions are linear in the previous observations. We obtain an explicit expression for the regret in terms of the parameters defining the problem. For typical, simple definitions of smoothness, the computation of the optimal predictions involves only sparse matrices. In the case of norm-constrained data, where the smoothness is defined in terms of the squared norm of the comparator's increments, we show that the regret grows as T/ λ

Convex potential minimisation is the de facto approach to binary classification. However, Long and Servedio [2010] proved that under symmetric label noise (SLN), minimisation of any convex potential over a linear function class can result in classification performance equivalent to random guessing. This ostensibly shows that convex losses are not SLN-robust. In this paper, we propose a convex, classification-calibrated loss and prove that it is SLN-robust. The loss avoids the Long and Servedio [2010] result by virtue of being negatively unbounded. The loss is a modification of the hinge loss, where one does not clamp at zero; hence, we call it the unhinged loss.

Experiments on small datasets for various problems including regression, classification, Log Gaussian Cox processes, and warped GPs show that our method can perform as well as the full method under high sparsity levels.

Spectral clustering and co-clustering are well-known techniques in data analysis, and recent work has extended spectral clustering to square, symmetric tensors and hypermatrices derived from a network. We develop a new tensor spectral co-clustering method that simultaneously clusters the rows, columns, and slices of a nonnegative three-mode tensor and generalizes to tensors with any number of modes. The algorithm is based on a new random walk model which we call the super-spacey random surfer. We show that our method out-performs state-of-the-art co-clustering methods on several synthetic datasets with ground truth clusters and then use the algorithm to analyze several real-world datasets.

We introduce the study of fairness in multi-armed bandit problems. Our fairness definition demands that, given a pool of applicants, a worse applicant is never favored over a better one, despite a learning algorithm's uncertainty over the true payoffs. In the classic stochastic bandits problem we provide a provably fair algorithm based on "chained" confidence intervals, and prove a cumulative regret bound with a cubic dependence on the number of arms. We further show that any fair algorithm must have such a dependence, providing a strong separation between fair and unfair learning that extends to the general contextual case. In the general contextual case, we prove a tight connection between fairness and the KWIK (Knows What It Knows) learning model: a KWIK algorithm for a class of functions can be transformed into a provably fair contextual bandit algorithm and vice versa. This tight connection allows us to provide a provably fair algorithm for the linear contextual bandit problem with a polynomial dependence on the dimension, and to show (for a different class of functions) a worst-case exponential gap in regret between fair and non-fair learning algorithms.

Nyström method has been successfully used to improve the computational efficiency of kernel ridge regression (KRR). Recently, theoretical analysis of Nyström KRR, including generalization bound and convergence rate, has been established based on reproducing kernel Hilbert space (RKHS) associated with the symmetric positive semi-definite kernel. However, in real world applications, RKHS is not always optimal and kernel function is not necessary to be symmetric or positive semi-definite.

In this paper, we develop a novel homotopy smoothing (HOPS) algorithm for solving a family of non-smooth problems that is composed of a non-smooth term with an explicit max-structure and a smooth term or a simple non-smooth term whose proximal mapping is easy to compute. The best known iteration complexity for solving such non-smooth optimization problems is O(1/ɛ) without any assumption on the strong convexity.

The correlation between events is ubiquitous and important for temporal events modelling. In many cases, the correlation exists between not only events' emitted observations, but also their arrival times. State space models (e.g., hidden Markov model) and stochastic interaction point process models (e.g., Hawkes process) have been studied extensively yet separately for the two types of correlations in the past. In this paper, we propose a Bayesian nonparametric approach that considers both types of correlations via unifying and generalizing the hidden semi-Markov model and interaction point process model. The proposed approach can simultaneously model both the observations and arrival times of temporal events, and automatically determine the number of latent states from data.

We consider the problem of building continuous occupancy representations in dynamic environments for robotics applications. The problem has hardly been discussed previously due to the complexity of patterns in urban environments, which have both spatial and temporal dependencies. We address the problem as learning a kernel classifier on an efficient feature space. The key novelty of our approach is the incorporation of variations in the time domain into the spatial domain. We propose a method to propagate motion uncertainty into the kernel using a hierarchical model. The main benefit of this approach is that it can directly predict the occupancy state of the map in the future from past observations, being a valuable tool for robot trajectory planning under uncertainty. Our approach preserves the main computational benefits of static Hilbert maps -- using stochastic gradient descent for fast optimization of model parameters and incremental updates as new data are captured. Experiments conducted in road intersections of an urban environment demonstrated that spatio-temporal Hilbert maps can accurately model changes in the map while outperforming other techniques on various aspects.