Predicting pharmaceutical particle size distributions using kernel mean embedding

In the pharmaceutical industry, the transition to continuous manufacturing of solid dosage forms is adopted by more and more companies. For these continuous processes, high-quality process models are needed. In pharmaceutical wet granulation, a unit operation in the ConsiGmaTM-25 continuous powder-to-tablet system (GEA Pharma systems, Collette, Wommelgem, Belgium), the product under study presents itself as a collection of particles that differ in shape and size. The measurement of this collection results in a particle size distribution. However, the theoretical basis to describe the physical phenomena leading to changes in this particle size distribution is lacking. It is essential to understand how the particle size distribution changes as a function of the unit operation's process settings, as it has a profound effect on the behavior of the fluid bed dryer. Therefore, we suggest a data-driven modeling framework that links the machine settings of the wet granulation unit operation and the output distribution of granules. We do this without making any assumptions on the nature of the distributions under study. A simulation of the granule size distribution could act as a soft sensor when in-line measurements are challenging to perform. The method of this work is a two-step procedure: first, the measured distributions are transformed into a high-dimensional feature space, where the relation between the machine settings and the distributions can be learnt. Second, the inverse transformation is performed, allowing an interpretation of the results in the original measurement space. Further, a comparison is made with previous work, which employs a more mechanistic framework for describing the granules. A reliable prediction of the granule size is vital in the assurance of quality in the production line, and is needed in the assessment of upstream (feeding) and downstream (drying, milling, and tableting) issues. Now that a validated data-driven framework for predicting pharmaceutical particle size distributions is available, it can be applied in settings such as model-based experimental design and, due to its fast computation, there is potential in real-time model predictive control

Building a scientific workflow framework to enable real‐time machine learning and visualization

Nowadays, we have entered the era of big data. In the area of high performance computing, large‐scale simulations can generate huge amounts of data with potentially critical information. However, these data are usually saved in intermediate files and are not instantly visible until advanced data analytics techniques are applied after reading all simulation data from persistent storages (eg, local disks or a parallel file system). This approach puts users in a situation where they spend long time on waiting for running simulations while not knowing the status of the running job. In this paper, we build a new computational framework to couple scientific simulations with multi‐step machine learning processes and in‐situ data visualizations. We also design a new scalable simulation‐time clustering algorithm to automatically detect fluid flow anomalies. This computational framework is built upon different software components and provides plug‐in data analysis and visualization functions over complex scientific workflows. With this advanced framework, users can monitor and get real‐time notifications of special patterns or anomalies from ongoing extreme‐scale turbulent flow simulations

Vector-valued distribution regression: a simple and consistent approach

We address the distribution regression problem (DRP): regressing on the domain of probability measures, in the two-stage sampled setup when only samples from the distributions are given. The DRP formulation offers a unified framework for several important tasks in statistics and machine learning including multi-instance learning (MIL), or point estimation problems without analytical solution. Despite the large number of MIL heuristics, essentially there is no theoretically grounded approach to tackle the DRP problem in two-stage sampled case. To the best of our knowledge, the only existing technique with consistency guarantees requires kernel density estimation as an intermediate step (which often scale poorly in practice), and the domain of the distributions to be compact Euclidean. We analyse a simple (analytically computable) ridge regression alternative to DRP: we embed the distributions to a reproducing kernel Hilbert space, and learn the regressor from the embeddings to the outputs. We show that this scheme is consistent in the two-stage sampled setup under mild conditions, for probability measure inputs defined on separable, topological domains endowed with kernels, with vector-valued outputs belonging to an arbitrary separable Hilbert space. Specially, choosing the kernel on the space of embedded distributions to be linear and the output space to the real line, we get the consistency of set kernels in regression, which was a 15-year-old open question. In our talk we are going to present (i) the main ideas and results of consistency, (ii) concrete kernel constructions on mean embedded distributions, and (iii) two applications (supervised entropy learning, aerosol prediction based on multispectral satellite images) demonstrating the efficiency of our approach

Regression on Probability Measures: A Simple and Consistent Algorithm

We address the distribution regression problem: we regress from probability measures to Hilbert-space valued outputs, where only samples are available from the input distributions. Many important statistical and machine learning problems can be phrased within this framework including point estimation tasks without analytical solution, or multi-instance learning. However, due to the two-stage sampled nature of the problem, the theoretical analysis becomes quite challenging: to the best of our knowledge the only existing method with performance guarantees requires density estimation (which of ten performs poorly in practise) and the distributions to be defined on a compact Euclidean domain. We present a simple, analytically tractable alternative to solve the distribution regression problem: we embed the distributions to a reproducing kernel Hilbert space and perform ridge regression from the embedded distributions to the outputs. We prove that this scheme is consistent under mild conditions (for distributions on separable topological domains endowed with kernels), and construct explicit finite sample bounds on the excess risk as a function of the sample numbers and the problem difficulty, which hold with high probability. Specifically, we establish the consistency of set kernels in regression, which was a 15-year-old-openquestion, and also present new kernels on embedded distributions. The practical efficiency of the studied technique is illustrated in supervised entropy learning and aerosol prediction using multispectral satellite images