Strong cryptography or cryptographically strong are general terms used to designate the cryptographic algorithms that, when used correctly, provide a very high (usually insurmountable) level of protection against any eavesdropper, including the government agencies. There is no precise definition of the boundary line between the strong cryptography and (breakable) weak cryptography, as this border constantly shifts due to improvements in hardware and cryptanalysis techniques. These improvements eventually place the capabilities once available only to the NSA within the reach of a skilled individual, so in practice there are only two levels of cryptographic security, "cryptography that will stop your kid sister from reading your files, and cryptography that will stop major governments from reading your files" (Bruce Schneier). The strong cryptography algorithms have high security strength, for practical purposes usually defined as a number of bits in the key. For example, the United States government, when dealing with export control of encryption, considered as of 1999 any implementation of the symmetric encryption algorithm with the key length above 56 bits or its public key equivalent to be strong and thus potentially a subject to the export licensing. To be strong, an algorithm needs to have a sufficiently long key and be free of known mathematical weaknesses, as exploitation of these effectively reduces the key size. At the beginning of the 21st century, the typical security strength of the strong symmetrical encryption algorithms is 128 bits (slightly lower values still can be strong, but usually there is little technical gain in using smaller key sizes). Demonstrating the resistance of any cryptographic scheme to attack is a complex matter, requiring extensive testing and reviews, preferably in a public forum. Good algorithms and protocols are required (similarly, good materials are required to construct a strong building), but good system design and implementation is needed as well: "it is possible to build a cryptographically weak system using strong algorithms and protocols" (just like the use of good materials in construction does not guarantee a solid structure). Many real-life systems turn out to be weak when the strong cryptography is not used properly, for example, random nonces are reused A successful attack might not even involve algorithm at all, for example, if the key is generated from a password, guessing a weak password is easy and does not depend on the strength of the cryptographic primitives. A user can become the weakest link in the overall picture, for example, by sharing passwords and hardware tokens with the colleagues. == Background == The level of expense required for strong cryptography originally restricted its use to the government and military agencies, until the middle of the 20th century the process of encryption required a lot of human labor and errors (preventing the decryption) were very common, so only a small share of written information could have been encrypted. US government, in particular, was able to keep a monopoly on the development and use of cryptography in the US into the 1960s. In the 1970, the increased availability of powerful computers and unclassified research breakthroughs (Data Encryption Standard, the Diffie-Hellman and RSA algorithms) made strong cryptography available for civilian use. Mid-1990s saw the worldwide proliferation of knowledge and tools for strong cryptography. By the 21st century the technical limitations were gone, although the majority of the communication were still unencrypted. At the same the cost of building and running systems with strong cryptography became roughly the same as the one for the weak cryptography. The use of computers changed the process of cryptanalysis, famously with Bletchley Park's Colossus. But just as the development of digital computers and electronics helped in cryptanalysis, it also made possible much more complex ciphers. It is typically the case that use of a quality cipher is very efficient, while breaking it requires an effort many orders of magnitude larger - making cryptanalysis so inefficient and impractical as to be effectively impossible. == Cryptographically strong algorithms == This term "cryptographically strong" is often used to describe an encryption algorithm, and implies, in comparison to some other algorithm (which is thus cryptographically weak), greater resistance to attack. But it can also be used to describe hashing and unique identifier and filename creation algorithms. See for example the description of the Microsoft .NET runtime library function Path.GetRandomFileName. In this usage, the term means "difficult to guess". An encryption algorithm is intended to be unbreakable (in which case it is as strong as it can ever be), but might be breakable (in which case it is as weak as it can ever be) so there is not, in principle, a continuum of strength as the idiom would seem to imply: Algorithm A is stronger than Algorithm B which is stronger than Algorithm C, and so on. The situation is made more complex, and less subsumable into a single strength metric, by the fact that there are many types of cryptanalytic attack and that any given algorithm is likely to force the attacker to do more work to break it when using one attack than another. There is