Concentration without Independence via Information Measures

We propose a novel approach to concentration for non-independent random variables. The main idea is to ``pretend'' that the random variables are independent and pay a multiplicative price measuring how far they are from actually being independent. This price is encapsulated in the Hellinger integral between the joint and the product of the marginals, which is then upper bounded leveraging tensorisation properties. Our bounds represent a natural generalisation of concentration inequalities in the presence of dependence: we recover exactly the classical bounds (McDiarmid's inequality) when the random variables are independent. Furthermore, in a ``large deviations'' regime, we obtain the same decay in the probability as for the independent case, even when the random variables display non-trivial dependencies. To show this, we consider a number of applications of interest. First, we provide a bound for Markov chains with finite state space. Then, we consider the Simple Symmetric Random Walk, which is a non-contracting Markov chain, and a non-Markovian setting in which the stochastic process depends on its entire past. To conclude, we propose an application to Markov Chain Monte Carlo methods, where our approach leads to an improved lower bound on the minimum burn-in period required to reach a certain accuracy. In all of these settings, we provide a regime of parameters in which our bound fares better than what the state of the art can provide

Lower-bounds on the Bayesian Risk in Estimation Procedures via ff-Divergences

We consider the problem of parameter estimation in a Bayesian setting and propose a general lower-bound that includes part of the family of $f$-Divergences. The results are then applied to specific settings of interest and compared to other notable results in the literature. In particular, we show that the known bounds using Mutual Information can be improved by using, for example, Maximal Leakage, Hellinger divergence, or generalizations of the Hockey-Stick divergence.Comment: Submitted to ISIT 202

Lower Bounds on the Bayesian Risk via Information Measures

This paper focuses on parameter estimation and introduces a new method for lower bounding the Bayesian risk. The method allows for the use of virtually \emph{any} information measure, including R\'enyi's $\alpha$, $\varphi$-Divergences, and Sibson's $\alpha$-Mutual Information. The approach considers divergences as functionals of measures and exploits the duality between spaces of measures and spaces of functions. In particular, we show that one can lower bound the risk with any information measure by upper bounding its dual via Markov's inequality. We are thus able to provide estimator-independent impossibility results thanks to the Data-Processing Inequalities that divergences satisfy. The results are then applied to settings of interest involving both discrete and continuous parameters, including the ``Hide-and-Seek'' problem, and compared to the state-of-the-art techniques. An important observation is that the behaviour of the lower bound in the number of samples is influenced by the choice of the information measure. We leverage this by introducing a new divergence inspired by the ``Hockey-Stick'' Divergence, which is demonstrated empirically to provide the largest lower-bound across all considered settings. If the observations are subject to privatisation, stronger impossibility results can be obtained via Strong Data-Processing Inequalities. The paper also discusses some generalisations and alternative directions

In-label, off-label prescription, efficacy and tolerability of dalbavancin: report from a National Registry

PurposeAlthough dalbavancin is currently approved for the treatment of ABSSIs, several studies suggest its efficacy and tolerance as long-term therapy for other off-label indications requiring prolonged intravenous antibiotic administration.MethodsWe conducted a prospective nationwide study of dalbavancin use in real-life settings for both approved and off-label indications analysing for each case the clinical and microbiological characteristics of infection the efficacy and safety of treatments.ResultsDuring the study period (from December 2018 to July 2021), the ID specialists from 14 different centres enrolled 223 patients treated with dalbavancin [141 males (63%) and 82 females (37%); male/female ratio 1.72; mean age 59 (SD 17.2) years, (range 15-96). Most patients in the study population (136/223; 61.0%) came from community rather than health care facilities and most of them were visited in Infectious Diseases wards (93/223; 41.7%) and clinics (55/223; 24.7%) even though some patients were cured in other settings, such as surgery wards (18/223; 8.1%), orthopaedic wards (11/223; 4.9%), Emergency Rooms (7/223; 3.1%) and non-surgical other than ID wards (6/223; 2.7%). The most common ID diagnoses were osteomyelitis (44 cases/223; 19.7%; of which 29 acute and 15 chronic osteomyelitis), cellulitis (28/223; 12.5%), cutaneous abscess (23/223; 10.3%), orthopaedic prosthesis-associated infection (22/223; 9.9%), surgical site infection (20/223; 9.0%) and septic arthritis (15/223; 6.7%).ConclusionIn conclusion, by virtue of its PK/PD properties, dalbavancin represents a valuable option to daily in-hospital intravenous or outpatient antimicrobial regimens also for off-label indications requiring a long-term treatment of Gram-positive infections

MORFEO enters final design phase

MORFEO (Multi-conjugate adaptive Optics Relay For ELT Observations, formerly MAORY), the MCAO system for the ELT, will provide diffraction-limited optical quality to the large field camera MICADO. MORFEO has officially passed the Preliminary Design Review and it is entering the final design phase. We present the current status of the project, with a focus on the adaptive optics system aspects and expected milestones during the next project phase

How future surgery will benefit from SARS-COV-2-related measures: a SPIGC survey conveying the perspective of Italian surgeons

COVID-19 negatively affected surgical activity, but the potential benefits resulting from adopted measures remain unclear. The aim of this study was to evaluate the change in surgical activity and potential benefit from COVID-19 measures in perspective of Italian surgeons on behalf of SPIGC. A nationwide online survey on surgical practice before, during, and after COVID-19 pandemic was conducted in March-April 2022 (NCT:05323851). Effects of COVID-19 hospital-related measures on surgical patients' management and personal professional development across surgical specialties were explored. Data on demographics, pre-operative/peri-operative/post-operative management, and professional development were collected. Outcomes were matched with the corresponding volume. Four hundred and seventy-three respondents were included in final analysis across 14 surgical specialties. Since SARS-CoV-2 pandemic, application of telematic consultations (4.1% vs. 21.6%; p < 0.0001) and diagnostic evaluations (16.4% vs. 42.2%; p < 0.0001) increased. Elective surgical activities significantly reduced and surgeons opted more frequently for conservative management with a possible indication for elective (26.3% vs. 35.7%; p < 0.0001) or urgent (20.4% vs. 38.5%; p < 0.0001) surgery. All new COVID-related measures are perceived to be maintained in the future. Surgeons' personal education online increased from 12.6% (pre-COVID) to 86.6% (post-COVID; p < 0.0001). Online educational activities are considered a beneficial effect from COVID pandemic (56.4%). COVID-19 had a great impact on surgical specialties, with significant reduction of operation volume. However, some forced changes turned out to be benefits. Isolation measures pushed the use of telemedicine and telemetric devices for outpatient practice and favored communication for educational purposes and surgeon-patient/family communication. From the Italian surgeons' perspective, COVID-related measures will continue to influence future surgical clinical practice