The cross-entropy (CE) method is a Monte Carlo method for importance sampling and optimization. It is applicable to both combinatorial and continuous problems, with either a static or noisy objective. The method approximates the optimal importance sampling estimator by repeating two phases: Draw a sample from a probability distribution. Minimize the cross-entropy between this distribution and a target distribution to produce a better sample in the next iteration. Reuven Rubinstein developed the method in the context of rare-event simulation, where tiny probabilities must be estimated, for example in network reliability analysis, queueing models, or performance analysis of telecommunication systems. The method has also been applied to the traveling salesman, quadratic assignment, DNA sequence alignment, max-cut and buffer allocation problems. == Estimation via importance sampling == Consider the general problem of estimating the quantity ℓ = E u [ H ( X ) ] = ∫ H ( x ) f ( x ; u ) d x {\displaystyle \ell =\mathbb {E} _{\mathbf {u} }[H(\mathbf {X} )]=\int H(\mathbf {x} )\,f(\mathbf {x} ;\mathbf {u} )\,{\textrm {d}}\mathbf {x} } , where H {\displaystyle H} is some performance function and f ( x ; u ) {\displaystyle f(\mathbf {x} ;\mathbf {u} )} is a member of some parametric family of distributions. Using importance sampling this quantity can be estimated as ℓ ^ = 1 N ∑ i = 1 N H ( X i ) f ( X i ; u ) g ( X i ) {\displaystyle {\hat {\ell }}={\frac {1}{N}}\sum _{i=1}^{N}H(\mathbf {X} _{i}){\frac {f(\mathbf {X} _{i};\mathbf {u} )}{g(\mathbf {X} _{i})}}} , where X 1 , … , X N {\displaystyle \mathbf {X} _{1},\dots ,\mathbf {X} _{N}} is a random sample from g {\displaystyle g\,} . For positive H {\displaystyle H} , the theoretically optimal importance sampling density (PDF) is given by g ∗ ( x ) = H ( x ) f ( x ; u ) / ℓ {\displaystyle g^{}(\mathbf {x} )=H(\mathbf {x} )f(\mathbf {x} ;\mathbf {u} )/\ell } . This, however, depends on the unknown ℓ {\displaystyle \ell } . The CE method aims to approximate the optimal PDF by adaptively selecting members of the parametric family that are closest (in the Kullback–Leibler sense) to the optimal PDF g ∗ {\displaystyle g^{}} . == Generic CE algorithm == Choose initial parameter vector v ( 0 ) {\displaystyle \mathbf {v} ^{(0)}} ; set t = 1. Generate a random sample X 1 , … , X N {\displaystyle \mathbf {X} _{1},\dots ,\mathbf {X} _{N}} from f ( ⋅ ; v ( t − 1 ) ) {\displaystyle f(\cdot ;\mathbf {v} ^{(t-1)})} Solve for v ( t ) {\displaystyle \mathbf {v} ^{(t)}} , where v ( t ) = argmax v 1 N ∑ i = 1 N H ( X i ) f ( X i ; u ) f ( X i ; v ( t − 1 ) ) log f ( X i ; v ) {\displaystyle \mathbf {v} ^{(t)}=\mathop {\textrm {argmax}} _{\mathbf {v} }{\frac {1}{N}}\sum _{i=1}^{N}H(\mathbf {X} _{i}){\frac {f(\mathbf {X} _{i};\mathbf {u} )}{f(\mathbf {X} _{i};\mathbf {v} ^{(t-1)})}}\log f(\mathbf {X} _{i};\mathbf {v} )} If convergence is reached then stop; otherwise, increase t by 1 and reiterate from step 2. In several cases, the solution to step 3 can be found analytically. Situations in which this occurs are When f {\displaystyle f\,} belongs to the natural exponential family When f {\displaystyle f\,} is discrete with finite support When H ( X ) = I { x ∈ A } {\displaystyle H(\mathbf {X} )=\mathrm {I} _{\{\mathbf {x} \in A\}}} and f ( X i ; u ) = f ( X i ; v ( t − 1 ) ) {\displaystyle f(\mathbf {X} _{i};\mathbf {u} )=f(\mathbf {X} _{i};\mathbf {v} ^{(t-1)})} , then v ( t ) {\displaystyle \mathbf {v} ^{(t)}} corresponds to the maximum likelihood estimator based on those X k ∈ A {\displaystyle \mathbf {X} _{k}\in A} . == Continuous optimization—example == The same CE algorithm can be used for optimization, rather than estimation. Suppose the problem is to maximize some function S {\displaystyle S} , for example, S ( x ) = e − ( x − 2 ) 2 + 0.8 e − ( x + 2 ) 2 {\displaystyle S(x)={\textrm {e}}^{-(x-2)^{2}}+0.8\,{\textrm {e}}^{-(x+2)^{2}}} . To apply