only one known unbreakable cryptographic system, the one-time pad, which is not generally possible to use because of the difficulties involved in exchanging one-time pads without them being compromised. So any encryption algorithm can be compared to the perfect algorithm, the one-time pad. The usual sense in which this term is (loosely) used, is in reference to a particular attack, brute force key search — especially in explanations for newcomers to the field. Indeed, with this attack (always assuming keys to have been randomly chosen), there is a continuum of resistance depending on the length of the key used. But even so there are two major problems: many algorithms allow use of different length keys at different times, and any algorithm can forgo use of the full key length possible. Thus, Blowfish and RC5 are block cipher algorithms whose design specifically allowed for several key lengths, and who cannot therefore be said to have any particular strength with respect to brute force key search. Furthermore, US export regulations restrict key length for exportable cryptographic products and in several cases in the 1980s and 1990s (e.g., famously in the case of Lotus Notes' export approval) only partial keys were used, decreasing 'strength' against brute force attack for those (export) versions. More or less the same thing happened outside the US as well, as for example in the case of more than one of the cryptographic algorithms in the GSM cellular telephone standard. The term is commonly used to convey that some algorithm is suitable for some task in cryptography or information security, but also resists cryptanalysis and has no, or fewer, security weaknesses. Tasks are varied, and might include: generating randomness encrypting data providing a method to ensure data integrity Cryptographically strong would seem to mean that the described method has some kind of maturity, perhaps even approved for use against different kinds of systematic attacks in theory and/or practice. Indeed, that the method may resist those attacks long enough to protect the information carried (and what stands behind the information) for a useful length of time. But due to the complexity and subtlety of the field, neither is almost ever the case. Since such assurances are not actually available in real practice, sleight of hand in language which implies that they are will generally be misleading. There will always be uncertainty as advances (e.g., in cryptanalytic theory or merely affordable computer capacity) may reduce the effort needed to successfully use some attack method against an algorithm. In addition, actual use of cryptographic algorithms requires their encapsulation in a cryptosystem, and doing so often introduces vulnerabilities which are not due to faults in an algorithm. For example, essentially all algorithms require random choice of keys, and any cryptosystem which does not provide such keys will be subject to attack regardless of any attack resistant qualities of the encryption algorithm(s) used. == Legal issues == Widespread use of encryption increases the costs of surveillance, so the government policies aim to regulate the use of the strong cryptography. In the 2000s, the effect of encryption on the surveillance capabilities was limited by the ever-increasing share of communications going through the global social media platforms, that did not use the strong encryption and provided governments with the requested data. Murphy talks about a legislative balance that needs to be struck between the power of the government that are broad enough to be able to follow the qui
Inception score
The Inception Score (IS) is an algorithm used to assess the quality of images created by a generative image model such as a generative adversarial network (GAN). The score is calculated based on the output of a separate, pretrained Inception v3 image classification model applied to a sample of (typically around 30,000) images generated by the generative model. The Inception Score is maximized when the following conditions are true: The entropy of the distribution of labels predicted by the Inceptionv3 model for the generated images is minimized. In other words, the classification model confidently predicts a single label for each image. Intuitively, this corresponds to the desideratum of generated images being "sharp" or "distinct". The predictions of the classification model are evenly distributed across all possible labels. This corresponds to the desideratum that the output of the generative model is "diverse". It has been somewhat superseded by the related Fréchet inception distance. While the Inception Score only evaluates the distribution of generated images, the FID compares the distribution of generated images with the distribution of a set of real images ("ground truth"). == Definition == Let there be two spaces, the space of images Ω X {\displaystyle \Omega _{X}} and the space of labels Ω Y {\displaystyle \Omega _{Y}} . The space of labels is finite. Let p g e n {\displaystyle p_{gen}} be a probability distribution over Ω X {\displaystyle \Omega _{X}} that we wish to judge. Let a discriminator be a function of type p d i s : Ω X → M ( Ω Y ) {\displaystyle p_{dis}:\Omega _{X}\to M(\Omega _{Y})} where M ( Ω Y ) {\displaystyle M(\Omega _{Y})} is the set of all probability distributions on Ω Y {\displaystyle \Omega _{Y}} . For any image x {\displaystyle x} , and any label y {\displaystyle y} , let p d i s ( y | x ) {\displaystyle p_{dis}(y|x)} be the probability that image x {\displaystyle x} has label y {\displaystyle y} , according to the discriminator. It is usually implemented as an Inception-v3 network trained on ImageNet. The Inception Score of p g e n {\displaystyle p_{gen}} relative to p d i s {\displaystyle p_{dis}} is I S ( p g e n , p d i s ) := exp ( E x ∼ p g e n [ D K L ( p d i s ( ⋅ | x ) ‖ ∫ p d i s ( ⋅ | x ) p g e n ( x ) d x ) ] ) {\displaystyle IS(p_{gen},p_{dis}):=\exp \left(\mathbb {E} _{x\sim p_{gen}}\left[D_{KL}\left(p_{dis}(\cdot |x)\|\int p_{dis}(\cdot |x)p_{gen}(x)dx\right)\right]\right)} Equivalent rewrites include ln I S ( p g e n , p d i s ) := E x ∼ p g e n [ D K L ( p d i s ( ⋅ | x ) ‖ E x ∼ p g e n [ p d i s ( ⋅ | x ) ] ) ] {\displaystyle \ln IS(p_{gen},p_{dis}):=\mathbb {E} _{x\sim p_{gen}}\left[D_{KL}\left(p_{dis}(\cdot |x)\|\mathbb {E} _{x\sim p_{gen}}[p_{dis}(\cdot |x)]\right)\right]} ln I S ( p g e n , p d i s ) := H [ E x ∼ p g e n [ p d i s ( ⋅ | x ) ] ] − E x ∼ p g e n [ H [ p d i s ( ⋅ | x ) ] ] {\displaystyle \ln IS(p_{gen},p_{dis}):=H[\mathbb {E} _{x\sim p_{gen}}[p_{dis}(\cdot |x)]]-\mathbb {E} _{x\sim p_{gen}}[H[p_{dis}(\cdot |x)]]} ln I S {\displaystyle \ln IS} is nonnegative by Jensen's inequality. Pseudocode:INPUT discriminator p d i s {\displaystyle p_{dis}} . INPUT generator g {\displaystyle g} . Sample images x i {\displaystyle x_{i}} from generator. Compute p d i s ( ⋅ | x i ) {\displaystyle p_{dis}(\cdot |x_{i})} , the probability distribution over labels conditional on image x i {\displaystyle x_{i}} . Sum up the results to obtain p ^ {\displaystyle {\hat {p}}} , an empirical estimate of ∫ p d i s ( ⋅ | x ) p g e n ( x ) d x {\displaystyle \int p_{dis}(\cdot |x)p_{gen}(x)dx} . Sample more images x i {\displaystyle x_{i}} from generator, and for each, compute D K L ( p d i s ( ⋅ | x i ) ‖ p ^ ) {\displaystyle D_{KL}\left(p_{dis}(\cdot |x_{i})\|{\hat {p}}\right)} . Average the results, and take its exponential. RETURN the result. === Interpretation === A higher inception score is interpreted as "better", as it means that p g e n {\displaystyle p_{gen}} is a "sharp and distinct" collection of pictures. ln I S ( p g e n , p d i s ) ∈ [ 0 , ln N ] {\displaystyle \ln IS(p_{gen},p_{dis})\in [0,\ln N]} , where N {\displaystyle N} is the total number of possible labels. ln I S ( p g e n , p d i s ) = 0 {\displaystyle \ln IS(p_{gen},p_{dis})=0} iff for almost all x ∼ p g e n {\displaystyle x\sim p_{gen}} p d i s ( ⋅ | x ) = ∫ p d i s ( ⋅ | x ) p g e n ( x ) d x {\displaystyle p_{dis}(\cdot |x)=\int p_{dis}(\cdot |x)p_{gen}(x)dx} That means p g e n {\displaystyle p_{gen}} is completely "indistinct". That is, for any image x {\displaystyle x} sampled from p g e n {\displaystyle p_{gen}} , discriminator returns exactly the same label predictions p d i s ( ⋅ | x ) {\displaystyle p_{dis}(\cdot |x)} . The highest inception score N {\displaystyle N} is achieved if and only if the two conditions are both true: For almost all x ∼ p g e n {\displaystyle x\sim p_{gen}} , the distribution p d i s ( y | x ) {\displaystyle p_{dis}(y|x)} is concentrated on one label. That is, H y [ p d i s ( y | x ) ] = 0 {\displaystyle H_{y}[p_{dis}(y|x)]=0} . That is, every image sampled from p g e n {\displaystyle p_{gen}} is exactly classified by the discriminator. For every label y {\displaystyle y} , the proportion of generated images labelled as y {\displaystyle y} is exactly E x ∼ p g e n [ p d i s ( y | x ) ] = 1 N {\displaystyle \mathbb {E} _{x\sim p_{gen}}[p_{dis}(y|x)]={\frac {1}{N}}} . That is, the generated images are equally distributed over all labels.
Multiclass classification
In machine learning and statistical classification, multiclass classification or multinomial classification is the problem of classifying instances into one of three or more classes (classifying instances into one of two classes is called binary classification). For example, deciding on whether an image is showing a banana, peach, orange, or an apple is a multiclass classification problem, with four possible classes (banana, peach, orange, apple), while deciding on whether an image contains an apple or not is a binary classification problem (with the two possible classes being: apple, no apple). While many classification algorithms (e.g., decision trees, k-NN, neural networks and multinomial logistic regression) naturally permit the use of more than two classes, some are by nature binary algorithms (e.g., classical binary support vector machine) and require decomposition strategies such as one-vs-all, one-vs-one, or ECOC to solve multiclass problems. Multiclass classification should not be confused with multi-label classification, where multiple labels are to be predicted for each instance (e.g., predicting that an image contains both an apple and an orange, in the previous example). == Better-than-random multiclass models == From the confusion matrix of a multiclass model, we can determine whether a model does better than chance. Let K ≥ 3 {\displaystyle K\geq 3} be the number of classes, O {\displaystyle {\mathcal {O}}} a set of observations, y ^ : O → { 1 , . . . , K } {\displaystyle {\hat {y}}:{\mathcal {O}}\to \{1,...,K\}} a model of the target variable y : O → { 1 , . . . , K } {\displaystyle y:{\mathcal {O}}\to \{1,...,K\}} and n i , j {\displaystyle n_{i,j}} be the number of observations in the set { y = i } ∩ { y ^ = j } {\displaystyle \{y=i\}\cap \{{\hat {y}}=j\}} . We note n i . = ∑ j n i , j {\displaystyle n_{i.