Relaxing the I.I.D. Assumption: Adaptively Minimax Optimal Regret via Root-Entropic Regularization

We consider sequential prediction with expert advice when data are generated from distributions varying arbitrarily within an unknown constraint set. We quantify relaxations of the classical i.i.d. assumption in terms of these constraint sets, with i.i.d. sequences at one extreme and adversarial mechanisms at the other. The Hedge algorithm, long known to be minimax optimal in the adversarial regime, was recently shown to be minimax optimal for i.i.d. data. We show that Hedge with deterministic learning rates is suboptimal between these extremes, and present a new algorithm that adaptively achieves the minimax optimal rate of regret with respect to our relaxations of the i.i.d. assumption, and does so without knowledge of the underlying constraint set. We analyze our algorithm using the follow-the-regularized-leader framework, and prove it corresponds to Hedge with an adaptive learning rate that implicitly scales as the square root of the entropy of the current predictive distribution, rather than the entropy of the initial predictive distribution.Comment: 71 pages, 2 figures. Blair Bilodeau and Jeffrey Negrea are equal-contribution authors; order was determined randoml

Concept Algebra for Score-Based Conditional Models

This paper concerns the structure of learned representations in text-guided generative models, focusing on score-based models. Here, we focus on the idea that concepts are encoded as subspaces (or directions) of some representation space. We develop a mathematical formalization of this idea.Using this formalism, we show there's a natural choice of representation with this property, and we develop a simple method for identifying the part of the representation corresponding to a given concept. In particular, this allows us to manipulate the concepts expressed by the model through algebraic manipulation of the representation. We demonstrate the idea with examples text-guided image generation, using Stable Diffusion

Minimax optimal quantile and semi-adversarial regret via root-logarithmic regularizers

Quantile (and, more generally, KL) regret bounds, such as those achieved by NormalHedge (Chaudhuri, Freund, and Hsu 2009) and its variants, relax the goal of competing against the best individual expert to only competing against a majority of experts on adversarial data. More recently, the semi-adversarial paradigm (Bilodeau, Negrea, and Roy 2020) provides an alternative relaxation of adversarial online learning by considering data that may be neither fully adversarial nor stochastic (i.i.d.). We achieve the minimax optimal regret in both paradigms using FTRL with separate, novel, root-logarithmic regularizers, both of which can be interpreted as yielding variants of NormalHedge. We extend existing KL regret upper bounds, which hold uniformly over target distributions, to possibly uncountable expert classes with arbitrary priors; provide the first full-information lower bounds for quantile regret on finite expert classes (which are tight); and provide an adaptively minimax optimal algorithm for the semi-adversarial paradigm that adapts to the true, unknown constraint faster, leading to uniformly improved regret bounds over existing methods.https://arxiv.org/pdf/2110.14804.pdfPublished versio

Statistical inference with stochastic gradient algorithms

The tuning of stochastic gradient algorithms (SGAs) for optimization and sampling is often based on heuristics and trial-and-error rather than generalizable theory. We address this theory–practice gap by characterizing the large-sample statistical asymptotics of SGAs via a joint step-size–sample-size scaling limit. We show that iterate averaging with a large fixed step size is robust to the choice of tuning parameters and asymptotically has covariance proportional to that of the MLE sampling distribution. We also prove a Bernstein–von Mises-like theorem to guide tuning, including for generalized posteriors that are robust to model misspecification. Numerical experiments validate our results and recommendations in realistic finite-sample regimes. Our work lays the foundation for a systematic analysis of other stochastic gradient Markov chain Monte Carlo algorithms for a wide range of models.https://arxiv.org/abs/2207.12395First author draf

Efficacy and safety of sparsentan versus irbesartan in patients with IgA nephropathy (PROTECT): 2-year results from a randomised, active-controlled, phase 3 trial

