Statistical learning theory is a framework for machine learning drawing from the fields of statistics and functional analysis. Statistical learning theory deals with the statistical inference problem of finding a predictive function based on data. Statistical learning theory has led to successful applications in fields such as computer vision, speech recognition, and bioinformatics. == Introduction == The goals of learning are understanding and prediction. Learning falls into many categories, including supervised learning, unsupervised learning, online learning, and reinforcement learning. From the perspective of statistical learning theory, supervised learning is best understood. Supervised learning involves learning from a training set of data. Every point in the training is an input–output pair, where the input maps to an output. The learning problem consists of inferring the function that maps between the input and the output, such that the learned function can be used to predict the output from future input. Depending on the type of output, supervised learning problems are either problems of regression or problems of classification. If the output takes a continuous range of values, it is a regression problem. Using Ohm's law as an example, a regression could be performed with voltage as input and current as an output. The regression would find the functional relationship between voltage and current to be R {\displaystyle R} , such that V = I R {\displaystyle V=IR} Classification problems are those for which the output will be an element from a discrete set of labels. Classification is very common for machine learning applications. In facial recognition, for instance, a picture of a person's face would be the input, and the output label would be that person's name. The input would be represented by a large multidimensional vector whose elements represent pixels in the picture. After learning a function based on the training set data, that function is validated on a test set of data, data that did not appear in the training set. == Formal description == Take X {\displaystyle X} to be the vector space of all possible inputs, and Y {\displaystyle Y} to be the vector space of all possible outputs. Statistical learning theory takes the perspective that there is some unknown probability distribution over the product space Z = X × Y {\displaystyle Z=X\times Y} , i.e. there exists some unknown p ( z ) = p ( x , y ) {\displaystyle p(z)=p(\mathbf {x} ,y)} . The training set is made up of n {\displaystyle n} samples from this probability distribution, and is notated S = { ( x 1 , y 1 ) , … , ( x n , y n ) } = { z 1 , … , z n } {\displaystyle S=\{(\mathbf {x} _{1},y_{1}),\dots ,(\mathbf {x} _{n},y_{n})\}=\{\mathbf {z} _{1},\dots ,\mathbf {z} _{n}\}} Every x i {\displaystyle \mathbf {x} _{i}} is an input vector from the training data, and y i {\displaystyle y_{i}} is the output that corresponds to it. In this formalism, the inference problem consists of finding a function f : X → Y {\displaystyle f:X\to Y} such that f ( x ) ∼ y {\displaystyle f(\mathbf {x} )\sim y} . Let H {\displaystyle {\mathcal {H}}} be a space of functions f : X → Y {\displaystyle f:X\to Y} called the hypothesis space. The hypothesis space is the space of functions the algorithm will search through. Let V ( f ( x ) , y ) {\displaystyle V(f(\mathbf {x} ),y)} be the loss function, a metric for the difference between the predicted value f ( x ) {\displaystyle f(\mathbf {x} )} and the actual value y {\displaystyle y} . The expected risk is defined to be I [ f ] = ∫ X × Y V ( f ( x ) , y ) p ( x , y ) d x d y {\displaystyle I[f]=\int _{X\times Y}V(f(\mathbf {x} ),y)\,p(\mathbf {x} ,y)\,d\mathbf {x} \,dy} The target function, the best possible function f {\displaystyle f} that can be chosen, is given by the f {\displaystyle f} that satisfies f = argmin h ∈ H I [ h ] {\displaystyle f=\mathop {\operatorname {argmin} } _{h\in {\mathcal {H}}}I[h]} Because the probability distribution p ( x , y ) {\displaystyle p(\mathbf {x} ,y)} is unknown, a proxy measure for the expected risk must be used. This measure is based on the training set, a sample from this unknown probability distribution. It is called the