Open set recognition is designed to identify known classes and to reject unknown classes simultaneously. Specifically, identifying known classes and rejecting unknown classes correspond to reducing the empirical risk and the open space risk, respectively. First, the motorial prototype framework (MPF) is proposed, which classifies known classes according to the prototype classification idea. Moreover, a motorial margin constraint term is added into the loss function of the MPF, which can further improve the clustering compactness of known classes in the feature space to reduce both risks. Second, this paper proposes the adversarial motorial prototype framework (AMPF) based on the MPF. On the one hand, this model can generate adversarial samples and add these samples into the training phase; on the other hand, it can further improve the differential mapping ability of the model to known and unknown classes with the adversarial motion of the margin constraint radius. Finally, this paper proposes an upgraded version of the AMPF, AMPF++, which adds much more generated unknown samples into the training phase. In this paper, a large number of experiments prove that the performance of the proposed models is superior to that of other current works.

A dynamic treatment regimen (DTR) is a set of decision rules to personalize treatments for an individual using their medical history. The Q-learning based Q-shared algorithm has been used to develop DTRs that involve decision rules shared across multiple stages of intervention. We show that the existing Q-shared algorithm can suffer from non-convergence due to the use of linear models in the Q-learning setup, and identify the condition in which Q-shared fails. Leveraging properties from expansion-constrained ordinary least-squares, we give a penalized Q-shared algorithm that not only converges in settings that violate the condition, but can outperform the original Q-shared algorithm even when the condition is satisfied. We give evidence for the proposed method in a real-world application and several synthetic simulations.

Hierarchical Bayesian methods enable information sharing across multiple related regression problems. While standard practice is to model regression parameters (effects) as (1) exchangeable across datasets and (2) correlated to differing degrees across covariates, we show that this approach exhibits poor statistical performance when the number of covariates exceeds the number of datasets. For instance, in statistical genetics, we might regress dozens of traits (defining datasets) for thousands of individuals (responses) on up to millions of genetic variants (covariates). When an analyst has more covariates than datasets, we argue that it is often more natural to instead model effects as (1) exchangeable across covariates and (2) correlated to differing degrees across datasets. To this end, we propose a hierarchical model expressing our alternative perspective. We devise an empirical Bayes estimator for learning the degree of correlation between datasets. We develop theory that demonstrates that our method outperforms the classic approach when the number of covariates dominates the number of datasets, and corroborate this result empirically on several high-dimensional multiple regression and classification problems.

Understanding an agent's priorities by observing their behavior is critical for transparency and accountability in decision processes, such as in healthcare. While conventional approaches to policy learning almost invariably assume stationarity in behavior, this is hardly true in practice: Medical practice is constantly evolving, and clinical professionals are constantly fine-tuning their priorities. We desire an approach to policy learning that provides (1) interpretable representations of decision-making, accounts for (2) non-stationarity in behavior, as well as operating in an (3) offline manner. First, we model the behavior of learning agents in terms of contextual bandits, and formalize the problem of inverse contextual bandits (ICB). Second, we propose two algorithms to tackle ICB, each making varying degrees of assumptions regarding the agent's learning strategy. Finally, through both real and simulated data for liver transplantations, we illustrate the applicability and explainability of our method, as well as validating its accuracy.

We present a winning method of the IEEE DataPort Competition on Day-Ahead Electricity Demand Forecasting: Post-COVID Paradigm. The day-ahead load forecasting approach is based on online forecast combination of multiple point prediction models. It contains four steps: i) data cleaning and preprocessing, ii) a holiday adjustment procedure, iii) training of individual forecasting models, iv) forecast combination by smoothed Bernstein Online Aggregation (BOA). The approach is flexible and can quickly adopt to new energy system situations as they occurred during and after COVID-19 shutdowns. The pool of individual prediction models ranges from rather simple time series models to sophisticated models like generalized additive models (GAMs) and high-dimensional linear models estimated by lasso. They incorporate autoregressive, calendar and weather effects efficiently. All steps contain novel concepts that contribute to the excellent forecasting performance of the proposed method. This holds particularly for the holiday adjustment procedure and the fully adaptive smoothed BOA approach.

Time series forecasting is an important problem across many domains, playing a crucial role in multiple real-world applications. In this paper, we propose a forecasting architecture that combines deep autoregressive models with a Spectral Attention (SA) module, which merges global and local frequency domain information in the model's embedded space. By characterizing in the spectral domain the embedding of the time series as occurrences of a random process, our method can identify global trends and seasonality patterns. Two spectral attention models, global and local to the time series, integrate this information within the forecast and perform spectral filtering to remove time series's noise. The proposed architecture has a number of useful properties: it can be effectively incorporated into well-know forecast architectures, requiring a low number of parameters and producing interpretable results that improve forecasting accuracy. We test the Spectral Attention Autoregressive Model (SAAM) on several well-know forecast datasets, consistently demonstrating that our model compares favorably to state-of-the-art approaches.

