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We prove impossibility results for adaptivity in non-smooth stochastic convex optimization. Given a set of problem parameters we wish to adapt to, we define a "price of adaptivity" (PoA) that, roughly speaking, measures the multiplicative increase in suboptimality due to uncertainty in these parameters. When the initial distance to the optimum is unknown but a gradient norm bound is known, we show that the PoA is at least logarithmic for expected suboptimality, and double-logarithmic for median suboptimality. When there is uncertainty in both distance and gradient norm, we show that the PoA must be polynomial in the level of uncertainty. Our lower bounds nearly match existing upper bounds, and establish that there is no parameter-free lunch.

The convergence rate of a Markov chain to its stationary distribution is typically assessed using the concept of total variation mixing time. However, this worst-case measure often yields pessimistic estimates and is challenging to infer from observations. In this paper, we advocate for the use of the average-mixing time as a more optimistic and demonstrably easier-to-estimate alternative. We further illustrate its applicability across a range of settings, from two-point to countable spaces, and discuss some practical implications.

This study explores the impact of peer acknowledgement on learner engagement and implicit psychological attributes in written annotations on an online social reading platform. Participants included 91 undergraduates from a large North American University. Using log file data, we analyzed the relationship between learners' received peer acknowledgement and their subsequent annotation behaviours using cross-lag regression. Higher peer acknowledgements correlate with increased initiation of annotations and responses to peer annotations. By applying text mining techniques and calculating Shapley values to analyze 1,969 social annotation entries, we identified prominent psychological themes within three dimensions (i.e., affect, cognition, and motivation) that foster peer acknowledgment in digital social annotation. These themes include positive affect, openness to learning and discussion, and expression of motivation. The findings assist educators in improving online learning communities and provide guidance to technology developers in designing effective prompts, drawing from both implicit psychological cues and explicit learning behaviours.

Gradient methods are experiencing a growth in methodological and theoretical developments owing to the challenges of optimization problems arising in data science. Focusing on data science applications with expensive objective function evaluations yet inexpensive gradient function evaluations, gradient methods that never make objective function evaluations are either being rejuvenated or actively developed. However, as we show, such gradient methods are all susceptible to catastrophic divergence under realistic conditions for data science applications. In light of this, gradient methods which make use of objective function evaluations become more appealing, yet, as we show, can result in an exponential increase in objective evaluations between accepted iterates. As a result, existing gradient methods are poorly suited to the needs of optimization problems arising from data science. In this work, we address this gap by developing a generic methodology that economically uses objective function evaluations in a problem-driven manner to prevent catastrophic divergence and avoid an explosion in objective evaluations between accepted iterates. Our methodology allows for specific procedures that can make use of specific step size selection methodologies or search direction strategies, and we develop a novel step size selection methodology that is well-suited to data science applications. We show that a procedure resulting from our methodology is highly competitive with standard optimization methods on CUTEst test problems. We then show a procedure resulting from our methodology is highly favorable relative to standard optimization methods on optimization problems arising in our target data science applications. Thus, we provide a novel gradient methodology that is better suited to optimization problems arising in data science.

We revisit the problems of pitch spelling and tonality guessing with a new algorithm for their joint estimation from a MIDI file including information about the measure boundaries. Our algorithm does not only identify a global key but also local ones all along the analyzed piece. It uses Dynamic Programming techniques to search for an optimal spelling in term, roughly, of the number of accidental symbols that would be displayed in the engraved score. The evaluation of this number is coupled with an estimation of the global key and some local keys, one for each measure. Each of the three informations is used for the estimation of the other, in a multi-steps procedure. An evaluation conducted on a monophonic and a piano dataset, comprising 216 464 notes in total, shows a high degree of accuracy, both for pitch spelling (99.5% on average on the Bach corpus and 98.2% on the whole dataset) and global key signature estimation (93.0% on average, 95.58% on the piano dataset). Designed originally as a backend tool in a music transcription framework, this method should also be useful in other tasks related to music notation processing.