empirical risk I S [ f ] = 1 n ∑ i = 1 n V ( f ( x i ) , y i ) {\displaystyle I_{S}[f]={\frac {1}{n}}\sum _{i=1}^{n}V(f(\mathbf {x} _{i}),y_{i})} A learning algorithm that chooses the function f S {\displaystyle f_{S}} that minimizes the empirical risk is called empirical risk minimization. == Loss functions == The choice of loss function is a determining factor on the function f S {\displaystyle f_{S}} that will be chosen by the learning algorithm. The loss function also affects the convergence rate for an algorithm. It is important for the loss function to be convex. Different loss functions are used depending on whether the problem is one of regression or one of classification. === Regression === The most common loss function for regression is the square loss function (also known as the L2-norm). This familiar loss function is used in Ordinary Least Squares regression. The form is: V ( f ( x ) , y ) = ( y − f ( x ) ) 2 {\displaystyle V(f(\mathbf {x} ),y)=(y-f(\mathbf {x} ))^{2}} The absolute value loss (also known as the L1-norm) is also sometimes used: V ( f ( x ) , y ) = | y − f ( x ) | {\displaystyle V(f(\mathbf {x} ),y)=|y-f(\mathbf {x} )|} === Classification === In some sense the 0-1 indicator function is the most natural loss function for classification. It takes the value 0 if the predicted output is the same as the actual output, and it takes the value 1 if the predicted output is different from the actual output. For binary classification with Y = { − 1 , 1 } {\displaystyle Y=\{-1,1\}} , this is: V ( f ( x ) , y ) = θ ( − y f ( x ) ) {\displaystyle V(f(\mathbf {x} ),y)=\theta (-yf(\mathbf {x} ))} where θ {\displaystyle \theta } is the Heaviside step function. == Regularization == In machine learning problems, a major problem that arises is that of overfitting. Because learning is a prediction problem, the goal is not to find a function that most closely fits the (previously observed) data, but to find one that will most accurately predict output from future input. Empirical risk minimization runs this risk of overfitting: finding a function that matches the data exactly but does not predict future output well. Overfitting is symptomatic of unstable solutions; a small perturbation in the training set data would cause a large variation in the learned function. It can be shown that if the stability for the solution can be guaranteed, generalization and consistency are guaranteed as well. Regularization can solve the overfitting problem and give the problem stability. Regularization can be accomplished by restricting the hypothesis space H {\displaystyle {\mathcal {H}}} . A common example would be restricting H {\displaystyle {\mathcal {H}}} to linear functions: this can be seen as a reduction to the standard problem of linear regression. H {\displaystyle {\mathcal {H}}} could also be restricted to polynomial of degree p {\displaystyle p} , exponentials, or bounded functions on L1. Restriction of the hypothesis space avoids overfitting because the form of the potential functions are limited, and so does not allow for the choice of a function that gives empirical risk arbitrarily close to zero. One example of regularization is Tikhonov regularization. This consists of minimizing 1 n ∑ i = 1 n V ( f ( x i ) , y i ) + γ ‖ f ‖ H 2 {\displaystyle {\frac {1}{n}}\sum _{i=1}^{n}V(f(\mathbf {x} _{i}),y_{i})+\gamma \left\|f\right\|_{\mathcal {H}}^{2}} where γ {\displaystyle \gamma } is a fixed and positive parameter, the regularization parameter. Tikhonov regularization ensures existence, uniqueness, and stability of the solution. == Bounding empirical risk == Consider a binary classifier f : X → { 0 , 1 } {\displaystyle f:{\mathcal {X}}\to \{0,1\}} . We can apply Hoeffding's inequality to bound the probability that the empirical risk deviates from the true risk to be a Sub-Gaussian distribution. P ( | R ^ ( f ) − R ( f ) | ≥ ϵ ) ≤ 2 e − 2 n ϵ 2 {\displaystyle \mathbb {P} (|{\hat {R}}(f)-R(f)|\geq \epsilon )\leq 2e^{-2n\epsilon ^{2}}} But generally, when we do empirical risk minimization, we are not given a classifier; we must choose it. Therefore, a more useful result is to bound the probability of the supremum of the difference over the whole class. P ( sup f ∈ F | R ^ ( f ) − R ( f ) | ≥ ϵ ) ≤ 2 S ( F , n ) e − n ϵ 2 / 8 ≈ n d e − n ϵ 2 / 8 {\displaystyle \mathbb {P} {\bigg (}\sup _{f\in {\mathcal {F}}}|{\hat {R}}(f)-R(f)|\geq \epsilon {\bigg )}\leq 2S({\mathcal {F}},n)e^{-n\epsilon ^{2}/8}\approx n^{d}e^{-n\epsilon ^{2}/8}} where S ( F , n ) {\displaystyle S({\mathcal {F}},n)} is the shattering number and n {\displaystyle n} is the number of samples in your dataset. The exponential term comes from Hoeffding but there is an extra cost of taking the supremum over the whole cla