We formulate the problem of induced domain adaptation (IDA) when the underlying distribution/domain shift is introduced by the model being deployed. Our formulation is motivated by applications where the deployed machine learning models interact with human agents, and will ultimately face responsive and interactive data distributions. We formalize the discussions of the transferability of learning in our IDA setting by studying how the model trained on the available source distribution (data) would translate to the performance on the induced domain. We provide both upper bounds for the performance gap due to the induced domain shift, as well as lower bound for the trade-offs a classifier has to suffer on either the source training distribution or the induced target distribution. We provide further instantiated analysis for two popular domain adaptation settings with covariate shift and label shift. We highlight some key properties of IDA, as well as computational and learning challenges.

We address the problem of model selection for the finite horizon episodic Reinforcement Learning (RL) problem where the transition kernel $P^*$ belongs to a family of models $\mathcal{P}^*$ with finite metric entropy. In the model selection framework, instead of $\mathcal{P}^*$, we are given $M$ nested families of transition kernels $\cP_1 \subset \cP_2 \subset \ldots \subset \cP_M$. We propose and analyze a novel algorithm, namely \emph{Adaptive Reinforcement Learning (General)} (\texttt{ARL-GEN}) that adapts to the smallest such family where the true transition kernel $P^*$ lies. \texttt{ARL-GEN} uses the Upper Confidence Reinforcement Learning (\texttt{UCRL}) algorithm with value targeted regression as a blackbox and puts a model selection module at the beginning of each epoch. Under a mild separability assumption on the model classes, we show that \texttt{ARL-GEN} obtains a regret of $\Tilde{\mathcal{O}}(d_{\mathcal{E}}^*H^2+\sqrt{d_{\mathcal{E}}^* \mathbb{M}^* H^2 T})$, with high probability, where $H$ is the horizon length, $T$ is the total number of steps, $d_{\mathcal{E}}^*$ is the Eluder dimension and $\mathbb{M}^*$ is the metric entropy corresponding to $\mathcal{P}^*$. Note that this regret scaling matches that of an oracle that knows $\mathcal{P}^*$ in advance. We show that the cost of model selection for \texttt{ARL-GEN} is an additive term in the regret having a weak dependence on $T$. Subsequently, we remove the separability assumption and consider the setup of linear mixture MDPs, where the transition kernel $P^*$ has a linear function approximation. With this low rank structure, we propose novel adaptive algorithms for model selection, and obtain (order-wise) regret identical to that of an oracle with knowledge of the true model class.

The divide-and-conquer method has been widely used for estimating large-scale kernel ridge regression estimates. Unfortunately, when the response variable is highly skewed, the divide-and-conquer kernel ridge regression (dacKRR) may overlook the underrepresented region and result in unacceptable results. We develop a novel response-adaptive partition strategy to overcome the limitation. In particular, we propose to allocate the replicates of some carefully identified informative observations to multiple nodes (local processors). The idea is analogous to the popular oversampling technique. Although such a technique has been widely used for addressing discrete label skewness, extending it to the dacKRR setting is nontrivial. We provide both theoretical and practical guidance on how to effectively over-sample the observations under the dacKRR setting. Furthermore, we show the proposed estimate has a smaller asymptotic mean squared error (AMSE) than that of the classical dacKRR estimate under mild conditions. Our theoretical findings are supported by both simulated and real-data analyses.

We study differentially private stochastic optimization in convex and non-convex settings. For the convex case, we focus on the family of non-smooth generalized linear losses (GLLs). Our algorithm for the $\ell_2$ setting achieves optimal excess population risk in near-linear time, while the best known differentially private algorithms for general convex losses run in super-linear time. Our algorithm for the $\ell_1$ setting has nearly-optimal excess population risk $\tilde{O}\big(\sqrt{\frac{\log{d}}{n}}\big)$, and circumvents the dimension dependent lower bound of [AFKT21] for general non-smooth convex losses. In the differentially private non-convex setting, we provide several new algorithms for approximating stationary points of the population risk. For the $\ell_1$-case with smooth losses and polyhedral constraint, we provide the first nearly dimension independent rate, $\tilde O\big(\frac{\log^{2/3}{d}}{{n^{1/3}}}\big)$ in linear time. For the constrained $\ell_2$-case, with smooth losses, we obtain a linear-time algorithm with rate $\tilde O\big(\frac{1}{n^{3/10}d^{1/10}}+\big(\frac{d}{n^2}\big)^{1/5}\big)$. Finally, for the $\ell_2$-case we provide the first method for {\em non-smooth weakly convex} stochastic optimization with rate $\tilde O\big(\frac{1}{n^{1/4}}+\big(\frac{d}{n^2}\big)^{1/6}\big)$ which matches the best existing non-private algorithm when $d= O(\sqrt{n})$. We also extend all our results above for the non-convex $\ell_2$ setting to the $\ell_p$ setting, where $1 < p \leq 2$, with only polylogarithmic (in the dimension) overhead in the rates.