Iterative Viterbi decoding

Iterative Viterbi decoding is an algorithm that spots the subsequence S of an observation O = {o1, ..., on} having the highest average probability (i.e., probability scaled by the length of S) of being generated by a given hidden Markov model M with m states. The algorithm uses a modified Viterbi algorithm as an internal step. The scaled probability measure was first proposed by John S. Bridle. An early algorithm to solve this problem, sliding window, was proposed by Jay G. Wilpon et al., 1989, with constant cost T = mn2/2. A faster algorithm consists of an iteration of calls to the Viterbi algorithm, reestimating a filler score until convergence. == The algorithm == A basic (non-optimized) version, finding the sequence s with the smallest normalized distance from some subsequence of t is: // input is placed in observation s[1..n], template t[1..m], // and [[distance matrix]] d[1..n,1..m] // remaining elements in matrices are solely for internal computations (int, int, int) AverageSubmatchDistance(char s[0..(n+1)], char t[0..(m+1)], int d[1..n,0..(m+1)]) { // score, subsequence start, subsequence end declare int e, B, E t'[0] := t'[m+1] := s'[0] := s'[n+1] := 'e' e := random() do e' := e for i := 1 to n do d'[i,0] := d'[i,m+1] := e (e, B, E) := ViterbiDistance(s', t', d') e := e/(E-B+1) until (e == e') return (e, B, E) } The ViterbiDistance() procedure returns the tuple (e, B, E), i.e., the Viterbi score "e" for the match of t and the selected entry (B) and exit (E) points from it. "B" and "E" have to be recorded using a simple modification to Viterbi. A modification that can be applied to CYK tables, proposed by Antoine Rozenknop, consists in subtracting e from all elements of the initial matrix d.

DreamLab

DreamLab was a volunteer computing Android and iOS app launched in 2015 by Imperial College London and the Vodafone Foundation. It was discontinued on 2nd April 2025. == Description == The app helped to research cancer, COVID-19, new drugs and tropical cyclones. To do this, DreamLab accessed part of the device's processing power, with the user's consent, while the owner charged their smartphone, to speed up the calculations of the algorithms from Imperial College London. The aim of the tropical cyclone project was to prepare for climate change risks. Other projects aimed to find existing drugs and food molecules that could help people with COVID-19 and other diseases. The performance of 100,000 smartphones would reach the annual output of all research computers at Imperial College in just three months, with a nightly runtime of six hours. The app was developed in 2015 by the Garvan Institute of Medical Research in Sydney and the Vodafone Foundation. In May 2020, the project had over 490,000 registered users.