Curvelet
Curvelets are a non-adaptive technique for multi-scale object representation. Being an extension of the wavelet concept, they are becoming popular in similar fields, namely in image processing and scientific computing. Wavelets generalize the Fourier transform by using a basis that represents both location and spatial frequency. For 2D or 3D signals, directional wavelet transforms go further, by using basis functions that are also localized in orientation. A curvelet transform differs from other directional wavelet transforms in that the degree of localisation in orientation varies with scale. In particular, fine-scale basis functions are long ridges; the shape of the basis functions at scale j is 2 − j {\displaystyle 2^{-j}} by 2 − j / 2 {\displaystyle 2^{-j/2}} so the fine-scale bases are skinny ridges with a precisely determined orientation. Curvelets are an appropriate basis for representing images (or other functions) which are smooth apart from singularities along smooth curves, where the curves have bounded curvature, i.e. where objects in the image have a minimum length scale. This property holds for cartoons, geometrical diagrams, and text. As one zooms in on such images, the edges they contain appear increasingly straight. Curvelets take advantage of this property, by defining the higher resolution curvelets to be more elongated than the lower resolution curvelets. However, natural images (photographs) do not have this property; they have detail at every scale. Therefore, for natural images, it is preferable to use some sort of directional wavelet transform whose wavelets have the same aspect ratio at every scale. When the image is of the right type, curvelets provide a representation that is considerably sparser than other wavelet transforms. This can be quantified by considering the best approximation of a geometrical test image that can be represented using only n {\displaystyle n} wavelets, and analysing the approximation error as a function of n {\displaystyle n} . For a Fourier transform, the squared error decreases only as O ( 1 / n ) {\displaystyle O(1/{\sqrt {n}})} . For a wide variety of wavelet transforms, including both directional and non-directional variants, the squared error decreases as O ( 1 / n ) {\displaystyle O(1/n)} . The extra assumption underlying the curvelet transform allows it to achieve O ( ( log n ) 3 / n 2 ) {\displaystyle O({(\log n)}^{3}/{n^{2}})} . Efficient numerical algorithms exist for computing the curvelet transform of discrete data. The computational cost of the discrete curvelet transforms proposed by Candès et al. (Discrete curvelet transform based on unequally-spaced fast Fourier transforms and based on the wrapping of specially selected Fourier samples) is approximately 6–10 times that of an FFT, and has the same dependence of O ( n 2 log n ) {\displaystyle O(n^{2}\log n)} for an image of size n × n {\displaystyle n\times n} . == Curvelet construction == To construct a basic curvelet ϕ {\displaystyle \phi } and provide a tiling of the 2-D frequency space, two main ideas should be followed: Consider polar coordinates in frequency domain Construct curvelet elements being locally supported near wedges The number of wedges is N j = 4 ⋅ 2 ⌈ j 2 ⌉ {\displaystyle N_{j}=4\cdot 2^{\left\lceil {\frac {j}{2}}\right\rceil }} at the scale 2 − j {\displaystyle 2^{-j}} , i.e., it doubles in each second circular ring. Let ξ = ( ξ 1 , ξ 2 ) T {\displaystyle {\boldsymbol {\xi }}=\left(\xi _{1},\xi _{2}\right)^{T}} be the variable in frequency domain, and r = ξ 1 2 + ξ 2 2 , ω = arctan ξ 1 ξ 2 {\displaystyle r={\sqrt {\xi _{1}^{2}+\xi _{2}^{2}}},\omega =\arctan {\frac {\xi _{1}}{\xi _{2}}}} be the polar