BackgroundSparsentan, a novel, non-immunosuppressive, single-molecule, dual endothelin angiotensin receptor antagonist, significantly reduced proteinuria versus irbesartan, an angiotensin II receptor blocker, at 36 weeks (primary endpoint) in patients with immunoglobulin A nephropathy in the phase 3 PROTECT trial's previously reported interim analysis. Here, we report kidney function and outcomes over 110 weeks from the double-blind final analysis.MethodsPROTECT, a double-blind, randomised, active-controlled, phase 3 study, was done across 134 clinical practice sites in 18 countries throughout the Americas, Asia, and Europe. Patients aged 18 years or older with biopsy-proven primary IgA nephropathy and proteinuria of at least 1·0 g per day despite maximised renin–angiotensin system inhibition for at least 12 weeks were randomly assigned (1:1) to receive sparsentan (target dose 400 mg oral sparsentan once daily) or irbesartan (target dose 300 mg oral irbesartan once daily) based on a permuted-block randomisation method. The primary endpoint was proteinuria change between treatment groups at 36 weeks. Secondary endpoints included rate of change (slope) of the estimated glomerular filtration rate (eGFR), changes in proteinuria, a composite of kidney failure (confirmed 40% eGFR reduction, end-stage kidney disease, or all-cause mortality), and safety and tolerability up to 110 weeks from randomisation. Secondary efficacy outcomes were assessed in the full analysis set and safety was assessed in the safety set, both of which were defined as all patients who were randomly assigned and received at least one dose of randomly assigned study drug. This trial is registered with ClinicalTrials.gov, NCT03762850.FindingsBetween Dec 20, 2018, and May 26, 2021, 203 patients were randomly assigned to the sparsentan group and 203 to the irbesartan group. One patient from each group did not receive the study drug and was excluded from the efficacy and safety analyses (282 [70%] of 404 included patients were male and 272 [67%] were White) . Patients in the sparsentan group had a slower rate of eGFR decline than those in the irbesartan group. eGFR chronic 2-year slope (weeks 6–110) was −2·7 mL/min per 1·73 m2 per year versus −3·8 mL/min per 1·73 m2 per year (difference 1·1 mL/min per 1·73 m2 per year, 95% CI 0·1 to 2·1; p=0·037); total 2-year slope (day 1–week 110) was −2·9 mL/min per 1·73 m2 per year versus −3·9 mL/min per 1·73 m2 per year (difference 1·0 mL/min per 1·73 m2 per year, 95% CI −0·03 to 1·94; p=0·058). The significant reduction in proteinuria at 36 weeks with sparsentan was maintained throughout the study period; at 110 weeks, proteinuria, as determined by the change from baseline in urine protein-to-creatinine ratio, was 40% lower in the sparsentan group than in the irbesartan group (−42·8%, 95% CI −49·8 to −35·0, with sparsentan versus −4·4%, −15·8 to 8·7, with irbesartan; geometric least-squares mean ratio 0·60, 95% CI 0·50 to 0·72). The composite kidney failure endpoint was reached by 18 (9%) of 202 patients in the sparsentan group versus 26 (13%) of 202 patients in the irbesartan group (relative risk 0·7, 95% CI 0·4 to 1·2). Treatment-emergent adverse events were well balanced between sparsentan and irbesartan, with no new safety signals.InterpretationOver 110 weeks, treatment with sparsentan versus maximally titrated irbesartan in patients with IgA nephropathy resulted in significant reductions in proteinuria and preservation of kidney function

Sparsentan in patients with IgA nephropathy: a prespecified interim analysis from a randomised, double-blind, active-controlled clinical trial