Best arm identification

Best arm identification (BAI) is a sequential one-player game where the player has to find the best action (arm) among a list of actions (arms) by collecting information in the most efficient way. It is a multi-armed bandit game as a player only gets information about an arm by playing it. The most common objective in multi-armed bandit games is to minimize the regret (i.e., play the best action as much as possible), but in BAI, the goal is to find the best arm as efficiently as possible. This problem naturally arises in scenarios such as adaptive clinical trials where the number of patients is limited and the quantification of the confidence in a treatment is important. It also arises in hyperparameter optimization where the goal is to find the optimal choice of hyperparameters for an algorithm with the smallest possible number of experiments, as it can be costly in terms of time, energy, or money. == Stochastic multi-armed bandit == The stochastic multi-armed bandit (MAB) is a sequential game with one player and K {\displaystyle K} actions (arms). Each arm has an unknown probability distribution associated with it. At each turn, the player has to choose one action and receive an observation from the probability distribution associated with the arm. The more you play an arm, the more you get information on its probability distribution. === Best arm identification === In BAI the goal is to find the arm that has the probability distribution with the highest mean. BAI may be either fixed confidence or fixed horizon. In a fixed-confidence game, a confidence level δ {\displaystyle \delta } is fixed at the beginning of the game and the goal is to find the best arm with this confidence level in as few turns as possible. In a fixed horizon game, the number of turns T {\displaystyle T} is fixed, and the goal is to find the best arm with the highest possible confidence in T {\displaystyle T} turns. === Math formalisation === We have one player and K {\displaystyle K} actions (arms). Behind each arm k ∈ { 1 , … , K } {\displaystyle k\in \{1,\ldots ,K\}} lies an unknown distribution ν k {\displaystyle \nu _{k}} with mean μ k {\displaystyle \mu _{k}} . Each distribution ν k {\displaystyle \nu _{k}} belongs to a known family D {\displaystyle {\mathcal {D}}} (such as the set of Gaussian distributions or Bernoulli distributions). At each time step t {\displaystyle t} , the player selects an arm a t {\displaystyle a_{t}} and observes an independent sample X t ∼ ν a t {\displaystyle X_{t}\sim \nu _{a_{t}}} from the corresponding distribution. We will note μ ∗ := max μ a {\displaystyle \mu ^{}:=\max \mu _{a}} the highest mean. An arm a {\displaystyle a} that satisfies μ a = μ ∗ {\displaystyle \mu _{a}=\mu ^{}} is called an optimal arm; otherwise it is called suboptimal arm. In best arm identification (BAI) the objective is to identify an optimal arm. Two main settings for BAI appear in the literature: Fixed confidence: In this setting, one typically assumes that there exists a unique optimal arm. A confidence level δ ∈ ( 0 , 1 ) {\displaystyle \delta \in (0,1)} is specified at the beginning. The algorithm must stop at some finite stopping time τ δ < + ∞ {\displaystyle \tau _{\delta }<+\infty } and return an arm a ^ τ δ {\displaystyle {\hat {a}}_{\tau _{\delta }}} such that the probability of error is bounded: P ( a ^ τ δ ≠ a ∗ ) ≤ δ {\displaystyle \mathbb {P} ({\hat {a}}_{\tau _{\delta }}\neq a^{})\leq \delta } . The objective is to minimize the expected sample complexity E [ τ δ ] {\displaystyle \mathbb {E} [\tau _{\delta }]} . Such a setting appears, for example, when a constraint on the confidence is required (for example, if we require a confidence level of 95%, so δ = 1 − 0.95 = 0.05 {\displaystyle \delta =1-0.95=0.05} ). Fixed horizon: In this setting, the number of samples T {\displaystyle T} is fixed in advance. The goal is to design an algorithm that minimizes the probability of misidentifying the optimal arm: P ( a ^ T ≠ a ∗ ) {\displaystyle \mathbb {P} ({\hat {a}}_{T}\neq a^{})} . This setting appears when the number of experiments is limited (for drug tests, the number of patients can be fixed in advance). === Example of simple modelling === In the case where we have K {\displaystyle K} treatments and we want to be sure with a confidence level of 95% which treatment is the best to heal a specific disease. Each treatment heals or does not heal the disease with a probability μ k {\displaystyle \mu _{k}} , which means that each distribution is a Bernoulli distribution, so D {\displaystyle {\mathcal {D}}} is the set of Bernoulli distributions. We can use a BAI algorithm to minimize E [ τ 0.05 ] {\displaystyle \mathbb {E} [\tau _{0.05}]} , the number of patients required to find the best treatment with probability 95%. == Applications == Best arm identification naturally arises in several practical domains: Adaptive clinical trials: The objective is to identify the most effective treatment based on sequentially collected patient data. Each treatment can be modeled as having an underlying distribution of outcomes. The goal is to identify the treatment with the highest expected outcome with high confidence (fixed confidence setting δ {\displaystyle \delta } ) while minimizing the number of drug test patients (minimise E [ τ δ ] {\displaystyle \mathbb {E} [\tau _{\delta }]} ), as it costs to pay patients for this and we would like to use as little as possible less effective drugs. Hyperparameter tuning: Selecting the best configuration for machine learning models efficiently by treating each hyperparameter setting as an arm. The goal is to find the best hyperparameter with as few experiments possible as experiments are costly in time and in energy == Fixed confidence level == In the fixed-confidence setting, the goal is to design an algorithm that identifies the best arm with a prescribed confidence level δ {\displaystyle \delta } while minimizing the expected number of samples. Any such algorithm requires two key components: Stopping rule: A decision criterion that determines when to stop sampling. Formally, this defines a stopping time τ δ {\displaystyle \tau _{\delta }} and returns an arm a ^ τ δ {\displaystyle {\hat {a}}_{\tau _{\delta }}} such that P ( a ^ τ δ ≠ a ⋆ ) ≤ δ {\displaystyle \mathbb {P} ({\hat {a}}_{\tau _{\delta }}\neq a^{\star })\leq \delta } and P ( τ δ < + ∞ ) = 1 {\displaystyle \mathbb {P} (\tau _{\delta }<+\infty )=1} . Sampling rule: A policy π {\displaystyle \pi } that, at each round t {\displaystyle t} , selects the next arm to sample a t {\displaystyle a_{t}} based on all previous observations ( a s , X s ) s < t {\displaystyle (a_{s},X_{s})_{s

