Age-Period-Cohort (APC) models are well used in the context of modelling health and demographic data to produce smooth estimates of each time trend. When smoothing in the context of APC models, there are two main schools, frequentist using penalised smoothing splines, and Bayesian using random processes with little crossover between them. In this article, we clearly lay out the theoretical link between the two schools, provide examples using simulated and real data to highlight similarities and difference, and help a general APC user understand potentially inaccessible theory from functional analysis. As intuition suggests, both approaches lead to comparable and almost identical in-sample predictions, but random processes within a Bayesian approach might be beneficial for out-of-sample prediction as the sources of uncertainty are captured in a more complete way.
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Deep equilibrium (DEQ) models are widely recognized as a memory efficient alternative to standard neural networks, achieving state-of-the-art performance in language modeling and computer vision tasks. These models solve a fixed point equation instead of explicitly computing the output, which sets them apart from standard neural networks. However, existing DEQ models often lack formal guarantees of the existence and uniqueness of the fixed point, and the convergence of the numerical scheme used for computing the fixed point is not formally established. As a result, DEQ models are potentially unstable in practice. To address these drawbacks, we introduce a novel class of DEQ models called positive concave deep equilibrium (pcDEQ) models. Our approach, which is based on nonlinear Perron-Frobenius theory, enforces nonnegative weights and activation functions that are concave on the positive orthant. By imposing these constraints, we can easily ensure the existence and uniqueness of the fixed point without relying on additional complex assumptions commonly found in the DEQ literature, such as those based on monotone operator theory in convex analysis. Furthermore, the fixed point can be computed with the standard fixed point algorithm, and we provide theoretical guarantees of geometric convergence, which, in particular, simplifies the training process. Experiments demonstrate the competitiveness of our pcDEQ models against other implicit models.
Constant (naive) imputation is still widely used in practice as this is a first easy-to-use technique to deal with missing data. Yet, this simple method could be expected to induce a large bias for prediction purposes, as the imputed input may strongly differ from the true underlying data. However, recent works suggest that this bias is low in the context of high-dimensional linear predictors when data is supposed to be missing completely at random (MCAR). This paper completes the picture for linear predictors by confirming the intuition that the bias is negligible and that surprisingly naive imputation also remains relevant in very low dimension.To this aim, we consider a unique underlying random features model, which offers a rigorous framework for studying predictive performances, whilst the dimension of the observed features varies.Building on these theoretical results, we establish finite-sample bounds on stochastic gradient (SGD) predictors applied to zero-imputed data, a strategy particularly well suited for large-scale learning.If the MCAR assumption appears to be strong, we show that similar favorable behaviors occur for more complex missing data scenarios.
By abstracting over well-known properties of De Bruijn's representation with nameless dummies, we design a new theory of syntax with variable binding and capture-avoiding substitution. We propose it as a simpler alternative to Fiore, Plotkin, and Turi's approach, with which we establish a strong formal link. We also show that our theory easily incorporates simple types and equations between terms.
This study proposes the use of Machine Learning models to predict the early onset of sepsis using deidentified clinical data from Montefiore Medical Center in Bronx, NY, USA. A supervised learning approach was adopted, wherein an XGBoost model was trained utilizing 80\% of the train dataset, encompassing 107 features (including the original and derived features). Subsequently, the model was evaluated on the remaining 20\% of the test data. The model was validated on prospective data that was entirely unseen during the training phase. To assess the model's performance at the individual patient level and timeliness of the prediction, a normalized utility score was employed, a widely recognized scoring methodology for sepsis detection, as outlined in the PhysioNet Sepsis Challenge paper. Metrics such as F1 Score, Sensitivity, Specificity, and Flag Rate were also devised. The model achieved a normalized utility score of 0.494 on test data and 0.378 on prospective data at threshold 0.3. The F1 scores were 80.8\% and 67.1\% respectively for the test data and the prospective data for the same threshold, highlighting its potential to be integrated into clinical decision-making processes effectively. These results bear testament to the model's robust predictive capabilities and its potential to substantially impact clinical decision-making processes.
In this article we consider an aggregate loss model with dependent losses. The losses occurrence process is governed by a two-state Markovian arrival process (MAP2), a Markov renewal process process that allows for (1) correlated inter-losses times, (2) non-exponentially distributed inter-losses times and, (3) overdisperse losses counts. Some quantities of interest to measure persistence in the loss occurrence process are obtained. Given a real operational risk database, the aggregate loss model is estimated by fitting separately the inter-losses times and severities. The MAP2 is estimated via direct maximization of the likelihood function, and severities are modeled by the heavy-tailed, double-Pareto Lognormal distribution. In comparison with the fit provided by the Poisson process, the results point out that taking into account the dependence and overdispersion in the inter-losses times distribution leads to higher capital charges.