Background: Sparsentan is a novel, non-immunosuppressive, single-molecule, dual endothelin and angiotensin receptor antagonist being examined in an ongoing phase 3 trial in adults with IgA nephropathy. We report the prespecified interim analysis of the primary proteinuria efficacy endpoint, and safety. Methods: PROTECT is an international, randomised, double-blind, active-controlled study, being conducted in 134 clinical practice sites in 18 countries. The study examines sparsentan versus irbesartan in adults (aged ≥18 years) with biopsy-proven IgA nephropathy and proteinuria of 1·0 g/day or higher despite maximised renin-angiotensin system inhibitor treatment for at least 12 weeks. Participants were randomly assigned in a 1:1 ratio to receive sparsentan 400 mg once daily or irbesartan 300 mg once daily, stratified by estimated glomerular filtration rate at screening (30 to 1·75 g/day). The primary efficacy endpoint was change from baseline to week 36 in urine protein-creatinine ratio based on a 24-h urine sample, assessed using mixed model repeated measures. Treatment-emergent adverse events (TEAEs) were safety endpoints. All endpoints were examined in all participants who received at least one dose of randomised treatment. The study is ongoing and is registered with ClinicalTrials.gov, NCT03762850. Findings: Between Dec 20, 2018, and May 26, 2021, 404 participants were randomly assigned to sparsentan (n=202) or irbesartan (n=202) and received treatment. At week 36, the geometric least squares mean percent change from baseline in urine protein-creatinine ratio was statistically significantly greater in the sparsentan group (-49·8%) than the irbesartan group (-15·1%), resulting in a between-group relative reduction of 41% (least squares mean ratio=0·59; 95% CI 0·51-0·69; p<0·0001). TEAEs with sparsentan were similar to irbesartan. There were no cases of severe oedema, heart failure, hepatotoxicity, or oedema-related discontinuations. Bodyweight changes from baseline were not different between the sparsentan and irbesartan groups. Interpretation: Once-daily treatment with sparsentan produced meaningful reduction in proteinuria compared with irbesartan in adults with IgA nephropathy. Safety of sparsentan was similar to irbesartan. Future analyses after completion of the 2-year double-blind period will show whether these beneficial effects translate into a long-term nephroprotective potential of sparsentan. Funding: Travere Therapeutics

Efficacy and safety of sparsentan versus irbesartan in patients with IgA nephropathy (PROTECT): 2-year results from a randomised, active-controlled, phase 3 trial

Background Sparsentan, a novel, non-immunosuppressive, single-molecule, dual endothelin angiotensin receptor antagonist, significantly reduced proteinuria versus irbesartan, an angiotensin II receptor blocker, at 36 weeks (primary endpoint) in patients with immunoglobulin A nephropathy in the phase 3 PROTECT trial's previously reported interim analysis. Here, we report kidney function and outcomes over 110 weeks from the double-blind final analysis. Methods PROTECT, a double-blind, randomised, active-controlled, phase 3 study, was done across 134 clinical practice sites in 18 countries throughout the Americas, Asia, and Europe. Patients aged 18 years or older with biopsy-proven primary IgA nephropathy and proteinuria of at least 1·0 g per day despite maximised renin–angiotensin system inhibition for at least 12 weeks were randomly assigned (1:1) to receive sparsentan (target dose 400 mg oral sparsentan once daily) or irbesartan (target dose 300 mg oral irbesartan once daily) based on a permuted-block randomisation method. The primary endpoint was proteinuria change between treatment groups at 36 weeks. Secondary endpoints included rate of change (slope) of the estimated glomerular filtration rate (eGFR), changes in proteinuria, a composite of kidney failure (confirmed 40% eGFR reduction, end-stage kidney disease, or all-cause mortality), and safety and tolerability up to 110 weeks from randomisation. Secondary efficacy outcomes were assessed in the full analysis set and safety was assessed in the safety set, both of which were defined as all patients who were randomly assigned and received at least one dose of randomly assigned study drug. This trial is registered with ClinicalTrials.gov, NCT03762850. Findings Between Dec 20, 2018, and May 26, 2021, 203 patients were randomly assigned to the sparsentan group and 203 to the irbesartan group. One patient from each group did not receive the study drug and was excluded from the efficacy and safety analyses (282 [70%] of 404 included patients were male and 272 [67%] were White) . Patients in the sparsentan group had a slower rate of eGFR decline than those in the irbesartan group. eGFR chronic 2-year slope (weeks 6–110) was −2·7 mL/min per 1·73 m2 per year versus −3·8 mL/min per 1·73 m2 per year (difference 1·1 mL/min per 1·73 m2 per year, 95% CI 0·1 to 2·1; p=0·037); total 2-year slope (day 1–week 110) was −2·9 mL/min per 1·73 m2 per year versus −3·9 mL/min per 1·73 m2 per year (difference 1·0 mL/min per 1·73 m2 per year, 95% CI −0·03 to 1·94; p=0·058). The significant reduction in proteinuria at 36 weeks with sparsentan was maintained throughout the study period; at 110 weeks, proteinuria, as determined by the change from baseline in urine protein-to-creatinine ratio, was 40% lower in the sparsentan group than in the irbesartan group (−42·8%, 95% CI −49·8 to −35·0, with sparsentan versus −4·4%, −15·8 to 8·7, with irbesartan; geometric least-squares mean ratio 0·60, 95% CI 0·50 to 0·72). The composite kidney failure endpoint was reached by 18 (9%) of 202 patients in the sparsentan group versus 26 (13%) of 202 patients in the irbesartan group (relative risk 0·7, 95% CI 0·4 to 1·2). Treatment-emergent adverse events were well balanced between sparsentan and irbesartan, with no new safety signals. Interpretation Over 110 weeks, treatment with sparsentan versus maximally titrated irbesartan in patients with IgA nephropathy resulted in significant reductions in proteinuria and preservation of kidney function.</p