}=\sum _{j}n_{i,j}} , n . j = ∑ i n i , j {\displaystyle n_{.j}=\sum _{i}n_{i,j}} , n = ∑ j n . j = ∑ i n i . {\displaystyle n=\sum _{j}n_{.j}=\sum _{i}n_{i.}} , λ i = n i . n {\displaystyle \lambda _{i}={\frac {n_{i.}}{n}}} and μ j = n . j n {\displaystyle \mu _{j}={\frac {n_{.j}}{n}}} . It is assumed that the confusion matrix ( n i , j ) i , j {\displaystyle (n_{i,j})_{i,j}} contains at least one non-zero entry in each row, that is λ i > 0 {\displaystyle \lambda _{i}>0} for any i {\displaystyle i} . Finally we call "normalized confusion matrix" the matrix of conditional probabilities ( P ( y ^ = j ∣ y = i ) ) i , j = ( n i , j n i . ) i , j {\displaystyle (\mathbb {P} ({\hat {y}}=j\mid y=i))_{i,j}=\left({\frac {n_{i,j}}{n_{i.}}}\right)_{i,j}} . === Intuitive explanation === The lift is a way of measuring the deviation from independence of two events A {\displaystyle A} and B {\displaystyle B} : L i f t ( A , B ) = P ( A ∩ B ) P ( A ) P ( B ) = P ( A ∣ B ) P ( A ) = P ( B ∣ A ) P ( B ) {\displaystyle \mathrm {Lift} (A,B)={\frac {\mathbb {P} (A\cap B)}{\mathbb {P} (A)\mathbb {P} (B)}}={\frac {\mathbb {P} (A\mid B)}{\mathbb {P} (A)}}={\frac {\mathbb {P} (B\mid A)}{\mathbb {P} (B)}}} We have L i f t ( A , B ) > 1 {\displaystyle \mathrm {Lift} (A,B)>1} if and only if events A {\displaystyle A} and B {\displaystyle B} occur simultaneously with a greater probability than if they were independent. In other words, if one of the two events occurs, the probability of observing the other event increases. A first condition to satisfy is to have L i f t ( y = i , y ^ = i ) ≥ 1 {\displaystyle \mathrm {Lift} (y=i,{\hat {y}}=i)\geq 1} for any i {\displaystyle i} . And the quality of a model (better or worse than chance) does not change if we over- or undersample the dataset, that is if we multiply each row R i {\displaystyle R_{i}} of the confusion matrix by a constant c i {\displaystyle c_{i}} . Thus the second condition is that the necessary and sufficient conditions for doing better than chance need only depend on the normalized confusion matrix. The condition on lifts can be reformulated with One versus Rest binary models : for any i {\displaystyle i} , we define the binary target variable y i {\displaystyle y_{i}} which is the indicator of event { y = i } {\displaystyle \{y=i\}} , and the binary model y ^ i {\displaystyle {\hat {y}}_{i}} of y i {\displaystyle y_{i}} which is the indicator of event { y ^ = i } {\displaystyle \{{\hat {y}}=i\}} . Each of the y ^ i {\displaystyle {\hat {y}}_{i}} models is a "One versus Rest" model. L i f t ( y = i , y ^ = i ) {\displaystyle \mathrm {Lift} (y=i,{\hat {y}}=i)} only depends on the events { y = i } {\displaystyle \{y=i\}} and { y ^ = i } {\displaystyle \{{\hat {y}}=i\}} , so merging or not merging the other classes doesn't change its value. We therefore have L i f t ( y = i , y ^ = i ) = L i f t ( y i = 1 , y ^ i = 1 ) {\displaystyle \mathrm {Lift} (y=i,{\hat {y}}=i)=\mathrm {Lift} (y_{i}=1,{\hat {y}}_{i}=1)} and the first condition is that all binary One versus Rest models are better than chance. ==== Example ==== If K = 2 {\displaystyle K=2} and 2 is the class of interest , the normalized confusion matrix is ( s p e c i f i c i t y 1 − s p e c i f i c i t y 1 − s e n s i t i v i t y s e n s i t i v i t y ) {\displaystyle {\begin{pmatrix}\mathrm {specificity} &1-\mathrm {specificity} \\1-\mathrm {sensitivity} &\mathrm {sensitivity} \end{pmatrix}}} and we have L i f t ( y = 1 , y ^ = 1 ) − 1 = P ( y = y ^ = 1 ) λ 1 μ 1 − 1 = n 1 , 1 n n 1. n .1 − 1 {\displaystyle \mathrm {Lift} (y=1,{\hat {y}}=1)-1={\frac {\mathbb {P} (y={\hat {y}}=1)}{\lambda _{1}\mu _{1}}}-1={\frac {n_{1,1}n}{n_{1.}n_{.1}}}-1} = n 1 , 1 ( n 1 , 1 + n 1 , 2 + n 2 , 1 + n 2 , 2 ) − ( n 1 , 1 + n 1 , 2 ) ( n 1 , 1 + n 2 , 1 ) n 1. n .1 = n 1 , 1 n 2 , 2 − n 1 , 2 n 2 , 1 n 1. n .1 {\displaystyle ={\frac {n_{1,1}(n_{1,1}+n_{1,2}+n_{2,1}+n_{2,2})-(n_{1,1}+n_{1,2})(n_{1,1}+n_{2,1})}{n_{1.}n_{.1}}}={\frac {n_{1,1}n_{2,2}-n_{1,2}n_{2,1}}{n_{1.}n_{.1}}}} . Thus L i f t ( y = 1 , y ^ = 1 ) ≥ 1 ⟺ n 1 , 1 n 2 , 2 − n 1 , 2 n 2 , 1 ≥ 0 {\displaystyle \mathrm {Lift} (y=1,{\hat {y}}=1)\geq 1\iff n_{1,1}n_{2,2}-n_{1,2}n_{2,1}\geq 0} . Similarly, by swapping the roles of 1 and 2, we find that L i f t ( y = 2 , y ^ = 2 ) ≥ 1 ⟺ n 1 , 1 n 2 , 2 − n 1 , 2 n 2 , 1 ≥ 0 {\displaystyle \mathrm {Lift} (y=2,{\hat {y}}=2)\geq 1\iff n_{1,1}n_{2,2}-n_{1,2}n_{2,1}\geq 0} . Dividing by n 1. n 2. {\displaystyle n_{1.}n_{2.