We study variation in policing outcomes attributable to differential policing practices in New York City (NYC) using geographic regression discontinuity designs (GeoRDDs). By focusing on small geographic windows near police precinct boundaries we can estimate local average treatment effects of police precincts on arrest rates. We propose estimands and develop estimators for the GeoRDD when the data come from a spatial point process. Additionally, standard GeoRDDs rely on continuity assumptions of the potential outcome surface or a local randomization assumption within a window around the boundary. These assumptions, however, can easily be violated in realistic applications. We develop a novel and robust approach to testing whether there are differences in policing outcomes that are caused by differences in police precincts across NYC. Importantly, this approach is applicable to standard regression discontinuity designs with both numeric and point process data. This approach is robust to violations of traditional assumptions made, and is valid under weaker assumptions. We use a unique form of resampling to provide a valid estimate of our test statistic's null distribution even under violations of standard assumptions. This procedure gives substantially different results in the analysis of NYC arrest rates than those that rely on standard assumptions.
We develop and implement methods for determining whether relaxing sparsity con- straints on portfolios improves the investment opportunity set for risk-averse investors. We formulate a new estimation procedure for sparse second-order stochastic spanning based on a greedy algorithm and Linear Programming. We show the optimal recovery of the sparse solution asymptotically whether spanning holds or not. From large equity datasets, we estimate the expected utility loss due to possible under-diversification, and find that there is no benefit from expanding a sparse opportunity set beyond 45 assets. The optimal sparse portfolio invests in 10 industry sectors and cuts tail risk when compared to a sparse mean-variance portfolio. On a rolling-window basis, the number of assets shrinks to 25 assets in crisis periods, while standard factor models cannot explain the performance of the sparse portfolios.
Automatic Speech Recognition (ASR) systems are used in the financial domain to enhance the caller experience by enabling natural language understanding and facilitating efficient and intuitive interactions. Increasing use of ASR systems requires that such systems exhibit very low error rates. The predominant ASR models to collect numeric data are large, general-purpose commercial models -- Google Speech-to-text (STT), or Amazon Transcribe -- or open source (OpenAI's Whisper). Such ASR models are trained on hundreds of thousands of hours of audio data and require considerable resources to run. Despite recent progress large speech recognition models, we highlight the potential of smaller, specialized "micro" models. Such light models can be trained perform well on number recognition specific tasks, competing with general models like Whisper or Google STT while using less than 80 minutes of training time and occupying at least an order of less memory resources. Also, unlike larger speech recognition models, micro-models are trained on carefully selected and curated datasets, which makes them highly accurate, agile, and easy to retrain, while using low compute resources. We present our work on creating micro models for multi-digit number recognition that handle diverse speaking styles reflecting real-world pronunciation patterns. Our work contributes to domain-specific ASR models, improving digit recognition accuracy, and privacy of data. An added advantage, their low resource consumption allows them to be hosted on-premise, keeping private data local instead uploading to an external cloud. Our results indicate that our micro-model makes less errors than the best-of-breed commercial or open-source ASRs in recognizing digits (1.8% error rate of our best micro-model versus 5.8% error rate of Whisper), and has a low memory footprint (0.66 GB VRAM for our model versus 11 GB VRAM for Whisper).
Text-to-speech models trained on large-scale datasets have demonstrated impressive in-context learning capabilities and naturalness. However, control of speaker identity and style in these models typically requires conditioning on reference speech recordings, limiting creative applications. Alternatively, natural language prompting of speaker identity and style has demonstrated promising results and provides an intuitive method of control. However, reliance on human-labeled descriptions prevents scaling to large datasets. Our work bridges the gap between these two approaches. We propose a scalable method for labeling various aspects of speaker identity, style, and recording conditions. We then apply this method to a 45k hour dataset, which we use to train a speech language model. Furthermore, we propose simple methods for increasing audio fidelity, significantly outperforming recent work despite relying entirely on found data. Our results demonstrate high-fidelity speech generation in a diverse range of accents, prosodic styles, channel conditions, and acoustic conditions, all accomplished with a single model and intuitive natural language conditioning. Audio samples can be heard at //text-description-to-speech.com/.
A rectangulation is a decomposition of a rectangle into finitely many rectangles. Via natural equivalence relations, rectangulations can be seen as combinatorial objects with a rich structure, with links to lattice congruences, flip graphs, polytopes, lattice paths, Hopf algebras, etc. In this paper, we first revisit the structure of the respective equivalence classes: weak rectangulations that preserve rectangle-segment adjacencies, and strong rectangulations that preserve rectangle-rectangle adjacencies. We thoroughly investigate posets defined by adjacency in rectangulations of both kinds, and unify and simplify known bijections between rectangulations and permutation classes. This yields a uniform treatment of mappings between permutations and rectangulations that unifies the results from earlier contributions, and emphasizes parallelism and differences between the weak and the strong cases. Then, we consider the special case of guillotine rectangulations, and prove that they can be characterized - under all known mappings between permutations and rectangulations - by avoidance of two mesh patterns that correspond to "windmills" in rectangulations. This yields new permutation classes in bijection with weak guillotine rectangulations, and the first known permutation class in bijection with strong guillotine rectangulations. Finally, we address enumerative issues and prove asymptotic bounds for several families of strong rectangulations.
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