Operational data store

An operational data store (ODS) is used for operational reporting and as a source of data for the enterprise data warehouse (EDW). It is a complementary element to an EDW in a decision support environment, and is used for operational reporting, controls, and decision making, as opposed to the EDW, which is used for tactical and strategic decision support. An ODS is a database designed to integrate data from multiple sources for additional operations on the data, for reporting, controls and operational decision support. Unlike a production master data store, the data is not passed back to operational systems. It may be passed for further operations and to the data warehouse for reporting. An ODS should not be confused with an enterprise data hub (EDH). An operational data store will take transactional data from one or more production systems and loosely integrate it, in some respects it is still subject oriented, integrated and time variant, but without the volatility constraints. This integration is mainly achieved through the use of EDW structures and content. An ODS is not an intrinsic part of an EDH solution, although an EDH may be used to subsume some of the processing performed by an ODS and the EDW. An EDH is a broker of data. An ODS is certainly not. Because the data originates from multiple sources, the integration often involves cleaning, resolving redundancy and checking against business rules for integrity. An ODS is usually designed to contain low-level or atomic (indivisible) data (such as transactions and prices) with limited history that is captured "real time" or "near real time" as opposed to the much greater volumes of data stored in the data warehouse generally on a less-frequent basis. == General use == The general purpose of an ODS is to integrate data from disparate source systems in a single structure, using data integration technologies like data virtualization, data federation, or extract, transform, and load (ETL). This will allow operational access to the data for operational reporting, master data or reference data management. An ODS is not a replacement or substitute for a data warehouse or for a data hub but in turn could become a source.

Vinberg's algorithm

In mathematics, Vinberg's algorithm is an algorithm, introduced by Ernest Borisovich Vinberg, for finding a fundamental domain of a hyperbolic reflection group. Conway (1983) used Vinberg's algorithm to describe the automorphism group of the 26-dimensional even unimodular Lorentzian lattice II25,1 in terms of the Leech lattice. == Description of the algorithm == Let Γ < I s o m ( H n ) {\displaystyle \Gamma <\mathrm {Isom} (\mathbb {H} ^{n})} be a hyperbolic reflection group. Choose any point v 0 ∈ H n {\displaystyle v_{0}\in \mathbb {H} ^{n}} ; we shall call it the basic (or initial) point. The fundamental domain P 0 {\displaystyle P_{0}} of its stabilizer Γ v 0 {\displaystyle \Gamma _{v_{0}}} is a polyhedral cone in H n {\displaystyle \mathbb {H} ^{n}} . Let H 1 , . . . , H m {\displaystyle H_{1},...,H_{m}} be the faces of this cone, and let a 1 , . . . , a m {\displaystyle a_{1},...,a_{m}} be outer normal vectors to it. Consider the half-spaces H k − = { x ∈ R n , 1 | ( x , a k ) ≤ 0 } . {\displaystyle H_{k}^{-}=\{x\in \mathbb {R} ^{n,1}|(x,a_{k})\leq 0\}.} There exists a unique fundamental polyhedron P {\displaystyle P} of Γ {\displaystyle \Gamma } contained in P 0 {\displaystyle P_{0}} and containing the point v 0 {\displaystyle v_{0}} . Its faces containing v 0 {\displaystyle v_{0}} are formed by faces H 1 , . . . , H m {\displaystyle H_{1},...,H_{m}} of the cone P 0 {\displaystyle P_{0}} . The other faces H m + 1 , . . . {\displaystyle H_{m+1},...} and the corresponding outward normals a m + 1 , . . . {\displaystyle a_{m+1},...} are constructed by induction. Namely, for H j {\displaystyle H_{j}} we take a mirror such that the root a j {\displaystyle a_{j}} orthogonal to it satisfies the conditions (1) ( v 0 , a j ) < 0 {\displaystyle (v_{0},a_{j})<0} ; (2) ( a i , a j ) ≤ 0 {\displaystyle (a_{i},a_{j})\leq 0} for all i < j {\displaystyle i