CE, one considers first the associated stochastic problem of estimating P θ ( S ( X ) ≥ γ ) {\displaystyle \mathbb {P} _{\boldsymbol {\theta }}(S(X)\geq \gamma )} for a given level γ {\displaystyle \gamma \,} , and parametric family { f ( ⋅ ; θ ) } {\displaystyle \left\{f(\cdot ;{\boldsymbol {\theta }})\right\}} , for example the 1-dimensional Gaussian distribution, parameterized by its mean μ t {\displaystyle \mu _{t}\,} and variance σ t 2 {\displaystyle \sigma _{t}^{2}} (so θ = ( μ , σ 2 ) {\displaystyle {\boldsymbol {\theta }}=(\mu ,\sigma ^{2})} here). Hence, for a given γ {\displaystyle \gamma \,} , the goal is to find θ {\displaystyle {\boldsymbol {\theta }}} so that D K L ( I { S ( x ) ≥ γ } ‖ f θ ) {\displaystyle D_{\mathrm {KL} }({\textrm {I}}_{\{S(x)\geq \gamma \}}\|f_{\boldsymbol {\theta }})} is minimized. This is done by solving the sample version (stochastic counterpart) of the KL divergence minimization problem, as in step 3 above. It turns out that parameters that minimize the stochastic counterpart for this choice of target distribution and parametric family are the sample mean and sample variance corresponding to the elite samples, which are those samples that have objective function value ≥ γ {\displaystyle \geq \gamma } . The worst of the elite samples is then used as the level parameter for the next iteration. This yields the following randomized algorithm that happens to coincide with the so-called Estimation of Multivariate Normal Algorithm (EMNA), an estimation of distribution algorithm. === Pseudocode === // Initialize parameters μ := −6 σ2 := 100 t := 0 maxits := 100 N := 100 Ne := 10 // While maxits not exceeded and not converged while t < maxits and σ2 > ε do // Obtain N samples from current sampling distribution X := SampleGaussian(μ, σ2, N) // Evaluate objective function at sampled points S := exp(−(X − 2) ^ 2) + 0.8 exp(−(X + 2) ^ 2) // Sort X by objective function values in descending order X := sort(X, S) // Update parameters of sampling distribution via elite samples μ := mean(X(1:Ne)) σ2 := var(X(1:Ne)) t := t + 1 // Return mean of final sampling distribution as solution return μ == Related methods == Simulated annealing Genetic algorithms Harmony search Estimation of distribution algorithm Tabu search Natural Evolution Strategy Ant colony optimization algorithms
Prequel (mobile application)
Prequel, Inc. is an American technology company and mobile app developer known for developing the Prequel mobile application, which enables editing photos and videos with filters and effects generated using artificial intelligence. Prequel was founded in 2018 by Serge Aliseenko and Timur Khabirov, who currently serves as the company's CEO. It is headquartered in New York City. As of August 2022, it had been downloaded more than 100 million times. == History == In 2016, entrepreneur Timur Khabirov and investor Serge Aliseenko registered a US corporation named AIAR Labs Inc, which was developing AR solutions as an outsourced contractor. Of several proprietary products, Prequel was selected for beta-testing as a product focused on editing photos and videos. In 2018, Prequel was released on the Apple App Store. The launch cost $3 million USD, financed with the founders’ personal funds. The first release included approximately 10 filters for photos and the same amount of effects that augmented images with rose petals, rain and snow, VHS and film reel simulations, glitch, grain, sun puddles, and lomography. By June 2020, the app had also been released for Android. In 2021, Prequel founders Timur Khabirov and Serge Aliseenko launched a venture studio for startups working with artificial, computer vision, and AR-based visual art. In December 2022, Prequel reached the number 14 slot on the global rankings for Apple App Store’s Top Charts and the number 5 slot on the App Store’s U.S. charts. In March 2023, Prequel launched a new app called Artique, which is an