coordinates in the frequency domain. We use the ansatz for the dilated basic curvelets in polar coordinates: ϕ ^ j , 0 , 0 := 2 − 3 j 4 W ( 2 − j r ) V ~ N j ( ω ) , r ≥ 0 , ω ∈ [ 0 , 2 π ) , j ∈ N 0 {\displaystyle {\hat {\phi }}_{j,0,0}:=2^{\frac {-3j}{4}}W(2^{-j}r){\tilde {V}}_{N_{j}}(\omega ),r\geq 0,\omega \in [0,2\pi ),j\in N_{0}} To construct a basic curvelet with compact support near a ″basic wedge″, the two windows W {\displaystyle W} and V ~ N j {\displaystyle {\tilde {V}}_{N_{j}}} need to have compact support. Here, we can simply take W ( r ) {\displaystyle W(r)} to cover ( 0 , ∞ ) {\displaystyle (0,\infty )} with dilated curvelets and V ~ N j {\displaystyle {\tilde {V}}_{N_{j}}} such that each circular ring is covered by the translations of V ~ N j {\displaystyle {\tilde {V}}_{N_{j}}} . Then the admissibility yields ∑ j = − ∞ ∞ | W ( 2 − j r ) | 2 = 1 , r ∈ ( 0 , ∞ ) . {\displaystyle \sum _{j=-\infty }^{\infty }\left|W(2^{-j}r)\right|^{2}=1,r\in (0,\infty ).} see Window Functions for more information For tiling a circular ring into N {\displaystyle N} wedges, where N {\displaystyle N} is an arbitrary positive integer, we need a 2 π {\displaystyle 2\pi } -periodic nonnegative window V ~ N {\displaystyle {\tilde {V}}_{N}} with support inside [ − 2 π N , 2 π N ] {\displaystyle \left[{\frac {-2\pi }{N}},{\frac {2\pi }{N}}\right]} such that ∑ l = 0 N − 1 V ~ N 2 ( ω − 2 π l N ) = 1 {\displaystyle \sum _{l=0}^{N-1}{\tilde {V}}_{N}^{2}\left(\omega -{\frac {2\pi l}{N}}\right)=1} , for all ω ∈ [ 0 , 2 π ) {\displaystyle \omega \in \left[0,2\pi \right)} , V ~ N {\displaystyle {\tilde {V}}_{N}} can be simply constructed as 2 π {\displaystyle 2\pi } -periodizations of a scaled window V ( N ω 2 π ) {\displaystyle V\left({\frac {N\omega }{2\pi }}\right)} . Then, it follows that ∑ l = 0 N j − 1 | 2 3 j 4 ϕ ^ j , 0 , 0 ( r , ω − 2 π l N j ) | 2 = | W ( 2 − j r ) | 2 ∑ l = 0 N j − 1 V ~ N j 2 ( ω − 2 π l N ) = | W ( 2 − j r ) | 2 {\displaystyle \sum _{l=0}^{N_{j}-1}\left|2^{\frac {3j}{4}}{\hat {\phi }}_{j,0,0}\left(r,\omega -{\frac {2\pi l}{N_{j}}}\right)\right|^{2}=\left|W(2^{-j}r)\right|^{2}\sum _{l=0}^{N_{j}-1}{\tilde {V}}_{N_{j}}^{2}\left(\omega -{\frac {2\pi l}{N}}\right)=\left|W(2^{-j}r)\right|^{2}} For a complete covering of the frequency plane including the region around zero, we need to define a low pass element ϕ ^ − 1 := W 0 ( | ξ | ) {\displaystyle {\hat {\phi }}_{-1}:=W_{0}(\left|\xi \right|)} with W 0 2 ( r ) 2 := 1 − ∑ j = 0 ∞ W ( 2 − j r ) 2 {\displaystyle W_{0}^{2}(r)^{2}:=1-\sum _{j=0}^{\infty }W(2^{-j}r)^{2}} that is supported on the unit circle, and where we do not consider any rotation. == Applications == Image processing Seismic exploration Fluid mechanics PDEs solving Compressed sensing
List of monochrome and RGB color formats
This list of monochrome and RGB palettes includes generic repertoires of colors (color palettes) to produce black-and-white and RGB color pictures by a computer's display hardware. RGB is the most common method to produce colors for displays; so these complete RGB color repertoires have every possible combination of R-G-B triplets within any given maximum number of levels per component. Each palette is represented by a series of color patches. When the number of colors is low, a 1-pixel-size version of the palette appears below it, for easily comparing relative palette sizes. Huge palettes are given directly in one-color-per-pixel color patches. For each unique palette, an image color test chart and sample image (truecolor original follows) rendered with that palette (without dithering) are given. The test chart shows the full 256 levels of the red, green, and blue (RGB) primary colors and cyan, magenta, and yellow complementary colors, along with a full 256-level grayscale. Gradients of RGB intermediate colors (orange, lime green, sea green, sky blue, violet, and fuchsia), and a full hue spectrum are also present. Color charts are not gamma corrected. These elements illustrate the color depth and distribution of the colors of any given palette, and the sample image indicates how the color selection of such palettes could represent real-life images. These images are not necessarily representative of how the image would