}} we find that the necessary and sufficient condition on the normalized confusion matrix is s e n s i t i v i t y s p e c i f i c i t y − ( 1 − s e n s i t i v i t y ) ( 1 − s p e c i f i c i t y ) ≥ 0 ⟺ s e n s i t i v i t y + s p e c i f i c i t y − 1 ≥ 0 ⟺ J ≥ 0 {\displaystyle \mathrm {sensitivity} \ \mathrm {specificity} -(1-\mathrm {sensitivity} )(1-\mathrm {specificity} )\geq 0\iff \mathrm {sensitivity} +\mathrm {specificity} -1\geq 0\iff J\geq 0} . This brings us back to the classical binary condition: Youden's J must be positive (or zero for random models). === Random models === A random model is a model that is independent of the target variable. This property is easily reformulated with the confusion matrix. This proposition shows that the model y ^ {\displaystyle {\hat {y}}} of y {\displaystyle y} is uninformative if and only if there are two families of numbers ( α i ) i {\displaystyle (\alpha _{i})_{i}} and ( β j ) j {\displaystyle (\beta _{j})_{j}} such that P ( { y = i } ∩ { y ^ = j } ) = α i β j {\displaystyle \mathbb {P} (\{y=i\}\cap \{{\hat {y}}=j\})=\alpha _{i}\beta _{j}} for any i {\displaystyle i} and j {\displaystyle j} . === Multiclass likelihood ratios and diagnostic odds ratios === We define generalized likelihood ratios calculated from the normalized confusion matrix: for any i {\displaystyle i} and j ≠ i {\displaystyle j\not =i} , let L R i , j = P ( y ^ = j ∣ y = j ) P ( y ^ = j ∣ y = i ) {\displaystyle \mathrm {LR} _{i,j}={\frac {\mathbb {P} ({\hat {y}}=j\mid y=j)}{\mathbb {P} ({\hat {y}}=j\mid y=i)}}} . When K = 2 {\displaystyle K=2} , if 2 is the class of interest,, we find the classical likelihood ratios L R 1 , 2 = L R + {\displaystyle \mathrm {LR} _{1,2}=\mathrm {LR} _{+}} and L R 2 , 1 = 1 L R − {\displaystyle \mathrm {LR} _{2,1}={\frac {1}{\mathrm {LR} _{-}}}} . Multiclass diagnostic odds ratios can also be defined using the formula D O R i , j = D O R j , i = L R i , j L R j , i = n i , i n j , j n i , j n j , i = P ( y ^ = j ∣ y = j ) / P ( y ^ = i ∣ y = j ) P ( y ^ = j ∣ y = i ) / P ( y ^ = i ∣ y = i ) {\displaystyle \mathrm {DOR} _{i,j}=\mathrm {DOR} _{j,i}=\mathrm {LR} _{i,j}\mathrm {LR} _{j,i}={\frac {n_{i,i}n_{j,j}}{n_{i,j}n_{j,i}}}={\frac {\mathbb {P} ({\hat {y}}=j\mid y=j)/\mathbb {P} ({\hat {y}}=i\mid y=j)}{\mathbb {P} ({\hat {y}}=j\mid y=i)/\mathbb {P} ({\hat {y}}=i\mid y=i)}}} We saw above that a better-than-chance model (or a random model) must verify L i f t ( y = i , y ^ = i ) ≥ 1 {\displaystyle \mathrm {Lift} (y=i,{\hat {y}}=i)\geq 1} for any i {\displaystyle i} and λ i {\displaystyle \lambda _{i}} . According to the previous corollary, likelihood ratios are thus greater
Waffles (machine learning)
Waffles is a collection of command-line tools for performing machine learning operations developed at Brigham Young University. These tools are written in C++, and are available under the GNU Lesser General Public License. == Description == The Waffles machine learning toolkit contains command-line tools for performing various operations related to machine learning, data mining, and predictive modeling. The primary focus of Waffles is to provide tools that are simple to use in scripted experiments or processes. For example, the supervised learning algorithms included in Waffles are all designed to support multi-dimensional labels, classification and regression, automatically impute missing values, and automatically apply necessary filters to transform the data to a type that the algorithm can support, such that arbitrary learning algorithms can be used with arbitrary data sets. Many other machine learning toolkits provide similar functionality, but require the user to explicitly configure data filters and transformations to make it compatible with a particular learning algorithm. The algorithms provided in Waffles also have the ability to automatically tune their own parameters (with the cost of additional computational overhead). Because Waffles is designed for script-ability, it deliberately avoids presenting its tools in a graphical environment. It does, however, include a graphical "wizard" tool that guides the user to generate a command that will perform a desired task. This wizard does not actually perform the operation, but requires the user to paste the command that it generates into a command terminal or a script. The idea motivating this design is to prevent the user from becoming "locked in" to a graphical interface. All of the Waffles tools are implemented as thin wrappers around functionality in a C++ class library. This makes it possible to convert scripted processes into native applications with minimal effort. Waffles was first released as an open source project in 2005. Since that time, it has been developed at Brigham Young University, with a new version having been released approximately every 6–9 months. Waffles is not an acronym—the toolkit was named after the food for historical reasons. == Advantages == Some of the advantages of Waffles in contrast with other popular open source machine learning toolkits include: Waffles automatically takes care of many issues related to data format in order to simplify its tools. Because it is implemented in C++, many of its algorithms are particularly fast. Also, the lack of dependency on any virtual machine makes it easier to deploy in conjunction with other applications. The functionality included in Waffles is very broad, including algorithms for dimensionality reduction, collaborative filtering, visualization, clustering, supervised learning, optimization, linear algebra, data transformation, image and signal processing, policy learning, and sparse matrix operations. == Disadvantages == Although Waffles provides significant breadth, it lacks the depth of many toolkits that focus on a particular area of machine learning. The Weka (machine learning) toolkit, for example, provides many more classification algorithms than Waffles provides. Waffles only has a limited graphical interface.