AI-powered image editing app for businesses. Artique provides advertising and marketing graphic design using ready-made templates that users can customize, while giving suggestions and visual cues through artificial intelligence. Prequel was also one of the companies participating in discussions about artificial intelligence at SXSW 2023. == Features == Prequel describes its app as an "Aesthetic Pic Editor. The app uses artificial intelligence to create and edit content. Prequel can be used to touch up faces on images and videos and can also tie various decorative elements to certain points on the human body and face. Prequel filters include the "Cartoon" filter, which converts selfies into cartoon-style pictures. Other filters include Kidcore, Dust, Grain, Fisheye, Retro Style, Miami, Disco, and VHS-style filters, as well as the ability to create Renaissance-style pictures. Prequel also gives users the ability to apply color correction tools and to make moving images with 3D effects out of 2D images. Prequel allows users to take photos and videos directly through the app and apply filters and effects in real time. The app also comes with manual editing options for photos, such as adjusting the brightness and/or exposure and cropping photos, as well as an option to automatically apply adjustments. The Prequel app uses the Core ML, MNN, and TFLight frameworks to work with its neural networks. Some AI solutions are launched server-side, and some on the user's mobile device. A resulting photo or video edited with the app is called "a prequel." The app daily generates over 2 million such prequels, which are published by users in Instagram, TikTok, and other social media. As of 2022, the app has more than 800 filters and effects, along with video templates and support for GIFs and stickers. Prequel is free-to-use, but has a premium version that gives users access to more effects, filters, and beauty tools. Since its launch in 2018, Prequel has been downloaded more than 100 million times.
Collocation extraction
Collocation extraction is the task of using a computer to extract collocations automatically from a corpus. The traditional method of performing collocation extraction is to find a formula based on the statistical quantities of those words to calculate a score associated to every word pairs. Proposed formulas are mutual information, t-test, z test, chi-squared test and likelihood ratio. Within the area of corpus linguistics, collocation is defined as a sequence of words or terms which co-occur more often than would be expected by chance. 'Crystal clear', 'middle management', 'nuclear family', and 'cosmetic surgery' are examples of collocated pairs of words. Some words are often found together because they make up a compound noun, for example 'riding boots' or 'motor cyclist' or ‘collocation extraction’ its very self.
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Node2vec
node2vec is an algorithm to generate vector representations of nodes on a graph. The node2vec framework learns low-dimensional representations for nodes in a graph through the use of random walks through a graph starting at a target node. It is useful for a variety of machine learning applications. node2vec follows the intuition that random walks through a graph can be treated like sentences in a corpus. Each node in a graph is treated like an individual word, and a random walk is treated as a sentence. By feeding these "sentences" into a skip-gram, or by using the continuous bag of words model, paths found by random walks can be treated as sentences, and traditional data-mining techniques for documents can be used. The algorithm generalizes prior work which is based on rigid notions of network neighborhoods, and argues that the added flexibility in exploring neighborhoods is the key to learning richer representations of nodes in graphs. The algorithm is considered one of the best graph classifiers.