Empagliflozin in Patients with Chronic Kidney Disease

Background The effects of empagliflozin in patients with chronic kidney disease who are at risk for disease progression are not well understood. The EMPA-KIDNEY trial was designed to assess the effects of treatment with empagliflozin in a broad range of such patients. Methods We enrolled patients with chronic kidney disease who had an estimated glomerular filtration rate (eGFR) of at least 20 but less than 45 ml per minute per 1.73 m(2) of body-surface area, or who had an eGFR of at least 45 but less than 90 ml per minute per 1.73 m(2) with a urinary albumin-to-creatinine ratio (with albumin measured in milligrams and creatinine measured in grams) of at least 200. Patients were randomly assigned to receive empagliflozin (10 mg once daily) or matching placebo. The primary outcome was a composite of progression of kidney disease (defined as end-stage kidney disease, a sustained decrease in eGFR to &lt; 10 ml per minute per 1.73 m(2), a sustained decrease in eGFR of &amp; GE;40% from baseline, or death from renal causes) or death from cardiovascular causes. Results A total of 6609 patients underwent randomization. During a median of 2.0 years of follow-up, progression of kidney disease or death from cardiovascular causes occurred in 432 of 3304 patients (13.1%) in the empagliflozin group and in 558 of 3305 patients (16.9%) in the placebo group (hazard ratio, 0.72; 95% confidence interval [CI], 0.64 to 0.82; P &lt; 0.001). Results were consistent among patients with or without diabetes and across subgroups defined according to eGFR ranges. The rate of hospitalization from any cause was lower in the empagliflozin group than in the placebo group (hazard ratio, 0.86; 95% CI, 0.78 to 0.95; P=0.003), but there were no significant between-group differences with respect to the composite outcome of hospitalization for heart failure or death from cardiovascular causes (which occurred in 4.0% in the empagliflozin group and 4.6% in the placebo group) or death from any cause (in 4.5% and 5.1%, respectively). The rates of serious adverse events were similar in the two groups. Conclusions Among a wide range of patients with chronic kidney disease who were at risk for disease progression, empagliflozin therapy led to a lower risk of progression of kidney disease or death from cardiovascular causes than placebo