Variational message passing
Variational message passing (VMP) is an approximate inference technique for continuous- or discrete-valued Bayesian networks, with conjugate-exponential parents, developed by John Winn. VMP was developed as a means of generalizing the approximate variational methods used by such techniques as latent Dirichlet allocation, and works by updating an approximate distribution at each node through messages in the node's Markov blanket. == Likelihood lower bound == Given some set of hidden variables H {\displaystyle H} and observed variables V {\displaystyle V} , the goal of approximate inference is to maximize a lower-bound on the probability that a graphical model is in the configuration V {\displaystyle V} . Over some probability distribution Q {\displaystyle Q} (to be defined later), ln P ( V ) = ∑ H Q ( H ) ln P ( H , V ) P ( H | V ) = ∑ H Q ( H ) [ ln P ( H , V ) Q ( H ) − ln P ( H | V ) Q ( H ) ] {\displaystyle \ln P(V)=\sum _{H}Q(H)\ln {\frac {P(H,V)}{P(H|V)}}=\sum _{H}Q(H){\Bigg [}\ln {\frac {P(H,V)}{Q(H)}}-\ln {\frac {P(H|V)}{Q(H)}}{\Bigg ]}} . So, if we define our lower bound to be L ( Q ) = ∑ H Q ( H ) ln P ( H , V ) Q ( H ) {\displaystyle L(Q)=\sum _{H}Q(H)\ln {\frac {P(H,V)}{Q(H)}}} , then the likelihood is simply this bound plus the relative entropy between P {\displaystyle P} and Q {\displaystyle Q} . Because the relative entropy is non-negative, the function L {\displaystyle L} defined above is indeed a lower bound of the log likelihood of our observation V {\displaystyle V} . The distribution Q {\displaystyle Q} will have a simpler character than that of P {\displaystyle P} because marginalizing over P {\displaystyle P} is intractable for all but the simplest of graphical models. In particular, VMP uses a factorized distribution Q ( H ) = ∏ i Q i ( H i ) , {\displaystyle Q(H)=\prod _{i}Q_{i}(H_{i}),} where H i {\displaystyle H_{i}} is a disjoint part of the graphical model. == Determining the update rule == The likelihood estimate needs to be as large as possible; because it's a lower bound, getting closer log P {\displaystyle \log P} improves the approximation of the log likelihood. By substituting in the factorized version of Q {\displaystyle Q} , L ( Q ) {\displaystyle L(Q)} , parameterized over the hidden nodes H i {\displaystyle H_{i}} as above, is simply the negative relative entropy between Q j {\displaystyle Q_{j}} and Q j ∗ {\displaystyle Q_{j}^{}} plus other terms independent of Q j {\displaystyle Q_{j}} if Q j ∗ {\displaystyle Q_{j}^{}} is defined as Q j ∗ ( H j ) = 1 Z e E − j { ln P ( H , V ) } {\displaystyle Q_{j}^{}(H_{j})={\frac {1}{Z}}e^{\mathbb {E} _{-j}\{\ln P(H,V)\}}} , where E − j { ln P ( H , V ) } {\displaystyle \mathbb {E} _{-j}\{\ln P(H,V)\}} is the expectation over all distributions Q i {\displaystyle Q_{i}} except Q j {\displaystyle Q_{j}} . Thus, if we set Q j {\displaystyle Q_{j}} to be Q j ∗ {\displaystyle Q_{j}^{}} , the bound L {\displaystyle L} is maximized. == Messages in variational message passing == Parents send their children the expectation of their sufficient statistic while children send their parents their natural parameter, which also requires messages to be sent from the co-parents of the node. == Relationship to exponential families == Because all nodes in VMP come from exponential families and all parents of nodes are conjugate to their children nodes, the expectation of the sufficient statistic can be computed from the normalization factor. == VMP algorithm == The algorithm begins by computing the expected value of the sufficient statistics for that vector. Then, until the likelihood converges to a stable value (this is usually accomplished by setting a small threshold value and running the algorithm until it increases by less than that threshold value), do the following at each node: Get all messages from parents. Get all messages from children (this might require the children to get messages from the co-parents). Compute the expected value of the nodes sufficient statistics. == Constraints == Because every child must be conjugate to its parent, this has limited the types of distributions that can be used in the model. For example, the parents of a Gaussian distribution must be a Gaussian distribution (corresponding to the Mean) and a gamma distribution (corresponding to the precision, or one over σ {\displaystyle \sigma } in more common parameterizations). Discrete variables can have Dirichlet parents, and Poisson and exponential nodes must have gamma parents. More recently, VMP has been extended to handle models that violate this conditional conjugacy constraint. == Literature == John Winn; Christopher M. Bishop (2005). "Variational Message Passing" (PDF). Journal of Machine Learning Research. 6: 661–694. ISSN 1533-7928. Wikidata Q139488859. Beal, M.J. (2003). Variational Algorithms for Approximate Bayesian Inference (PDF) (PhD). Gatsby Computational Neuroscience Unit, University College London. Archived from the original (PDF) on 2005-04-28. Retrieved 2007-02-15.