Observational studies of treatment effects require adjustment for confounding variables. However, causal inference methods typically cannot deliver perfect adjustment on all measured baseline variables, and there is often ambiguity about which variables should be prioritized. Standard prioritization methods based on treatment imbalance alone neglect variables' relationships with the outcome. We propose the joint variable importance plot to guide variable prioritization for observational studies. Since not all variables are equally relevant to the outcome, the plot adds outcome associations to quantify the potential confounding jointly with the standardized mean difference. To enhance comparisons on the plot between variables with different confounding relationships, we also derive and plot bias curves. Variable prioritization using the plot can produce recommended values for tuning parameters in many existing matching and weighting methods. We showcase the use of the joint variable importance plots in the design of a balance-constrained matched study to evaluate whether taking an antidiabetic medication, glyburide, increases the incidence of C-section delivery among pregnant individuals with gestational diabetes.

The objective of the KPR agents are to learn themselves in the minimum (learning) time to have maximum success or utilization probability ($f$). A dictator can easily solve the problem with $f = 1$ in no time, by asking every one to form a queue and go to the respective restaurant, resulting in no fluctuation and full utilization from the first day (convergence time $\tau = 0$). It has already been shown that if each agent chooses randomly the restaurants, $f = 1 - e^{-1} \simeq 0.63$ (where $e \simeq 2.718$ denotes the Euler number) in zero time ($\tau = 0$). With the only available information about yesterday's crowd size in the restaurant visited by the agent (as assumed for the rest of the strategies studied here), the crowd avoiding (CA) strategies can give higher values of $f$ but also of $\tau$. Several numerical studies of modified learning strategies actually indicated increased value of $f = 1 - \alpha$ for $\alpha \to 0$, with $\tau \sim 1/\alpha$. We show here using Monte Carlo technique, a modified Greedy Crowd Avoiding (GCA) Strategy can assure full utilization ($f = 1$) in convergence time $\tau \simeq eN$, with of course non-zero probability for an even larger convergence time. All these observations suggest that the strategies with single step memory of the individuals can never collectively achieve full utilization ($f = 1$) in finite convergence time and perhaps the maximum possible utilization that can be achieved is about eighty percent ($f \simeq 0.80$) in an optimal time $\tau$ of order ten, even when $N$ the number of customers or of the restaurants goes to infinity.

Traditional rigid endoscopes have challenges in flexibly treating tumors located deep in the brain, and low operability and fixed viewing angles limit its development. This study introduces a novel dual-segment flexible robotic endoscope MicroNeuro, designed to perform biopsies with dexterous surgical manipulation deep in the brain. Taking into account the uncertainty of the control model, an image-based visual servoing with online robot Jacobian estimation has been implemented to enhance motion accuracy. Furthermore, the application of model predictive control with constraints significantly bolsters the flexible robot's ability to adaptively track mobile objects and resist external interference. Experimental results underscore that the proposed control system enhances motion stability and precision. Phantom testing substantiates its considerable potential for deployment in neurosurgery.

We conduct a systematic study of the approximation properties of Transformer for sequence modeling with long, sparse and complicated memory. We investigate the mechanisms through which different components of Transformer, such as the dot-product self-attention, positional encoding and feed-forward layer, affect its expressive power, and we study their combined effects through establishing explicit approximation rates. Our study reveals the roles of critical parameters in the Transformer, such as the number of layers and the number of attention heads, and these insights also provide natural suggestions for alternative architectures.

In the last two decades, the linear model of coregionalization (LMC) has been widely used to model multivariate spatial processes. From a computational standpoint, the LMC is a substantially easier model to work with than other multidimensional alternatives. Up to now, this fact has been largely overlooked in the literature. Starting from an analogy with matrix normal models, we propose a reformulation of the LMC likelihood that highlights the linear, rather than cubic, computational complexity as a function of the dimension of the response vector. Further, we describe in detail how those simplifications can be included in a Gaussian hierarchical model. In addition, we demonstrate in two examples how the disentangled version of the likelihood we derive can be exploited to improve Markov chain Monte Carlo (MCMC) based computations when conducting Bayesian inference. The first is an interwoven approach that combines samples from centered and whitened parametrizations of the latent LMC distributed random fields. The second is a sparsity-inducing method that introduces structural zeros in the coregionalization matrix in an attempt to reduce the number of parameters in a principled way. It also provides a new way to investigate the strength of the correlation among the components of the outcome vector. Both approaches come at virtually no additional cost and are shown to significantly improve MCMC performance and predictive performance respectively. We apply our methodology to a dataset comprised of air pollutant measurements in the state of California.