be displayed on the original graphics hardware, as the hardware may have additional limitations regarding the maximum display resolution, pixel aspect ratio and color placement. Implementation of these formats is specific to each machine. Therefore, the number of colors that can be simultaneously displayed in a given text or graphic mode might be different. Also, the actual displayed colors are subject to the output format used - PAL or NTSC, composite or component video, etc. - and might be slightly different. For simulated images and specific hardware and alternate methods to produce colors other than RGB (ex: composite), see the List of 8-bit computer hardware palettes, the List of 16-bit computer hardware palettes and the List of video game console palettes. For various software arrangements and sorts of colors, including other possible full RGB arrangements within 8-bit color depth displays, see the List of software palettes. == Monochrome palettes == These palettes only have some shades of gray, from black to white (considered the darkest and lightest "grays", respectively). The general rule is that those palettes have 2n different shades of gray, where n is the number of bits needed to represent a single pixel. === Monochrome (1-bit grayscale) === Monochrome graphics displays typically have a black background with a white or light gray image, though green and amber monochrome monitors were also common. Such a palette requires only one bit per pixel. Where photo-realism was desired, these early computer systems had a heavy reliance on dithering to make up for the limits of the technology. In some systems, as Hercules and CGA graphic cards for the IBM PC, a bit value of 1 represents white pixels (light on) and a value of 0 the black ones (light off); others, like the Playdate and Atari ST and Apple Macintosh with monochrome monitors, a bit value of 0 means a white pixel (no ink) and a value of 1 means a black pixel (dot of ink), which it approximates to the printing logic. === 2-bit Grayscale === In a 2-bit color palette each pixel's value is represented by 2 bits resulting in a 4-value palette (22 = 4). 2-bit dithering: It has black, white and two intermediate levels of gray as follows: A monochrome 2-bit palette is used on: The Monochrome Display Adapter for the IBM PC NeXT Computer, NeXTcube and NeXTstation monochrome graphic displays. Original Game Boy system portable video game console. Macintosh PowerBook 150 monochrome LC displays. Amiga with A2024 monochrome monitor in high-resolution mode. The original Amazon Kindle The original WonderSwan The Tiger Electronics Game.com portable video game console The original Neo Geo Pocket. === 4-bit Grayscale === In a 4-bit color palette each pixel's value is represented by 4 bits resulting in a 16-value palette (24 = 16): 4-bit grayscale dithering does a fairly good job of reducing visible banding of the level changes: A monochrome 4-bit palette is used on: MOS Technology VDC (on the Commodore 128 with monochrome monitor) Amstrad CPC series with a GT64/GT65 Green Monitor (16 unique green shades) Amstrad CPC Plus series with the MM12 Monochrome monitor (16 shades of grey) Some Apple PowerBooks equipped with monochrome displays like the PowerBook 5300 The original VideoNow === 8-bit Grayscale === In an 8-bit color palette each pixel's value is represented by 8 bits resulting in a 256-value palette (28 = 256). This is usually the maximum number of grays in ordinary monochrome systems; each image pixel occupies a single memory byte. Most scanners can capture images in 8-bit grayscale, and image file formats like TIFF and JPEG natively support this monochrome palette size. Alpha channels employed for video overlay also use (conceptually) this palette. The gray level indicates the opacity of the blended image pixel over the background image pixel. == Dichrome palettes == === 16-bit RG palette === The RG or red–green color space is a color space that uses only two primary colors: red and green. It was used on early color processes for films. It was used as an additive format, similar to the RGB color model but without a blue channel, on processes such as Kinemacolor, Prizma, Technicolor I, Raycol, etc., producing