Medical imaging
Medical imaging is the technique and process of imaging the interior of a body for clinical analysis and medical intervention, as well as visual representation of the function of some organs or tissues (physiology). Medical imaging seeks to reveal internal structures hidden by the skin and bones, as well as to diagnose and treat disease. Medical imaging also establishes a database of normal anatomy and physiology to make it possible to identify abnormalities. Although imaging of removed organs and tissues can be performed for medical reasons, such procedures are usually considered part of pathology instead of medical imaging. Measurement and recording techniques that are not primarily designed to produce images, such as electroencephalography (EEG), magnetoencephalography (MEG), electrocardiography (ECG), and others, represent other technologies that produce data susceptible to representation as a parameter graph versus time or maps that contain data about the measurement locations. In a limited comparison, these technologies can be considered forms of medical imaging in another discipline of medical instrumentation. As of 2010, 5 billion medical imaging studies had been conducted worldwide. Radiation exposure from medical imaging in 2006 made up about 50% of total ionizing radiation exposure in the United States. Medical imaging equipment is manufactured using technology from the semiconductor industry, including CMOS integrated circuit chips, power semiconductor devices, sensors such as image sensors (particularly CMOS sensors) and biosensors, and processors such as microcontrollers, microprocessors, digital signal processors, media processors and system-on-chip devices. As of 2015, annual shipments of medical imaging chips amount to 46 million units and $1.1 billion. The term "noninvasive" is used to denote a procedure where no instrument is introduced into a patient's body, which is the case for most imaging techniques used. == History == In 1972, engineer Godfrey Hounsfield from the British company EMI invented the X-ray computed tomography device for head diagnosis, which is commonly referred to as computed tomography (CT). The CT nucleus method is based on the projecting X-rays through a section of the human head, which are then processed by computer to reconstruct the cross-sectional image, known as image reconstruction. In 1975, EMI successfully developed a CT device for the entire body, enabling the clear acquisition of tomographic images of various parts of the human body. This revolutionary diagnostic technique earned Hounsfield and physicist Allan Cormack the Nobel Prize in Physiology or Medicine in 1979. Digital image processing technology for medical applications was inducted into the Space Foundation's Space Technology Hall of Fame in 1994. By 2010, over 5 billion medical imaging studies had been conducted worldwide. Radiation exposure from medical imaging in 2006 accounted for about 50% of total ionizing radiation exposure in the United States. Medical imaging equipment is manufactured using technology from the semiconductor industry, including CMOS integrated circuit chips, power semiconductor devices, sensors such as image sensors (particularly CMOS sensors) and biosensors, as well as processors like microcontrollers, microprocessors, digital signal processors, media processors and system-on-chip devices. As of 2015, annual shipments of medical imaging chips reached 46 million units, generating a market value of $1.1 billion. == Types == In the clinical context, "invisible light" medical imaging is generally equated to radiology or "clinical imaging". "Visible light" medical imaging involves digital video or still pictures that can be seen without special equipment. Dermatology and wound care are two modalities that use visible light imagery. Interpretation of medical images is generally undertaken by a physician specialising in radiology known as a radiologist; however, this may be undertaken by any healthcare professional who is trained and certified in radiological clinical evaluation. Increasingly interpretation is being undertaken by non-physicians, for example radiographers frequently train in interpretation as part of expanded practice. Diagnostic radiography designates the technical aspects of medical imaging and in particular the acquisition of medical images. The radiographer (also known as a radiologic technologist) is usually responsible for acquiring medical images of diagnostic quality; although other professionals may train in this area, notably some radiological interventions performed by radiologists are done so without a radiographer. As a field of scientific investigation, medical imaging constitutes a sub-discipline of biomedical engineering, medical physics or medicine depending on the context: Research and development in the area of instrumentation, image acquisition (e.g., radiography), modeling and quantification are usually the preserve of biomedical engineering, medical physics, and computer science; Research into the application and interpretation of medical images is usually the preserve of radiology and the medical sub-discipline relevant to medical condition or area of medical science (neuroscience, cardiology, psychiatry, psychology, etc.) under investigation. Many of the techniques developed for medical imaging also have scientific and industrial applications. === Radiography === Two forms of radiographic images are in use in medical imaging. Projection radiography and fluoroscopy, with the latter being useful for catheter guidance. These 2D techniques are still in wide use despite the advance of 3D tomography due to the low cost, high resolution, and depending on the application, lower radiation dosages with 2D technique. This imaging modality uses a wide