Choosing where to search matters. A time-tested path in the quest for new products or processes isthrough experimental optimization.

To this end, we propose DrugRec, a causal inference baseddrugrecommendationmodel.

A wide range of applications from Auto-ML [15] to chemistry [6] and drug design [3] require optimizing ablack-boxobjectivefunction (i.e.,itsclosed-form expression, gradient, andconvexity are unknown) through observing noisy function evaluations.

Table 2 shows theresults, likewisewithUMPIREasbest.

Survival analysis is a statistical technique used to estimate the time until an event occurs. Although it is applied across a wide range of fields, adjusting for reporting delays under practical constraints remains a significant challenge in the insurance industry. Such delays render event occurrences unobservable when their reports are subject to right censoring. This issue becomes particularly critical when estimating hazard rates for newly enrolled cohorts with limited follow-up due to administrative censoring. Our study addresses this challenge by jointly modeling the parametric hazard functions of event occurrences and report timings. The joint probability distribution is marginalized over the latent event occurrence status. We construct an estimator for the proposed survival model and establish its asymptotic consistency. Furthermore, we develop an expectation-maximization algorithm to compute its estimates. Using these findings, we propose a two-stage estimation procedure based on a parametric proportional hazards model to evaluate observations subject to administrative censoring. Experimental results demonstrate that our method effectively improves the timeliness of risk evaluation for newly enrolled cohorts.

In Online Convex Optimization (OCO), when the stochastic gradient has a finite variance, many algorithms provably work and guarantee a sublinear regret. However, limited results are known if the gradient estimate has a heavy tail, i.e., the stochastic gradient only admits a finite $\mathsf{p}$-th central moment for some $\mathsf{p}\in\left(1,2\right]$. Motivated by it, this work examines different old algorithms for OCO (e.g., Online Gradient Descent) in the more challenging heavy-tailed setting. Under the standard bounded domain assumption, we establish new regrets for these classical methods without any algorithmic modification. Remarkably, these regret bounds are fully optimal in all parameters (can be achieved even without knowing $\mathsf{p}$), suggesting that OCO with heavy tails can be solved effectively without any extra operation (e.g., gradient clipping). Our new results have several applications. A particularly interesting one is the first provable convergence result for nonsmooth nonconvex optimization under heavy-tailed noise without gradient clipping. Furthermore, we explore broader settings (e.g., smooth OCO) and extend our ideas to optimistic algorithms to handle different cases simultaneously.

We study the stochastic linear bandits with heavy-tailed noise. Two principled strategies for handling heavy-tailed noise, truncation and median-of-means, have been introduced to heavy-tailed bandits. Nonetheless, these methods rely on specific noise assumptions or bandit structures, limiting their applicability to general settings. The recent work [Huang et al.2024] develops a soft truncation method via the adaptive Huber regression to address these limitations. However, their method suffers undesired computational cost: it requires storing all historical data and performing a full pass over these data at each round. In this paper, we propose a \emph{one-pass} algorithm based on the online mirror descent framework. Our method updates using only current data at each round, reducing the per-round computational cost from $\widetilde{\mathcal{O}}(t \log T)$ to $\widetilde{\mathcal{O}}(1)$ with respect to current round $t$ and the time horizon $T$, and achieves a near-optimal and variance-aware regret of order $\widetilde{\mathcal{O}}\big(d T^{\frac{1-\epsilon}{2(1+\epsilon)}} \sqrt{\sum_{t=1}^T \nu_t^2} + d T^{\frac{1-\epsilon}{2(1+\epsilon)}}\big)$ where $d$ is the dimension and $\nu_t^{1+\epsilon}$ is the $(1+\epsilon)$-th central moment of reward at round $t$.

The present paper deals with construction of newly family of Neural Network operators, that is, Steklov Neural Network operators. By using Steklov type integral, we introduce a new version of Neural Network operators and we obtain some convergence theorems for the family, such as, pointwise and uniform convergence, rate of convergence via modulus of continuity.

Distributions in spatial model often exhibit localized features. Intuitively, this locality implies a low intrinsic dimensionality, which can be exploited for efficient approximation and computation of complex distributions. However, existing approximation theory mainly considers the joint distributions, which does not guarantee that the marginal errors are small. In this work, we establish a dimension independent error bound for the marginals of approximate distributions. This $\ell_\infty$-approximation error is obtained using Stein's method, and we propose a $\delta$-locality condition that quantifies the degree of localization in a distribution. We also show how $\delta$-locality can be derived from different conditions that characterize the distribution's locality. Our $\ell_\infty$ bound motivates the localization of existing approximation methods to respect the locality. As examples, we show how to use localized likelihood-informed subspace method and localized score matching, which not only avoid dimension dependence in the approximation error, but also significantly reduce the computational cost due to the local and parallel implementation based on the localized structure.

Score matching estimators have gained widespread attention in recent years partly because they are free from calculating the integral of normalizing constant, thereby addressing the computational challenges in maximum likelihood estimation (MLE). Some existing works have proposed score matching estimators for point processes. However, this work demonstrates that the incompleteness of the estimators proposed in those works renders them applicable only to specific problems, and they fail for more general point processes. To address this issue, this work introduces the weighted score matching estimator to point processes. Theoretically, we prove the consistency of our estimator and establish its rate of convergence. Experimental results indicate that our estimator accurately estimates model parameters on synthetic data and yields results consistent with MLE on real data. In contrast, existing score matching estimators fail to perform effectively.