shades of black, red, green and yellow. Alternatively, it was used as a subtractive format on Brewster Color I, Kodachrome I, Prizma II, Technicolor II, etc., producing shades of transparent, red, green and black. Until recently, its primary use was in low-cost light-emitting diode displays in which red and green tended to be far more common than the still nascent blue LED technology, but full-color LEDs with blue have become more common in recent years. ColorCode 3-D, a anaglyph stereoscopic color scheme, uses the RG color space to simulate a broad spectrum of color in one eye, while the blue portion of the spectrum transmits a black-and-white (black-and-blue) image to the other eye to give depth perception. === 16-bit RB palette === === 16-bit GB palette === == Regular RGB palettes == Here are grouped those full RGB hardware palettes that have the same number of binary levels (i.e., the same number of bits) for every red, green and blue components using the full RGB color model. Thus, the total number of colors are always the number of possible levels by component, n, raised to a power of 3: n×n×n = n3. === 3-bit RGB === 3-bit RGB dithering: Systems with a 3-bit RGB palette use 1 bit for each of the red, green and blue color components. That is, each component is either "on" or "off" with no intermediate states. This results in an 8-color palette ((21)3 = 23 = 8) that has black, white, the three RGB primary colors red, green and blue and their correspondent complementary colors cyan, magenta and yellow as follows: The color indices vary between implementations; therefore, index numbers are not given. The 3-bit RGB palette is used by: Text terminals following the ECMA-48 standard (sometimes known as the "ANSI standard", although ANSI X3.128 does not define colors) World System Teletext Level 1/1.5 Videotex Oric computers BBC Micro PC-8801 (up to the MkII) PC-9801 (with original 8086 CPU, before the VM/VX models) Sharp X1 (models before the X1 Turbo Z) Sharp MZ 700 FM-7, FM New 7, FM 77 (before the FM77AV) Sinclair QL Space Invaders Part II (arcade hardware) Macintosh SE (with a color printer or external monitor) Atari 2600 (SECAM version) Color Maximite (PIC32 based microcomputer) Arcadia 2001 PV-1000 Monkey Magic (arcade hardware) VIC-20 (high-res mode) Mouse Trap (arcade hardware) Sanyo MBC-550 series Windows 1.0 (includes dithering) === 6-bit RGB === Systems with a 6-bit RGB palette use 2 bits for each of the red, green, and blue color components. This results in a (22)3 = 43 = 64-color palette as follows: 6-bit RGB systems include the following: Enhanced Graphics Adapter (EGA) for IBM PC/AT (16 colors at once) Sega Master System video game console (32 colors at once) GIME for TRS-80 Color Computer 3 (16 colors at once) Pebble Time smartwatch which has a 6-bit (64 color) e-paper display Parallax Propeller using the reference VGA circuit === 9-bit RGB === Systems with a 9-bit RGB palette use 3 bits for each of the red, green, and blue color components. This results in a (23)3 = 83 = 512-color palette as follows: 9-bit RGB systems include the following: Atari ST (Normally 4 to 16 at once without tricks) MSX2 computers (up to 16 at once) Sega Genesis video game console, (64 colors at once) Sega Nomad TurboGrafx-16 (NEC PC-Engine) ZX Spectrum Next The NEC PC-88
Integrated test facility
An integrated test facility (ITF) creates a fictitious entity in a database to process test transactions simultaneously with live input. ITF can be used to incorporate test transactions into a normal production run of a system. Its advantage is that periodic testing does not require separate test processes. However, careful planning is necessary, and test data must be isolated from production data. Moreover, ITF validates the correct operation of a transaction in an application, but it does not ensure that a system is being operated correctly. Integrated test facility is considered a useful audit tool during an IT audit because it uses the same programs to compare processing using independently calculated data. This involves setting up dummy entities on an application system and processing test or production data against the entity as a means of verifying processing accuracy.