FIRST Global Challenge
The FIRST Global Challenge is a yearly robotics competition organized by the International First Committee Association. It promotes STEM education and careers for youth and was created by Dean Kamen in 2016 as an expansion of FIRST, an organization with similar objectives. == History == FIRST Global is a trade name for the International First Committee Association, a nonprofit corporation based in Manchester, New Hampshire, with a 501(c)(3) designation from the IRS. The nonprofit was founded by the co-founder of FIRST, Dean Kamen, with the objective of promoting STEM education and careers in the developing world through Olympics-style robotics competitions. Former US Congressman, Joe Sestak was the organization's president in 2017, but left after the 2017 Challenge. Each year, the FIRST Global Challenge is held in a different city. For example, Mexico City was selected to host the 2018 Challenge after the United States hosted the 2017 edition in Washington, DC. This is a change from FIRST's system of championships, where one city hosts for several years at a time. In May 2020, it was announced that FIRST Global would not host a traditional challenge in 2020 due to the COVID-19 pandemic and shifted to a remote model. One of the three champions were Team Bangladesh. In 2022, FIRST Global returned to in-person events with the 2022 Challenge in Geneva, Switzerland. == Editions == === Washington, D.C. 2017 === The 2017 FIRST Global Challenge was held in Washington, D.C., from July 16–18, and the challenge was the use of robots to separate different colored balls, representing clean water and impurities in water, symbolizing the Engineering Grand Challenge (based on the Millennium Development Goal) of improving access to clean water in the developing world. Around 160 teams composed of 15- to 18-year-olds from 157 countries participated, and around 60% of teams were created or led by young women. Six continental teams also participated. === Mexico City 2018 === The 2018 FIRST Global Challenge was held in Mexico City from August 15–18. The 2018 Challenge was called Energy Impact and explored the impact of various types of energy on the world and how they can be made more sustainable. In the challenge, robots worked together in teams of three to give cubes to human players, turn a crank, and score cubes in goals in order to generate electrical power. The challenge was based on three Engineering Grand Challenges; making solar energy affordable, making fusion energy a reality, and creating carbon sequestration methods. === Dubai 2019 === The 2019 challenge, called Ocean Opportunities, was held in Dubai from October 24–27 and was the first challenge hosted outside of North America. The challenge was themed around clearing the ocean of pollutants, and had two alliances of three teams each attempting to score large and small balls representing pollutants into processing areas and a processing barge. The processing barge had multiple levels, with higher levels worth more points. At the end of the match, robots "docked" with the barge by driving onto or climbing up it, with climbing worth more points. The event was opened by Sheikh Hamdan bin Mohammed Al Maktoum, Crown Prince of Dubai. === Geneva 2022 === The 2022 challenge called Carbon Capture, was held in Geneva from October 13–16. The challenge was themed around removing carbon dioxide (CO2) emissions from the atmosphere. In the Carbon Capture game, six different countries worked together to capture and store black balls representing carbon particles. The storage tower had multiple cantilevered bars that the robots mounted to, with the higher bars worth a greater multiplier. At the end of a match, robots "docked" on the storage tower's base or climbed the bars with their alliance indicator ball. Each match started with a "global alliance" of six countries, then divided into two "regional alliances" each consisting of three countries. The event was opened by Dr. Martina Hirayama, Switzerland State Secretary for Education, Research and Innovation (SERI). === Singapore 2023 === The 2023 challenge, called Hydrogen Horizons, was held in Singapore from October 7–10. The challenge is themed around renewable energy with a focus on hydrogen technologies. === Athens 2024 === The 2024 challenge was hosted in the Peace and Friendship Stadium in Attica, Greece. === Panama 2025 === The 2025 challenge, Eco Equilibrium, was hosted in the Panama Convention Centre in Panama City, Panama. == Subordinate programs == === Global STEM Corps === The Global STEM Corps is a FIRST Global initiative that connects qualified volunteer mentors with students in developing countries to prepare them for competitions. === New Technology Experience === The New Technology Experience (NTE) is an annual component of the FIRST Global Challenge that was added to the organization's offerings in 2021. It was established as a means for the student community to stay current with cutting-edge technology and is integrated with each year's theme. The 2021 NTE was the CubeSat Prototype Challenge. The 2022 NTE, Carbon Countermeasures, was presented in partnership with XPRIZE.
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