Microsoft Fresh Paint

Fresh Paint is a painting app developed by Microsoft and released on May 25, 2012. == History == Fresh Paint originated from a Microsoft Research project known as Project Gustav, an endeavor to reproduce the behavior of physical oil paint on a digital medium. To push the boundaries of simulating oil on a digital medium, the research team created a physics model that precisely replicated on a screen what would happen in the real world if you combined oil, a surface and a tool such as a paint brush. Two publications, Detail-Preserving Paint Modeling for 3D Brushes and Simple Data-Driven Modeling of Brushes, were released as a result of the team’s findings. After a variety of internal testing Project, Gustav was codenamed Digital Art. Partnering with The Museum of Modern Art, Digital Art was tested for a year by 60,000 people. With feedback culled from MoMA, developers expanded the existing physics model, experimenting with how real oil paint blended and reacted to the texture of a canvas. After final adjustments were made, Digital Art was rebranded as Fresh Paint. It was released to the public on 25 May 2012.

Evidence-based library and information practice

Evidence-based library and information practice (EBLIP) or evidence-based librarianship (EBL) is the use of evidence-based practices (EBP) in the field of library and information science (LIS). This means that all practical decisions made within LIS should 1) be based on research studies and 2) that these research studies are selected and interpreted according to some specific norms characteristic for EBP. Typically such norms disregard theoretical studies and qualitative studies and consider quantitative studies according to a narrow set of criteria of what counts as evidence. If such a narrow set of methodological criteria are not applied, it is better instead to speak of research based library and information practice. == Characteristics == Evidence-based practice in general has been characterised as a positivist approach; EBLIP is therefore also a positivist approach to LIS. As such, EBLIP is an approach in contrast to other approaches to LIS. The use of statistical approaches known as meta-analysis to conclude what evidence has been reported in the literature is one among other methods which is typical for the evidence-based approach. In 2002, Booth noted the three schools of EBILP had some commonalities, including the context of day-to-day decision-making, an emphasis on improving the quality of professional practice, a pragmatic focus on the 'best available evidence', incorporation of the user perspective, the acceptance of a broad range of quantitative and qualitative research designs, and access, either first-hand or second-hand, to the (process of) evidence-based practice and its products. He added one more, that EBILP is concerned with getting the best value for money. == The role of library and information science in EBP == Evidence-based practice in general is based on a very thorough search of the scientific literature and a very thorough selection and analysis of the retrieved literature. A close familiarity with database searching is needed, and library and information professionals have important roles to play in this respect. Therefore LIS professionals should be well suited to help professionals in other disciplines doing EBP. EBLIP is the application of this approach on LIS itself. It should be mentioned, however, that EBP started in medicine as evidence-based medicine (EBM) from which it spread to other fields. Only slowly and to a limited extent has EBP moved on to LIS. The EBLIP process can be applied to a variety of scenarios in LIS, including customer service, collection development, library management and information literacy instruction. In general, quantitative methods are used in LIS research. A 2010 study revealed five categories that capture the different ways library and information professionals experience evidence-based practice: Evidence-based practice is experienced as irrelevant; Evidence-based practice is experienced as learning from published research; Evidence-based practice is experienced as service improvement; Evidence-based practice is experienced as a way of being; Evidence-based practice is experienced as a weapon.