Hedgeable
Hedgeable, Inc. was a U.S. based financial services company and digital wealth management platform headquartered in New York City. Hedgeable was known for not following set allocations, and instead actively managing accounts in response to market movements. On August 9, 2018, Hedgeable closed its doors to new investors, with existing investors required to transfer out of the company. The company claimed that it was not shutting down but simply removing its SEC registration. == History == Hedgeable was founded in 2009 by twin brothers Michael and Matthew Kane, who previously worked at high-net worth investment managers such as Bridgewater Associates and Spruce Private Investors. Both Michael and Matthew graduated from Penn State University with degrees in finance. Hedgeable is a Registered Investment Advisor with the U.S. Securities and Exchange Commission. The company has received funding from SixThirty and Route 66 Ventures as well as various other angel investors. On August 9, 2018, Hedgeable closed its doors to new investors. == Investing Strategies == Hedgeable did not follow a buy-and-hold approach, but instead actively manages accounts in response to market movements focusing on downside protection in bear markets. Their strategy was different from other robo-advisors, which use Modern Portfolio Theory. Hedgeable offered investment options including Exchange Traded Funds (ETFs) to individual stocks, master limited partnerships, private equity and bitcoin. Mutual funds were not used in portfolios. Although the firm's focus was to provide a direct-to-consumer service, Hedgeable's investment strategies were available to financial advisors and institutions as well through a variety of platforms. == Product Features == When it was open to external clients, Hedgeable aimed to gamify their personal finance experience. Clients could open a new account or transfer an existing account. Hedgeable accepted retirement accounts, taxable accounts, business accounts and various other account types. Hedgeable offered the following features: Downside protection Account aggregation Alternative investments Alpha rewards API Mobile app It was awarded 4/5 for client transparency by Paladin Research. Hedgeable was the winner of the Finovate Fall 2015 Best of Show Award and the GREAT 2015 Tech Award (FinTech Category). In 2016, Hedgeable launched its first iOS mobile app in order to expand their product offerings.
Random (software)
Random was an iOS mobile app that used algorithms and human-curation to create an adaptive interface to the Internet. The app served a remix of relevance and serendipity that allowed people to find diverse topics and interesting content that they might not have encountered otherwise. Random did not require a login or sign-up - the use of the app was anonymous. The app was powered by an artificial intelligence that learned from direct and indirect user interactions inside the app. While learning and adapting to a person, Random created a unique anonymous choice profile that was then used for recommending topics and content. The app didn't recommend the same content twice. == User interface == Random's user interface was made of ever-changing topic blocks that contained keywords and images. By choosing any of the blocks, the user would see related web content. By closing the web content, the user could access new related topics. The user interface allowed people to get more information about a specific topic area or then just leap freely from topic to topic. The content recommended by Random could be any type of web content, varying from news articles to long-form stories and from photographs to videos. Every user of the Random was curating content for other users by using the app. == History == Random was launched in March 2014. The startup was backed by Skype co-founder Janus Friis. The Random app received a strong reception from the likes of The New York Times, TechCrunch, New Scientist, Vice, and other leading publications. The app went on to gain traction with an active and loyal user community of several hundreds of thousands. This was not enough to support the free app model the team strongly believed in, and the service was terminated in December 2015. == Reception == Various reviews in media have emphasized that Random enables people to break their filter bubble and find diverse content they might not find elsewhere. Alan Henry of Lifehacker wrote: "Random... breaks you out by intentionally guiding you to new topics and interesting articles at sites you may not otherwise read." Vice Motherboard's Claire Evans says that: "Random never turns into a filter bubble, because it perpetually injects the irrational into my experience… in a cocktail of relevancy and serendipity." The app has been said to have a unique, minimalistic user experience. Kit Eaton of The New York Times commented that Random "let's you browse the news in a different way to all the other news sites you've probably ever used." Mashable reviewed Random by concluding that the "app may be one of the most simple content-discovery apps on the market."
Data item
A data item describes an atomic state of a particular object concerning a specific property at a certain time point. A collection of data items for the same object at the same time forms an object instance (or table row). Any type of complex information can be broken down to elementary data items (atomic state). Data items are identified by object (o), property (p) and time (t), while the value (v) is a function of o, p and t: v = F(o,p,t). Values typically are represented by symbols like numbers, texts, images, sounds or videos. Values are not necessarily atomic. A value's complexity depends on the complexity of the property and time component. When looking at databases or XML files, the object is usually identified by an object name or other type of object identifier, which is part of the "data". Properties are defined as columns (table row), properties (object instance) or tags (XML). Often, time is not explicitly expressed and is an attribute applying to the complete data set. Other data collections provide time on the instance level (time series), column level, or even attribute/property level.