beam of X-rays for image acquisition and is the first imaging technique available in modern medicine. Fluoroscopy produces real-time images of internal structures of the body in a similar fashion to radiography, but employs a constant input of X-rays, at a lower dose rate. Contrast media, such as barium, iodine, and air are used to visualize internal organs as they work. Fluoroscopy is also used in image-guided procedures when constant feedback during a procedure is required. An image receptor is required to convert the radiation into an image after it has passed through the area of interest. Early on, this was a fluorescing screen, which gave way to an Image Amplifier (IA) which was a large vacuum tube that had the receiving end coated with cesium iodide, and a mirror at the opposite end. Eventually the mirror was replaced with a TV camera. Projectional radiographs, more commonly known as X-rays, are often used to determine the type and extent of a fracture as well as for detecting pathological changes in the lungs. With the use of radio-opaque contrast media, such as barium, they can also be used to visualize the structure of the stomach and intestines – this can help diagnose ulcers or certain types of colon cancer. === Magnetic resonance imaging === A magnetic resonance imaging instrument (MRI scanner), or "nuclear magnetic resonance (NMR) imaging" scanner as it was originally known, uses powerful magnets to polarize and excite hydrogen nuclei (i.e., single protons) of water molecules in human tissue, producing a detectable signal that is spatially encoded, resulting in images of the body. The MRI machine emits a radio frequency (RF) pulse at the resonant frequency of the hydrogen atoms on water molecules. Radio frequency antennas ("RF coils") send the pulse to the area of the body to be examined. The RF pulse is absorbed by protons, causing their direction with respect to the primary magnetic field to change. When the RF pulse is turned off, the protons "relax" back to alignment with the primary magnet and emit radio waves in the process. This radio-frequency emission from the hydrogen atoms on water is what is detected and reconstructed into an image. The resonant frequency of a spinning magnetic dipole (of which protons are one example) is called the Larmor frequency and is determined by the strength of the main magnetic field and the chemical environment of the nuclei of interest. MRI uses three electromagnetic fields: a very strong (typically 1.5 to 3 teslas) static magnetic field to polarize the hydrogen nuclei, called the primary field; gradient fields that can be modified to vary in space and time (on the order of 1 kHz) for spatial encoding, often simply called gradients; and a spatially homogeneous radio-frequency (RF) field for manipulation of the hydrogen nuclei to produce measurable signals, collected through an RF antenna. Like CT, MRI traditionally creates a two-dimensional image of a thin "slice" of the body and is therefore considered a tomographic imaging technique. Modern MRI instruments are capable of producing images in the form of 3D blocks, which may be considered a generalization of the single-slice
IBM Watsonx
Watsonx is a platform by IBM for building and managing artificial intelligence (AI) applications for business use. Released on May 9, 2023, the platform provides software tools and infrastructure for companies to work with both IBM's own AI models and models from third-party sources. The platform consists of three main components: watsonx.ai, a studio for training, validating, and deploying AI models; watsonx.data, a system for storing and managing data used by the models; and watsonx.governance, a toolkit to ensure AI applications are compliant with company policies and regulations. A key feature of the platform is that it can be trained on a company's private data to perform specialized tasks, a process known as fine-tuning. IBM states that this client-specific data is not used to train its own models. == History == Watsonx was introduced on May 9, 2023, at the annual IBM Think conference, as a platform that includes multiple services. Just like Watson AI computer with the similar name, Watsonx was named after Thomas J. Watson, IBM's founder and first CEO. On February 13, 2024, Anaconda partnered with IBM to embed its open-source Python packages into Watsonx. Watsonx is used at ESPN's Fantasy Football App for managing players' performance, and by Italian telecommunications company Wind Tre. It was employed to generate editorial content around nominees during the 66th Annual Grammy Awards. In 2025, Wimbledon integrated IBM watsonx generative AI into its app and website. Integrated with IBM Safer Payments, IBM watsonx has been used in banking sector fraud detection and anti-money laundering (AML) systems. == Services == === watsonx.ai === Watsonx.ai is a platform that allows AI developers to leverage a wide range of LLMs under IBM's own Granite series and others such as Facebook's LLaMA-2, free and open-source model Mistral, and many others present in the Hugging Face community. These models come pre-trained and optimized for various natural language processing (NLP) applications.The platform also allows fine-tuning with its Tuning Studio. === watsonx.data === Watsonx.data is a platform designed to assist clients in addressing issues related to data volume, complexity, cost, and governance.. The platform facilitates seamless data access, whether stored in the cloud or on-premises, through a single entry point. === watsonx.governance === Watsonx.governance is a platform that utilizes IBM's AI capabilities to implement AI lifecycle governance. This helps them manage risks and maintain compliance with evolving AI and industry regulations, while reducing AI bias through automated oversight.